Database - gps_subgroups ((description not yet updated on this server))

Formats: - HTML - YAML - JSON - 2024-09-21T00:43:46.109402 - next page

Query: /api/gps_subgroups/?_offset=0

Column	Type
abelian	boolean
ambient	text
ambient_order	numeric
ambient_tex	text
aut_centralizer_order	numeric
aut_label	text
aut_weyl_group	text
aut_weyl_index	numeric
central	boolean
centralizer	text
characteristic	boolean
complements	text[]
conjugacy_class_count	numeric
contained_in	text[]
contains	text[]
core	text
coset_action_label	text
count	numeric
cyclic	boolean
diagram_aut_x	integer
diagram_x	integer
diagramx	smallint[]
direct	boolean
generators	numeric[]
hall	numeric
label	text
maximal	boolean
maximal_normal	boolean
minimal	boolean
minimal_normal	boolean
mobius_quo	bigint
mobius_sub	bigint
nilpotent	boolean
normal	boolean
normal_closure	text
normalizer	text
outer_equivalence	boolean
perfect	boolean
projective_image	text
proper	boolean
quotient	text
quotient_abelian	boolean
quotient_action_image	text
quotient_action_kernel	text
quotient_action_kernel_order	numeric
quotient_cyclic	boolean
quotient_fusion	jsonb
quotient_order	numeric
quotient_solvable	boolean
quotient_tex	text
short_label	text
solvable	boolean
special_labels	text[]
split	boolean
standard_generators	boolean
stem	boolean
subgroup	text
subgroup_fusion	integer[]
subgroup_order	numeric
subgroup_tex	text
sylow	smallint
weyl_group	text

0. label: 1.1.1.a1.a1
   {'abelian': True, 'ambient': '1.1', 'ambient_order': 1, 'ambient_tex': 'C_1', 'aut_centralizer_order': 1, 'aut_label': '1.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 1, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': [], 'core': '1.a1.a1', 'coset_action_label': '1T1', 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [], 'hall': 1, 'label': '1.1.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 1, 'mobius_sub': 1, 'nilpotent': True, 'normal': True, 'normal_closure': '1.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, 'projective_image': '1.1', 'proper': False, 'quotient': '1.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 1, 'quotient_solvable': True, 'quotient_tex': 'C_1', 'short_label': '1.a1.a1', 'solvable': True, 'special_labels': ['Z', 'D', 'F', 'Phi', 'R', 'S', 'PC', 'U0', 'L0', 'D0', 'C0', '1.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_fusion': None, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'sylow': 1, 'weyl_group': '1.1'}
1. label: 2.1.1.a1.a1
   {'abelian': True, 'ambient': '2.1', 'ambient_order': 2, 'ambient_tex': 'C_2', 'aut_centralizer_order': 1, 'aut_label': '1.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 1, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['2.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [1], 'hall': 2, 'label': '2.1.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': 1, 'nilpotent': True, 'normal': True, 'normal_closure': '1.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '1.1', 'proper': False, 'quotient': '1.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 1, 'quotient_solvable': True, 'quotient_tex': 'C_1', 'short_label': '1.a1.a1', 'solvable': True, 'special_labels': ['Z', 'F', 'R', 'S', 'U0', 'L0', 'D0', 'C0', '1.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 2, 'weyl_group': '1.1'}
2. label: 2.1.2.a1.a1
   {'abelian': True, 'ambient': '2.1', 'ambient_order': 2, 'ambient_tex': 'C_2', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 1, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': [], 'core': '2.a1.a1', 'coset_action_label': '2T1', 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [], 'hall': 1, 'label': '2.1.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 1, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, 'projective_image': '2.1', 'proper': False, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.a1.a1', 'solvable': True, 'special_labels': ['D', 'Phi', 'PC', 'U1', 'L1', 'D1', 'C1', '2.a1.a1.N', '2.a1.a1.M'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_fusion': None, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'sylow': 1, 'weyl_group': '1.1'}
3. label: 3.1.1.a1.a1
   {'abelian': True, 'ambient': '3.1', 'ambient_order': 3, 'ambient_tex': 'C_3', 'aut_centralizer_order': 1, 'aut_label': '1.a1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 1, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['3.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [1], 'hall': 3, 'label': '3.1.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': 1, 'nilpotent': True, 'normal': True, 'normal_closure': '1.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '1.1', 'proper': False, 'quotient': '1.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 1, 'quotient_solvable': True, 'quotient_tex': 'C_1', 'short_label': '1.a1.a1', 'solvable': True, 'special_labels': ['Z', 'F', 'R', 'S', 'U0', 'L0', 'D0', 'C0', '1.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_fusion': None, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'sylow': 3, 'weyl_group': '1.1'}
4. label: 3.1.3.a1.a1
   {'abelian': True, 'ambient': '3.1', 'ambient_order': 3, 'ambient_tex': 'C_3', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 2, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': [], 'core': '3.a1.a1', 'coset_action_label': '3T1', 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [], 'hall': 1, 'label': '3.1.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 1, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '3.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, 'projective_image': '3.1', 'proper': False, 'quotient': '3.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 3, 'quotient_solvable': True, 'quotient_tex': 'C_3', 'short_label': '3.a1.a1', 'solvable': True, 'special_labels': ['D', 'Phi', 'PC', 'U1', 'L1', 'D1', 'C1', '3.a1.a1.N', '3.a1.a1.M'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_fusion': None, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'sylow': 1, 'weyl_group': '1.1'}
5. label: 4.1.1.a1.a1
   {'abelian': True, 'ambient': '4.1', 'ambient_order': 4, 'ambient_tex': 'C_4', 'aut_centralizer_order': 1, 'aut_label': '1.a1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 1, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['4.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [1], 'hall': 2, 'label': '4.1.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 0, 'mobius_sub': 1, 'nilpotent': True, 'normal': True, 'normal_closure': '1.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '1.1', 'proper': False, 'quotient': '1.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 1, 'quotient_solvable': True, 'quotient_tex': 'C_1', 'short_label': '1.a1.a1', 'solvable': True, 'special_labels': ['Z', 'F', 'R', 'U0', 'L0', 'D0', 'C0', '1.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_fusion': None, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'sylow': 2, 'weyl_group': '1.1'}
6. label: 4.1.2.a1.a1
   {'abelian': True, 'ambient': '4.1', 'ambient_order': 4, 'ambient_tex': 'C_4', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 2, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': False, 'generators': [2], 'hall': 0, 'label': '4.1.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '2.1', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.a1.a1', 'solvable': True, 'special_labels': ['Phi', 'S', 'C1', '2.a1.a1.N', '2.a1.a1.M'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 0, 'weyl_group': '1.1'}
7. label: 4.1.4.a1.a1
   {'abelian': True, 'ambient': '4.1', 'ambient_order': 4, 'ambient_tex': 'C_4', 'aut_centralizer_order': 2, 'aut_label': '4.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 2, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': [], 'core': '4.a1.a1', 'coset_action_label': '4T1', 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [], 'hall': 1, 'label': '4.1.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 1, 'mobius_sub': 0, 'nilpotent': True, 'normal': True, 'normal_closure': '4.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, 'projective_image': '4.1', 'proper': False, 'quotient': '4.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 4, 'quotient_solvable': True, 'quotient_tex': 'C_4', 'short_label': '4.a1.a1', 'solvable': True, 'special_labels': ['D', 'PC', 'U1', 'L1', 'D1', 'C2', '4.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_fusion': None, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'sylow': 1, 'weyl_group': '1.1'}
8. label: 4.2.1.a1.a1
   {'abelian': True, 'ambient': '4.2', 'ambient_order': 4, 'ambient_tex': 'C_2^2', 'aut_centralizer_order': 1, 'aut_label': '1.a1', 'aut_weyl_group': '6.1', 'aut_weyl_index': 1, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['4.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.b1', '2.a1.a1', '2.a1.c1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': False, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [1, 2], 'hall': 2, 'label': '4.2.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 2, 'mobius_sub': 1, 'nilpotent': True, 'normal': True, 'normal_closure': '1.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '1.1', 'proper': False, 'quotient': '1.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 1, 'quotient_solvable': True, 'quotient_tex': 'C_1', 'short_label': '1.a1.a1', 'solvable': True, 'special_labels': ['Z', 'F', 'R', 'S', 'U0', 'L0', 'D0', 'C0', '1.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_fusion': None, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'sylow': 2, 'weyl_group': '1.1'}
9. label: 4.2.2.a1.b1
   {'abelian': True, 'ambient': '4.2', 'ambient_order': 4, 'ambient_tex': 'C_2^2', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 6, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': False, 'complements': ['2.a1.a1', '2.a1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 1364, 'diagramx': [5000, 5000, 1364, 5000], 'direct': True, 'generators': [3], 'hall': 0, 'label': '4.2.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.a1.b1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '2.1', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.a1.b1', 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 0, 'weyl_group': '1.1'}
10. label: 4.2.2.a1.c1
    {'abelian': True, 'ambient': '4.2', 'ambient_order': 4, 'ambient_tex': 'C_2^2', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 6, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': False, 'complements': ['2.a1.b1', '2.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1'], 'core': '2.a1.c1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 8636, 'diagramx': [5000, 5000, 8636, 8636], 'direct': True, 'generators': [1], 'hall': 0, 'label': '4.2.2.a1.c1', 'maximal': True, 'maximal_normal': True, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.a1.c1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '2.1', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.a1.c1', 'solvable': True, 'special_labels': ['2.a1.a1.N', '2.a1.b1.N', '2.a1.c1.N', '2.a1.a1.M', '2.a1.b1.M', '2.a1.c1.M'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 0, 'weyl_group': '1.1'}
11. label: 4.2.2.a1.a1
    {'abelian': True, 'ambient': '4.2', 'ambient_order': 4, 'ambient_tex': 'C_2^2', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 6, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': False, 'complements': ['2.a1.b1', '2.a1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 1364], 'direct': True, 'generators': [2], 'hall': 0, 'label': '4.2.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '2.1', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.a1.a1', 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 0, 'weyl_group': '1.1'}
12. label: 4.2.4.a1.a1
    {'abelian': True, 'ambient': '4.2', 'ambient_order': 4, 'ambient_tex': 'C_2^2', 'aut_centralizer_order': 6, 'aut_label': '4.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 6, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.a1.a1', '2.a1.c1'], 'contains': [], 'core': '4.a1.a1', 'coset_action_label': '4T2', 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [], 'hall': 1, 'label': '4.2.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 1, 'mobius_sub': 2, 'nilpotent': True, 'normal': True, 'normal_closure': '4.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, 'projective_image': '4.2', 'proper': False, 'quotient': '4.2', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': False, 'quotient_fusion': None, 'quotient_order': 4, 'quotient_solvable': True, 'quotient_tex': 'C_2^2', 'short_label': '4.a1.a1', 'solvable': True, 'special_labels': ['D', 'Phi', 'PC', 'U1', 'L1', 'D1', 'C2', '4.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_fusion': None, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'sylow': 1, 'weyl_group': '1.1'}
13. label: 5.1.1.a1.a1
    {'abelian': True, 'ambient': '5.1', 'ambient_order': 5, 'ambient_tex': 'C_5', 'aut_centralizer_order': 1, 'aut_label': '1.a1', 'aut_weyl_group': '4.1', 'aut_weyl_index': 1, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['5.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['5.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [1], 'hall': 5, 'label': '5.1.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': 1, 'nilpotent': True, 'normal': True, 'normal_closure': '1.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '1.1', 'proper': False, 'quotient': '1.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 1, 'quotient_solvable': True, 'quotient_tex': 'C_1', 'short_label': '1.a1.a1', 'solvable': True, 'special_labels': ['Z', 'F', 'R', 'S', 'U0', 'L0', 'D0', 'C0', '1.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_fusion': None, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'sylow': 5, 'weyl_group': '1.1'}
14. label: 5.1.5.a1.a1
    {'abelian': True, 'ambient': '5.1', 'ambient_order': 5, 'ambient_tex': 'C_5', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 4, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': [], 'core': '5.a1.a1', 'coset_action_label': '5T1', 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [], 'hall': 1, 'label': '5.1.5.a1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 1, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '5.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, 'projective_image': '5.1', 'proper': False, 'quotient': '5.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 5, 'quotient_solvable': True, 'quotient_tex': 'C_5', 'short_label': '5.a1.a1', 'solvable': True, 'special_labels': ['D', 'Phi', 'PC', 'U1', 'L1', 'D1', 'C1', '5.a1.a1.N', '5.a1.a1.M'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_fusion': None, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'sylow': 1, 'weyl_group': '1.1'}
15. label: 6.1.1.a1.a1
    {'abelian': False, 'ambient': '6.1', 'ambient_order': 6, 'ambient_tex': 'S_3', 'aut_centralizer_order': 1, 'aut_label': '1.a1', 'aut_weyl_group': '6.1', 'aut_weyl_index': 1, 'central': False, 'centralizer': '6.a1.a1', 'characteristic': True, 'complements': ['6.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': False, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [1, 2], 'hall': 6, 'label': '6.1.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 0, 'mobius_sub': 1, 'nilpotent': False, 'normal': True, 'normal_closure': '1.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '6.1', 'proper': False, 'quotient': '1.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 1, 'quotient_solvable': True, 'quotient_tex': 'C_1', 'short_label': '1.a1.a1', 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0', '1.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_fusion': None, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'sylow': 0, 'weyl_group': '6.1'}
16. label: 6.1.2.a1.a1
    {'abelian': True, 'ambient': '6.1', 'ambient_order': 6, 'ambient_tex': 'S_3', 'aut_centralizer_order': 3, 'aut_label': '2.a1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 3, 'central': False, 'centralizer': '2.a1.a1', 'characteristic': True, 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 2143, 'diagram_x': 2143, 'diagramx': [2143, 5000, 2143, 5000], 'direct': False, 'generators': [2], 'hall': 3, 'label': '6.1.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '6.1', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.a1.a1', 'solvable': True, 'special_labels': ['D', 'F', 'S', 'L1', 'D1', 'C1', '2.a1.a1.N', '2.a1.a1.M'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_fusion': None, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'sylow': 3, 'weyl_group': '2.1'}
17. label: 6.1.3.a1.a1
    {'abelian': True, 'ambient': '6.1', 'ambient_order': 6, 'ambient_tex': 'S_3', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 6, 'central': False, 'centralizer': '3.a1.a1', 'characteristic': False, 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': '3T2', 'count': 3, 'cyclic': True, 'diagram_aut_x': 7857, 'diagram_x': 7857, 'diagramx': [7857, 7857], 'direct': None, 'generators': [1], 'hall': 2, 'label': '6.1.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'minimal': True, 'minimal_normal': False, 'mobius_quo': None, 'mobius_sub': -1, 'nilpotent': True, 'normal': False, 'normal_closure': '1.a1.a1', 'normalizer': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '6.1', 'proper': True, 'quotient': None, 'quotient_abelian': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': None, 'quotient_fusion': None, 'quotient_order': 3, 'quotient_solvable': None, 'quotient_tex': None, 'short_label': '3.a1.a1', 'solvable': True, 'special_labels': ['3.a1.a1.M'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 2, 'weyl_group': '1.1'}
18. label: 6.1.6.a1.a1
    {'abelian': True, 'ambient': '6.1', 'ambient_order': 6, 'ambient_tex': 'S_3', 'aut_centralizer_order': 6, 'aut_label': '6.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 6, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': [], 'core': '6.a1.a1', 'coset_action_label': '6T2', 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [], 'hall': 1, 'label': '6.1.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 1, 'mobius_sub': 3, 'nilpotent': True, 'normal': True, 'normal_closure': '6.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, 'projective_image': '6.1', 'proper': False, 'quotient': '6.1', 'quotient_abelian': False, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': False, 'quotient_fusion': None, 'quotient_order': 6, 'quotient_solvable': True, 'quotient_tex': 'S_3', 'short_label': '6.a1.a1', 'solvable': True, 'special_labels': ['Z', 'Phi', 'PC', 'U0', 'D2', 'C2', '6.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_fusion': None, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'sylow': 1, 'weyl_group': '1.1'}
19. label: 6.2.1.a1.a1
    {'abelian': True, 'ambient': '6.2', 'ambient_order': 6, 'ambient_tex': 'C_6', 'aut_centralizer_order': 1, 'aut_label': '1.a1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 1, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['6.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [3, 2], 'hall': 6, 'label': '6.2.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 1, 'mobius_sub': 1, 'nilpotent': True, 'normal': True, 'normal_closure': '1.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '1.1', 'proper': False, 'quotient': '1.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 1, 'quotient_solvable': True, 'quotient_tex': 'C_1', 'short_label': '1.a1.a1', 'solvable': True, 'special_labels': ['Z', 'F', 'R', 'S', 'U0', 'L0', 'D0', 'C0', '1.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_fusion': None, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'sylow': 0, 'weyl_group': '1.1'}
20. label: 6.2.2.a1.a1
    {'abelian': True, 'ambient': '6.2', 'ambient_order': 6, 'ambient_tex': 'C_6', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 1, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 2143, 'diagram_x': 2143, 'diagramx': [2143, 2143, 2143, 2143], 'direct': True, 'generators': [2], 'hall': 3, 'label': '6.2.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '2.1', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.a1.a1', 'solvable': True, 'special_labels': ['C1', '2.a1.a1.N', '2.a1.a1.M'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_fusion': None, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'sylow': 3, 'weyl_group': '1.1'}
21. label: 6.2.3.a1.a1
    {'abelian': True, 'ambient': '6.2', 'ambient_order': 6, 'ambient_tex': 'C_6', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 2, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['2.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 7857, 'diagram_x': 7857, 'diagramx': [7857, 7857, 7857, 7857], 'direct': True, 'generators': [3], 'hall': 2, 'label': '6.2.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '3.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '3.1', 'proper': True, 'quotient': '3.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 3, 'quotient_solvable': True, 'quotient_tex': 'C_3', 'short_label': '3.a1.a1', 'solvable': True, 'special_labels': ['3.a1.a1.N', '3.a1.a1.M'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 2, 'weyl_group': '1.1'}
22. label: 6.2.6.a1.a1
    {'abelian': True, 'ambient': '6.2', 'ambient_order': 6, 'ambient_tex': 'C_6', 'aut_centralizer_order': 2, 'aut_label': '6.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 2, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': [], 'core': '6.a1.a1', 'coset_action_label': '6T1', 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [], 'hall': 1, 'label': '6.2.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 1, 'mobius_sub': 1, 'nilpotent': True, 'normal': True, 'normal_closure': '6.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, 'projective_image': '6.2', 'proper': False, 'quotient': '6.2', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 6, 'quotient_solvable': True, 'quotient_tex': 'C_6', 'short_label': '6.a1.a1', 'solvable': True, 'special_labels': ['D', 'Phi', 'PC', 'U1', 'L1', 'D1', 'C2', '6.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_fusion': None, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'sylow': 1, 'weyl_group': '1.1'}
23. label: 7.1.1.a1.a1
    {'abelian': True, 'ambient': '7.1', 'ambient_order': 7, 'ambient_tex': 'C_7', 'aut_centralizer_order': 1, 'aut_label': '1.a1', 'aut_weyl_group': '6.2', 'aut_weyl_index': 1, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['7.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['7.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [1], 'hall': 7, 'label': '7.1.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': 1, 'nilpotent': True, 'normal': True, 'normal_closure': '1.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '1.1', 'proper': False, 'quotient': '1.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 1, 'quotient_solvable': True, 'quotient_tex': 'C_1', 'short_label': '1.a1.a1', 'solvable': True, 'special_labels': ['Z', 'F', 'R', 'S', 'U0', 'L0', 'D0', 'C0', '1.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '7.1', 'subgroup_fusion': None, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'sylow': 7, 'weyl_group': '1.1'}
24. label: 7.1.7.a1.a1
    {'abelian': True, 'ambient': '7.1', 'ambient_order': 7, 'ambient_tex': 'C_7', 'aut_centralizer_order': 6, 'aut_label': '7.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 6, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': [], 'core': '7.a1.a1', 'coset_action_label': '7T1', 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [], 'hall': 1, 'label': '7.1.7.a1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 1, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '7.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, 'projective_image': '7.1', 'proper': False, 'quotient': '7.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 7, 'quotient_solvable': True, 'quotient_tex': 'C_7', 'short_label': '7.a1.a1', 'solvable': True, 'special_labels': ['D', 'Phi', 'PC', 'U1', 'L1', 'D1', 'C1', '7.a1.a1.N', '7.a1.a1.M'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_fusion': None, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'sylow': 1, 'weyl_group': '1.1'}
25. label: 8.1.1.a1.a1
    {'abelian': True, 'ambient': '8.1', 'ambient_order': 8, 'ambient_tex': 'C_8', 'aut_centralizer_order': 1, 'aut_label': '1.a1', 'aut_weyl_group': '4.2', 'aut_weyl_index': 1, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['8.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [1], 'hall': 2, 'label': '8.1.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 0, 'mobius_sub': 1, 'nilpotent': True, 'normal': True, 'normal_closure': '1.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '1.1', 'proper': False, 'quotient': '1.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 1, 'quotient_solvable': True, 'quotient_tex': 'C_1', 'short_label': '1.a1.a1', 'solvable': True, 'special_labels': ['Z', 'F', 'R', 'U0', 'L0', 'D0', 'C0', '1.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_fusion': None, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'sylow': 2, 'weyl_group': '1.1'}
26. label: 8.1.2.a1.a1
    {'abelian': True, 'ambient': '8.1', 'ambient_order': 8, 'ambient_tex': 'C_8', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 2, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': False, 'generators': [2], 'hall': 0, 'label': '8.1.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 0, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '2.1', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.a1.a1', 'solvable': True, 'special_labels': ['Phi', 'C1', '2.a1.a1.N', '2.a1.a1.M'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_fusion': None, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'sylow': 0, 'weyl_group': '1.1'}
27. label: 8.1.4.a1.a1
    {'abelian': True, 'ambient': '8.1', 'ambient_order': 8, 'ambient_tex': 'C_8', 'aut_centralizer_order': 4, 'aut_label': '4.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 4, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': False, 'generators': [4], 'hall': 0, 'label': '8.1.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': 0, 'nilpotent': True, 'normal': True, 'normal_closure': '4.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '4.1', 'proper': True, 'quotient': '4.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 4, 'quotient_solvable': True, 'quotient_tex': 'C_4', 'short_label': '4.a1.a1', 'solvable': True, 'special_labels': ['S', 'C2', '4.a1.a1.N'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 0, 'weyl_group': '1.1'}
28. label: 8.1.8.a1.a1
    {'abelian': True, 'ambient': '8.1', 'ambient_order': 8, 'ambient_tex': 'C_8', 'aut_centralizer_order': 4, 'aut_label': '8.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 4, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': [], 'core': '8.a1.a1', 'coset_action_label': '8T1', 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [], 'hall': 1, 'label': '8.1.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 1, 'mobius_sub': 0, 'nilpotent': True, 'normal': True, 'normal_closure': '8.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, 'projective_image': '8.1', 'proper': False, 'quotient': '8.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 8, 'quotient_solvable': True, 'quotient_tex': 'C_8', 'short_label': '8.a1.a1', 'solvable': True, 'special_labels': ['D', 'PC', 'U1', 'L1', 'D1', 'C3', '8.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_fusion': None, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'sylow': 1, 'weyl_group': '1.1'}
29. label: 8.2.1.a1.a1
    {'abelian': True, 'ambient': '8.2', 'ambient_order': 8, 'ambient_tex': 'C_2\\times C_4', 'aut_centralizer_order': 1, 'aut_label': '1.a1', 'aut_weyl_group': '8.3', 'aut_weyl_index': 1, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['8.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.b1.a1', '2.a1.a1', '2.b1.b1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': False, 'diagram_aut_x': 4998, 'diagram_x': 4987, 'diagramx': [4779, 4779, 3667, 3667], 'direct': True, 'generators': [1, 2], 'hall': 2, 'label': '8.2.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 0, 'mobius_sub': 1, 'nilpotent': True, 'normal': True, 'normal_closure': '1.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '1.1', 'proper': False, 'quotient': '1.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 1, 'quotient_solvable': True, 'quotient_tex': 'C_1', 'short_label': '1.a1.a1', 'solvable': True, 'special_labels': ['Z', 'F', 'R', 'U0', 'L0', 'D0', 'C0', '1.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_fusion': None, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'sylow': 2, 'weyl_group': '1.1'}
30. label: 8.2.2.b1.b1
    {'abelian': True, 'ambient': '8.2', 'ambient_order': 8, 'ambient_tex': 'C_2\\times C_4', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 4, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': False, 'complements': ['4.b1.b1', '4.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 1985, 'diagram_x': 10000, 'diagramx': [1985, 1985, 3667, 3667], 'direct': True, 'generators': [3], 'hall': 0, 'label': '8.2.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 0, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.b1.b1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '2.1', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.b1.b1', 'solvable': True, 'special_labels': ['2.a1.a1.N', '2.b1.a1.N', '2.b1.b1.N', '2.a1.a1.M', '2.b1.a1.M', '2.b1.b1.M'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_fusion': None, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'sylow': 0, 'weyl_group': '1.1'}
31. label: 8.2.2.b1.a1
    {'abelian': True, 'ambient': '8.2', 'ambient_order': 8, 'ambient_tex': 'C_2\\times C_4', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 4, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': False, 'complements': ['4.b1.b1', '4.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 9872, 'diagram_x': 6285, 'diagramx': [1985, 1985, 1000, 1000], 'direct': True, 'generators': [2], 'hall': 0, 'label': '8.2.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 0, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.b1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '2.1', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.b1.a1', 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_fusion': None, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'sylow': 0, 'weyl_group': '1.1'}
32. label: 8.2.2.a1.a1
    {'abelian': True, 'ambient': '8.2', 'ambient_order': 8, 'ambient_tex': 'C_2\\times C_4', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 4, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.b1', '4.b1.a1', '4.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': False, 'diagram_aut_x': 2218, 'diagram_x': 2657, 'diagramx': [7647, 7647, 6518, 6518], 'direct': False, 'generators': [1, 4], 'hall': 0, 'label': '8.2.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 2, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '2.1', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.a1.a1', 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_fusion': None, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'sylow': 0, 'weyl_group': '1.1'}
33. label: 8.2.4.b1.b1
    {'abelian': True, 'ambient': '8.2', 'ambient_order': 8, 'ambient_tex': 'C_2\\times C_4', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 8, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': False, 'complements': ['2.b1.a1', '2.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1'], 'core': '4.b1.b1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 7647, 'diagram_x': 3787, 'diagramx': [7647, 7647, 6333, 9000], 'direct': True, 'generators': [1], 'hall': 0, 'label': '8.2.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': 0, 'nilpotent': True, 'normal': True, 'normal_closure': '4.b1.b1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '4.1', 'proper': True, 'quotient': '4.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 4, 'quotient_solvable': True, 'quotient_tex': 'C_4', 'short_label': '4.b1.b1', 'solvable': True, 'special_labels': ['4.a1.a1.N', '4.b1.a1.N', '4.b1.b1.N'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 0, 'weyl_group': '1.1'}
34. label: 8.2.4.a1.a1
    {'abelian': True, 'ambient': '8.2', 'ambient_order': 8, 'ambient_tex': 'C_2\\times C_4', 'aut_centralizer_order': 8, 'aut_label': '4.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 8, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.a1.a1', '2.b1.b1'], 'contains': ['8.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 7477, 'diagram_x': 7481, 'diagramx': [2353, 2353, 3667, 3667], 'direct': False, 'generators': [4], 'hall': 0, 'label': '8.2.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': 2, 'nilpotent': True, 'normal': True, 'normal_closure': '4.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '4.2', 'proper': True, 'quotient': '4.2', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_cyclic': False, 'quotient_fusion': None, 'quotient_order': 4, 'quotient_solvable': True, 'quotient_tex': 'C_2^2', 'short_label': '4.a1.a1', 'solvable': True, 'special_labels': ['Phi', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 0, 'weyl_group': '1.1'}
35. label: 8.2.4.b1.a1
    {'abelian': True, 'ambient': '8.2', 'ambient_order': 8, 'ambient_tex': 'C_2\\times C_4', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 8, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': False, 'complements': ['2.b1.a1', '2.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 3609, 'diagram_x': 527, 'diagramx': [7647, 7647, 9000, 6333], 'direct': True, 'generators': [5], 'hall': 0, 'label': '8.2.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': 0, 'nilpotent': True, 'normal': True, 'normal_closure': '4.b1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '4.1', 'proper': True, 'quotient': '4.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 4, 'quotient_solvable': True, 'quotient_tex': 'C_4', 'short_label': '4.b1.a1', 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 0, 'weyl_group': '1.1'}
36. label: 8.2.8.a1.a1
    {'abelian': True, 'ambient': '8.2', 'ambient_order': 8, 'ambient_tex': 'C_2\\times C_4', 'aut_centralizer_order': 8, 'aut_label': '8.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 8, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '4.b1.a1', '4.a1.a1'], 'contains': [], 'core': '8.a1.a1', 'coset_action_label': '8T2', 'count': 1, 'cyclic': True, 'diagram_aut_x': 4998, 'diagram_x': 4987, 'diagramx': [5000, 5000, 6333, 6333], 'direct': True, 'generators': [], 'hall': 1, 'label': '8.2.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 1, 'mobius_sub': 0, 'nilpotent': True, 'normal': True, 'normal_closure': '8.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, 'projective_image': '8.2', 'proper': False, 'quotient': '8.2', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': False, 'quotient_fusion': None, 'quotient_order': 8, 'quotient_solvable': True, 'quotient_tex': 'C_2\\times C_4', 'short_label': '8.a1.a1', 'solvable': True, 'special_labels': ['D', 'PC', 'U1', 'L1', 'D1', 'C3', '8.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_fusion': None, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'sylow': 1, 'weyl_group': '1.1'}
37. label: 8.3.1.a1.a1
    {'abelian': False, 'ambient': '8.3', 'ambient_order': 8, 'ambient_tex': 'D_4', 'aut_centralizer_order': 1, 'aut_label': '1.a1', 'aut_weyl_group': '8.3', 'aut_weyl_index': 1, 'central': False, 'centralizer': '4.a1.a1', 'characteristic': True, 'complements': ['8.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.a1.b1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': False, 'diagram_aut_x': 4989, 'diagram_x': 4974, 'diagramx': [4779, 5147, 5000, 5229], 'direct': True, 'generators': [1, 2], 'hall': 2, 'label': '8.3.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 0, 'mobius_sub': 1, 'nilpotent': True, 'normal': True, 'normal_closure': '1.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '4.2', 'proper': False, 'quotient': '1.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 1, 'quotient_solvable': True, 'quotient_tex': 'C_1', 'short_label': '1.a1.a1', 'solvable': True, 'special_labels': ['F', 'R', 'U0', 'L0', 'D0', 'C0', '1.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_fusion': None, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'sylow': 2, 'weyl_group': '4.2'}
38. label: 8.3.2.b1.a1
    {'abelian': True, 'ambient': '8.3', 'ambient_order': 8, 'ambient_tex': 'D_4', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 4, 'central': False, 'centralizer': '2.b1.a1', 'characteristic': True, 'complements': ['4.b1.b1', '4.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 9908, 'diagram_x': 4915, 'diagramx': [1985, 8015, 5000, 8761], 'direct': False, 'generators': [2], 'hall': 0, 'label': '8.3.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 0, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.b1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '4.2', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.b1.a1', 'solvable': True, 'special_labels': ['C1', '2.a1.a1.N', '2.a1.b1.N', '2.b1.a1.N', '2.a1.a1.M', '2.a1.b1.M', '2.b1.a1.M'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_fusion': None, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'sylow': 0, 'weyl_group': '2.1'}
39. label: 8.3.2.a1.a1
    {'abelian': True, 'ambient': '8.3', 'ambient_order': 8, 'ambient_tex': 'D_4', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 4, 'central': False, 'centralizer': '2.a1.a1', 'characteristic': False, 'complements': ['4.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': False, 'diagram_aut_x': 2, 'diagram_x': 7806, 'diagramx': [7647, 2353, 1468, 1468], 'direct': False, 'generators': [3, 4], 'hall': 0, 'label': '8.3.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 0, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '4.2', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.a1.a1', 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_fusion': None, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'sylow': 0, 'weyl_group': '2.1'}
40. label: 8.3.2.a1.b1
    {'abelian': True, 'ambient': '8.3', 'ambient_order': 8, 'ambient_tex': 'D_4', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 4, 'central': False, 'centralizer': '2.a1.b1', 'characteristic': False, 'complements': ['4.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.b1', '4.a1.a1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'cyclic': False, 'diagram_aut_x': 7647, 'diagram_x': 1828, 'diagramx': [7647, 2353, 8532, 5229], 'direct': False, 'generators': [1, 4], 'hall': 0, 'label': '8.3.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 0, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.a1.b1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '4.2', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.a1.b1', 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_fusion': None, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'sylow': 0, 'weyl_group': '2.1'}
41. label: 8.3.4.b1.b1
    {'abelian': True, 'ambient': '8.3', 'ambient_order': 8, 'ambient_tex': 'D_4', 'aut_centralizer_order': 2, 'aut_label': '4.b1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 8, 'central': False, 'centralizer': '2.a1.b1', 'characteristic': False, 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1'], 'contains': ['8.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': '4T3', 'count': 2, 'cyclic': True, 'diagram_aut_x': 7647, 'diagram_x': 1828, 'diagramx': [7647, 8395], 'direct': None, 'generators': [1], 'hall': 0, 'label': '8.3.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'minimal': True, 'minimal_normal': False, 'mobius_quo': None, 'mobius_sub': 0, 'nilpotent': True, 'normal': False, 'normal_closure': '2.a1.b1', 'normalizer': '2.a1.b1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '8.3', 'proper': True, 'quotient': None, 'quotient_abelian': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': None, 'quotient_fusion': None, 'quotient_order': 4, 'quotient_solvable': None, 'quotient_tex': None, 'short_label': '4.b1.b1', 'solvable': True, 'special_labels': ['4.a1.a1.N'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 0, 'weyl_group': '1.1'}
42. label: 8.3.4.b1.a1
    {'abelian': True, 'ambient': '8.3', 'ambient_order': 8, 'ambient_tex': 'D_4', 'aut_centralizer_order': 2, 'aut_label': '4.b1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 8, 'central': False, 'centralizer': '2.a1.a1', 'characteristic': False, 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': '4T3', 'count': 2, 'cyclic': True, 'diagram_aut_x': 2350, 'diagram_x': 7849, 'diagramx': [7647, 1605], 'direct': None, 'generators': [3], 'hall': 0, 'label': '8.3.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': True, 'minimal_normal': False, 'mobius_quo': None, 'mobius_sub': 0, 'nilpotent': True, 'normal': False, 'normal_closure': '2.a1.a1', 'normalizer': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '8.3', 'proper': True, 'quotient': None, 'quotient_abelian': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': None, 'quotient_fusion': None, 'quotient_order': 4, 'quotient_solvable': None, 'quotient_tex': None, 'short_label': '4.b1.a1', 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 0, 'weyl_group': '1.1'}
43. label: 8.3.4.a1.a1
    {'abelian': True, 'ambient': '8.3', 'ambient_order': 8, 'ambient_tex': 'D_4', 'aut_centralizer_order': 8, 'aut_label': '4.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 8, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.a1.b1'], 'contains': ['8.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 7501, 'diagram_x': 4958, 'diagramx': [2353, 5147, 5000, 5229], 'direct': False, 'generators': [4], 'hall': 0, 'label': '8.3.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': 2, 'nilpotent': True, 'normal': True, 'normal_closure': '4.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '4.2', 'proper': True, 'quotient': '4.2', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_cyclic': False, 'quotient_fusion': None, 'quotient_order': 4, 'quotient_solvable': True, 'quotient_tex': 'C_2^2', 'short_label': '4.a1.a1', 'solvable': True, 'special_labels': ['Z', 'D', 'Phi', 'S', 'U1', 'L1', 'D1', 'C2'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 0, 'weyl_group': '1.1'}
44. label: 8.3.8.a1.a1
    {'abelian': True, 'ambient': '8.3', 'ambient_order': 8, 'ambient_tex': 'D_4', 'aut_centralizer_order': 8, 'aut_label': '8.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 8, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '4.b1.a1', '4.a1.a1'], 'contains': [], 'core': '8.a1.a1', 'coset_action_label': '8T4', 'count': 1, 'cyclic': True, 'diagram_aut_x': 4989, 'diagram_x': 4974, 'diagramx': [5000, 5147, 5000, 5229], 'direct': True, 'generators': [], 'hall': 1, 'label': '8.3.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 1, 'mobius_sub': 0, 'nilpotent': True, 'normal': True, 'normal_closure': '8.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, 'projective_image': '8.3', 'proper': False, 'quotient': '8.3', 'quotient_abelian': False, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': False, 'quotient_fusion': None, 'quotient_order': 8, 'quotient_solvable': True, 'quotient_tex': 'D_4', 'short_label': '8.a1.a1', 'solvable': True, 'special_labels': ['PC', 'U2', 'L2', 'D2', 'C3', '8.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_fusion': None, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'sylow': 1, 'weyl_group': '1.1'}
45. label: 8.4.1.a1.a1
    {'abelian': False, 'ambient': '8.4', 'ambient_order': 8, 'ambient_tex': 'Q_8', 'aut_centralizer_order': 1, 'aut_label': '1.a1', 'aut_weyl_group': '24.12', 'aut_weyl_index': 1, 'central': False, 'centralizer': '4.a1.a1', 'characteristic': True, 'complements': ['8.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.c1', '2.a1.b1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': False, 'diagram_aut_x': 5000, 'diagram_x': 5006, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [1, 2], 'hall': 2, 'label': '8.4.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 0, 'mobius_sub': 1, 'nilpotent': True, 'normal': True, 'normal_closure': '1.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '4.2', 'proper': False, 'quotient': '1.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 1, 'quotient_solvable': True, 'quotient_tex': 'C_1', 'short_label': '1.a1.a1', 'solvable': True, 'special_labels': ['F', 'R', 'U0', 'L0', 'D0', 'C0', '1.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_fusion': None, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'sylow': 2, 'weyl_group': '4.2'}
46. label: 8.4.2.a1.a1
    {'abelian': True, 'ambient': '8.4', 'ambient_order': 8, 'ambient_tex': 'Q_8', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 12, 'central': False, 'centralizer': '2.a1.a1', 'characteristic': False, 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 1, 'diagramx': [5000, 5000, 1364, 1364], 'direct': False, 'generators': [2], 'hall': 0, 'label': '8.4.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 0, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '4.2', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.a1.a1', 'solvable': True, 'special_labels': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_fusion': None, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'sylow': 0, 'weyl_group': '2.1'}
47. label: 8.4.2.a1.b1
    {'abelian': True, 'ambient': '8.4', 'ambient_order': 8, 'ambient_tex': 'Q_8', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 12, 'central': False, 'centralizer': '2.a1.b1', 'characteristic': False, 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5044, 'diagramx': [5000, 5000, 8636, 5000], 'direct': False, 'generators': [3], 'hall': 0, 'label': '8.4.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 0, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.a1.b1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '4.2', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.a1.b1', 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_fusion': None, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'sylow': 0, 'weyl_group': '2.1'}
48. label: 8.4.2.a1.c1
    {'abelian': True, 'ambient': '8.4', 'ambient_order': 8, 'ambient_tex': 'Q_8', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 12, 'central': False, 'centralizer': '2.a1.c1', 'characteristic': False, 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1'], 'core': '2.a1.c1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 10000, 'diagramx': [5000, 5000, 5000, 8636], 'direct': False, 'generators': [1], 'hall': 0, 'label': '8.4.2.a1.c1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 0, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.a1.c1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '4.2', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.a1.c1', 'solvable': True, 'special_labels': ['2.a1.a1.N', '2.a1.b1.N', '2.a1.c1.N', '2.a1.a1.M', '2.a1.b1.M', '2.a1.c1.M'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_fusion': None, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'sylow': 0, 'weyl_group': '2.1'}
49. label: 8.4.4.a1.a1
    {'abelian': True, 'ambient': '8.4', 'ambient_order': 8, 'ambient_tex': 'Q_8', 'aut_centralizer_order': 24, 'aut_label': '4.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 24, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.c1', '2.a1.b1'], 'contains': ['8.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5066, 'diagramx': [5000, 5000, 5000, 5000], 'direct': False, 'generators': [4], 'hall': 0, 'label': '8.4.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': 2, 'nilpotent': True, 'normal': True, 'normal_closure': '4.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '4.2', 'proper': True, 'quotient': '4.2', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_cyclic': False, 'quotient_fusion': None, 'quotient_order': 4, 'quotient_solvable': True, 'quotient_tex': 'C_2^2', 'short_label': '4.a1.a1', 'solvable': True, 'special_labels': ['Z', 'D', 'Phi', 'S', 'U1', 'L1', 'D1', 'C2', '4.a1.a1.N'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 0, 'weyl_group': '1.1'}
50. label: 8.4.8.a1.a1
    {'abelian': True, 'ambient': '8.4', 'ambient_order': 8, 'ambient_tex': 'Q_8', 'aut_centralizer_order': 24, 'aut_label': '8.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 24, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': [], 'core': '8.a1.a1', 'coset_action_label': '8T5', 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5066, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [], 'hall': 1, 'label': '8.4.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 1, 'mobius_sub': 0, 'nilpotent': True, 'normal': True, 'normal_closure': '8.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, 'projective_image': '8.4', 'proper': False, 'quotient': '8.4', 'quotient_abelian': False, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': False, 'quotient_fusion': None, 'quotient_order': 8, 'quotient_solvable': True, 'quotient_tex': 'Q_8', 'short_label': '8.a1.a1', 'solvable': True, 'special_labels': ['PC', 'U2', 'L2', 'D2', 'C3', '8.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_fusion': None, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'sylow': 1, 'weyl_group': '1.1'}
51. label: 8.5.1.a1.a1
    {'abelian': True, 'ambient': '8.5', 'ambient_order': 8, 'ambient_tex': 'C_2^3', 'aut_centralizer_order': 1, 'aut_label': '1.a1', 'aut_weyl_group': '168.42', 'aut_weyl_index': 1, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['8.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.f1', '2.a1.g1', '2.a1.c1', '2.a1.a1', '2.a1.e1', '2.a1.d1', '2.a1.b1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': False, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [1, 2, 4], 'hall': 2, 'label': '8.5.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': -8, 'mobius_sub': 1, 'nilpotent': True, 'normal': True, 'normal_closure': '1.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '1.1', 'proper': False, 'quotient': '1.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 1, 'quotient_solvable': True, 'quotient_tex': 'C_1', 'short_label': '1.a1.a1', 'solvable': True, 'special_labels': ['Z', 'F', 'R', 'S', 'U0', 'L0', 'D0', 'C0', '1.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_fusion': None, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'sylow': 2, 'weyl_group': '1.1'}
52. label: 8.5.2.a1.d1
    {'abelian': True, 'ambient': '8.5', 'ambient_order': 8, 'ambient_tex': 'C_2^3', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_weyl_group': '6.1', 'aut_weyl_index': 28, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': False, 'complements': ['4.a1.a1', '4.a1.f1', '4.a1.e1', '4.a1.g1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.c1', '4.a1.d1', '4.a1.b1'], 'core': '2.a1.d1', 'coset_action_label': None, 'count': 1, 'cyclic': False, 'diagram_aut_x': 5000, 'diagram_x': 7950, 'diagramx': [5000, 5000, 7950, 7950], 'direct': True, 'generators': [1, 2], 'hall': 0, 'label': '8.5.2.a1.d1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 2, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.a1.d1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '2.1', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.a1.d1', 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_fusion': None, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'sylow': 0, 'weyl_group': '1.1'}
53. label: 8.5.2.a1.e1
    {'abelian': True, 'ambient': '8.5', 'ambient_order': 8, 'ambient_tex': 'C_2^3', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_weyl_group': '6.1', 'aut_weyl_index': 28, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': False, 'complements': ['4.a1.a1', '4.a1.c1', '4.a1.d1', '4.a1.g1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.e1', '4.a1.b1', '4.a1.f1'], 'core': '2.a1.e1', 'coset_action_label': None, 'count': 1, 'cyclic': False, 'diagram_aut_x': 5000, 'diagram_x': 2050, 'diagramx': [5000, 5000, 2050, 6475], 'direct': True, 'generators': [1, 4], 'hall': 0, 'label': '8.5.2.a1.e1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 2, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.a1.e1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '2.1', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.a1.e1', 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_fusion': None, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'sylow': 0, 'weyl_group': '1.1'}
54. label: 8.5.2.a1.g1
    {'abelian': True, 'ambient': '8.5', 'ambient_order': 8, 'ambient_tex': 'C_2^3', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_weyl_group': '6.1', 'aut_weyl_index': 28, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': False, 'complements': ['4.a1.a1', '4.a1.e1', '4.a1.c1', '4.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.d1', '4.a1.g1', '4.a1.f1'], 'core': '2.a1.g1', 'coset_action_label': None, 'count': 1, 'cyclic': False, 'diagram_aut_x': 5000, 'diagram_x': 3525, 'diagramx': [5000, 5000, 3525, 9425], 'direct': True, 'generators': [5, 2], 'hall': 0, 'label': '8.5.2.a1.g1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 2, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.a1.g1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '2.1', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.a1.g1', 'solvable': True, 'special_labels': ['2.a1.a1.N', '2.a1.b1.N', '2.a1.c1.N', '2.a1.d1.N', '2.a1.e1.N', '2.a1.f1.N', '2.a1.g1.N', '2.a1.a1.M', '2.a1.b1.M', '2.a1.c1.M', '2.a1.d1.M', '2.a1.e1.M', '2.a1.f1.M', '2.a1.g1.M'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_fusion': None, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'sylow': 0, 'weyl_group': '1.1'}
55. label: 8.5.2.a1.f1
    {'abelian': True, 'ambient': '8.5', 'ambient_order': 8, 'ambient_tex': 'C_2^3', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_weyl_group': '6.1', 'aut_weyl_index': 28, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': False, 'complements': ['4.a1.a1', '4.a1.f1', '4.a1.d1', '4.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.e1', '4.a1.c1', '4.a1.g1'], 'core': '2.a1.f1', 'coset_action_label': None, 'count': 1, 'cyclic': False, 'diagram_aut_x': 5000, 'diagram_x': 576, 'diagramx': [5000, 5000, 576, 576], 'direct': True, 'generators': [3, 4], 'hall': 0, 'label': '8.5.2.a1.f1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 2, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.a1.f1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '2.1', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.a1.f1', 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_fusion': None, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'sylow': 0, 'weyl_group': '1.1'}
56. label: 8.5.2.a1.b1
    {'abelian': True, 'ambient': '8.5', 'ambient_order': 8, 'ambient_tex': 'C_2^3', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_weyl_group': '6.1', 'aut_weyl_index': 28, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': False, 'complements': ['4.a1.e1', '4.a1.d1', '4.a1.b1', '4.a1.g1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.c1', '4.a1.a1', '4.a1.f1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'cyclic': False, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [5, 6], 'hall': 0, 'label': '8.5.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 2, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.a1.b1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '2.1', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.a1.b1', 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_fusion': None, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'sylow': 0, 'weyl_group': '1.1'}
57. label: 8.5.2.a1.c1
    {'abelian': True, 'ambient': '8.5', 'ambient_order': 8, 'ambient_tex': 'C_2^3', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_weyl_group': '6.1', 'aut_weyl_index': 28, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': False, 'complements': ['4.a1.f1', '4.a1.c1', '4.a1.b1', '4.a1.g1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.e1', '4.a1.d1', '4.a1.a1'], 'core': '2.a1.c1', 'coset_action_label': None, 'count': 1, 'cyclic': False, 'diagram_aut_x': 5000, 'diagram_x': 6475, 'diagramx': [5000, 5000, 6475, 2050], 'direct': True, 'generators': [2, 4], 'hall': 0, 'label': '8.5.2.a1.c1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 2, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.a1.c1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '2.1', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.a1.c1', 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_fusion': None, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'sylow': 0, 'weyl_group': '1.1'}
58. label: 8.5.2.a1.a1
    {'abelian': True, 'ambient': '8.5', 'ambient_order': 8, 'ambient_tex': 'C_2^3', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_weyl_group': '6.1', 'aut_weyl_index': 28, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': False, 'complements': ['4.a1.f1', '4.a1.e1', '4.a1.c1', '4.a1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.b1', '4.a1.g1', '4.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': False, 'diagram_aut_x': 5000, 'diagram_x': 9425, 'diagramx': [5000, 5000, 9425, 3525], 'direct': True, 'generators': [1, 6], 'hall': 0, 'label': '8.5.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 2, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '2.1', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.a1.a1', 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_fusion': None, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'sylow': 0, 'weyl_group': '1.1'}
59. label: 8.5.4.a1.g1
    {'abelian': True, 'ambient': '8.5', 'ambient_order': 8, 'ambient_tex': 'C_2^3', 'aut_centralizer_order': 24, 'aut_label': '4.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 168, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': False, 'complements': ['2.a1.c1', '2.a1.e1', '2.a1.d1', '2.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.f1', '2.a1.g1', '2.a1.a1'], 'contains': ['8.a1.a1'], 'core': '4.a1.g1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 2410, 'diagramx': [5000, 5000, 2410, 2410], 'direct': True, 'generators': [7], 'hall': 0, 'label': '8.5.4.a1.g1', 'maximal': False, 'maximal_normal': False, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': 2, 'nilpotent': True, 'normal': True, 'normal_closure': '4.a1.g1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '4.2', 'proper': True, 'quotient': '4.2', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_cyclic': False, 'quotient_fusion': None, 'quotient_order': 4, 'quotient_solvable': True, 'quotient_tex': 'C_2^2', 'short_label': '4.a1.g1', 'solvable': True, 'special_labels': ['4.a1.a1.N', '4.a1.b1.N', '4.a1.c1.N', '4.a1.d1.N', '4.a1.e1.N', '4.a1.f1.N', '4.a1.g1.N'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 0, 'weyl_group': '1.1'}
60. label: 8.5.4.a1.d1
    {'abelian': True, 'ambient': '8.5', 'ambient_order': 8, 'ambient_tex': 'C_2^3', 'aut_centralizer_order': 24, 'aut_label': '4.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 168, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': False, 'complements': ['2.a1.f1', '2.a1.a1', '2.a1.e1', '2.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.g1', '2.a1.c1', '2.a1.d1'], 'contains': ['8.a1.a1'], 'core': '4.a1.d1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 6295, 'diagramx': [5000, 5000, 6295, 8885], 'direct': True, 'generators': [2], 'hall': 0, 'label': '8.5.4.a1.d1', 'maximal': False, 'maximal_normal': False, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': 2, 'nilpotent': True, 'normal': True, 'normal_closure': '4.a1.d1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '4.2', 'proper': True, 'quotient': '4.2', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_cyclic': False, 'quotient_fusion': None, 'quotient_order': 4, 'quotient_solvable': True, 'quotient_tex': 'C_2^2', 'short_label': '4.a1.d1', 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 0, 'weyl_group': '1.1'}
61. label: 8.5.4.a1.f1
    {'abelian': True, 'ambient': '8.5', 'ambient_order': 8, 'ambient_tex': 'C_2^3', 'aut_centralizer_order': 24, 'aut_label': '4.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 168, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': False, 'complements': ['2.a1.f1', '2.a1.c1', '2.a1.a1', '2.a1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.g1', '2.a1.e1', '2.a1.b1'], 'contains': ['8.a1.a1'], 'core': '4.a1.f1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 3705, 'diagramx': [5000, 5000, 3705, 7590], 'direct': True, 'generators': [5], 'hall': 0, 'label': '8.5.4.a1.f1', 'maximal': False, 'maximal_normal': False, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': 2, 'nilpotent': True, 'normal': True, 'normal_closure': '4.a1.f1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '4.2', 'proper': True, 'quotient': '4.2', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_cyclic': False, 'quotient_fusion': None, 'quotient_order': 4, 'quotient_solvable': True, 'quotient_tex': 'C_2^2', 'short_label': '4.a1.f1', 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 0, 'weyl_group': '1.1'}
62. label: 8.5.4.a1.b1
    {'abelian': True, 'ambient': '8.5', 'ambient_order': 8, 'ambient_tex': 'C_2^3', 'aut_centralizer_order': 24, 'aut_label': '4.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 168, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': False, 'complements': ['2.a1.f1', '2.a1.g1', '2.a1.c1', '2.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.e1', '2.a1.d1'], 'contains': ['8.a1.a1'], 'core': '4.a1.b1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 8885, 'diagramx': [5000, 5000, 8885, 6295], 'direct': True, 'generators': [1], 'hall': 0, 'label': '8.5.4.a1.b1', 'maximal': False, 'maximal_normal': False, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': 2, 'nilpotent': True, 'normal': True, 'normal_closure': '4.a1.b1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '4.2', 'proper': True, 'quotient': '4.2', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_cyclic': False, 'quotient_fusion': None, 'quotient_order': 4, 'quotient_solvable': True, 'quotient_tex': 'C_2^2', 'short_label': '4.a1.b1', 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 0, 'weyl_group': '1.1'}
63. label: 8.5.4.a1.a1
    {'abelian': True, 'ambient': '8.5', 'ambient_order': 8, 'ambient_tex': 'C_2^3', 'aut_centralizer_order': 24, 'aut_label': '4.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 168, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': False, 'complements': ['2.a1.f1', '2.a1.g1', '2.a1.e1', '2.a1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.c1', '2.a1.a1', '2.a1.b1'], 'contains': ['8.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 7590, 'diagramx': [5000, 5000, 7590, 3705], 'direct': True, 'generators': [6], 'hall': 0, 'label': '8.5.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': 2, 'nilpotent': True, 'normal': True, 'normal_closure': '4.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '4.2', 'proper': True, 'quotient': '4.2', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_cyclic': False, 'quotient_fusion': None, 'quotient_order': 4, 'quotient_solvable': True, 'quotient_tex': 'C_2^2', 'short_label': '4.a1.a1', 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 0, 'weyl_group': '1.1'}
64. label: 8.5.4.a1.e1
    {'abelian': True, 'ambient': '8.5', 'ambient_order': 8, 'ambient_tex': 'C_2^3', 'aut_centralizer_order': 24, 'aut_label': '4.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 168, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': False, 'complements': ['2.a1.g1', '2.a1.a1', '2.a1.d1', '2.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.f1', '2.a1.c1', '2.a1.e1'], 'contains': ['8.a1.a1'], 'core': '4.a1.e1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 1115, 'diagramx': [5000, 5000, 1115, 1115], 'direct': True, 'generators': [4], 'hall': 0, 'label': '8.5.4.a1.e1', 'maximal': False, 'maximal_normal': False, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': 2, 'nilpotent': True, 'normal': True, 'normal_closure': '4.a1.e1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '4.2', 'proper': True, 'quotient': '4.2', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_cyclic': False, 'quotient_fusion': None, 'quotient_order': 4, 'quotient_solvable': True, 'quotient_tex': 'C_2^2', 'short_label': '4.a1.e1', 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 0, 'weyl_group': '1.1'}
65. label: 8.5.4.a1.c1
    {'abelian': True, 'ambient': '8.5', 'ambient_order': 8, 'ambient_tex': 'C_2^3', 'aut_centralizer_order': 24, 'aut_label': '4.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 168, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': False, 'complements': ['2.a1.g1', '2.a1.c1', '2.a1.a1', '2.a1.e1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.f1', '2.a1.d1', '2.a1.b1'], 'contains': ['8.a1.a1'], 'core': '4.a1.c1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [3], 'hall': 0, 'label': '8.5.4.a1.c1', 'maximal': False, 'maximal_normal': False, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': 2, 'nilpotent': True, 'normal': True, 'normal_closure': '4.a1.c1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '4.2', 'proper': True, 'quotient': '4.2', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_cyclic': False, 'quotient_fusion': None, 'quotient_order': 4, 'quotient_solvable': True, 'quotient_tex': 'C_2^2', 'short_label': '4.a1.c1', 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 0, 'weyl_group': '1.1'}
66. label: 8.5.8.a1.a1
    {'abelian': True, 'ambient': '8.5', 'ambient_order': 8, 'ambient_tex': 'C_2^3', 'aut_centralizer_order': 168, 'aut_label': '8.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 168, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.e1', '4.a1.c1', '4.a1.d1', '4.a1.b1', '4.a1.g1', '4.a1.a1', '4.a1.f1'], 'contains': [], 'core': '8.a1.a1', 'coset_action_label': '8T3', 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [], 'hall': 1, 'label': '8.5.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 1, 'mobius_sub': -8, 'nilpotent': True, 'normal': True, 'normal_closure': '8.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, 'projective_image': '8.5', 'proper': False, 'quotient': '8.5', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': False, 'quotient_fusion': None, 'quotient_order': 8, 'quotient_solvable': True, 'quotient_tex': 'C_2^3', 'short_label': '8.a1.a1', 'solvable': True, 'special_labels': ['D', 'Phi', 'PC', 'U1', 'L1', 'D1', 'C3', '8.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_fusion': None, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'sylow': 1, 'weyl_group': '1.1'}
67. label: 9.1.1.a1.a1
    {'abelian': True, 'ambient': '9.1', 'ambient_order': 9, 'ambient_tex': 'C_9', 'aut_centralizer_order': 1, 'aut_label': '1.a1', 'aut_weyl_group': '6.2', 'aut_weyl_index': 1, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['9.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['3.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [1], 'hall': 3, 'label': '9.1.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 0, 'mobius_sub': 1, 'nilpotent': True, 'normal': True, 'normal_closure': '1.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '1.1', 'proper': False, 'quotient': '1.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 1, 'quotient_solvable': True, 'quotient_tex': 'C_1', 'short_label': '1.a1.a1', 'solvable': True, 'special_labels': ['Z', 'F', 'R', 'U0', 'L0', 'D0', 'C0', '1.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_fusion': None, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'sylow': 3, 'weyl_group': '1.1'}
68. label: 9.1.3.a1.a1
    {'abelian': True, 'ambient': '9.1', 'ambient_order': 9, 'ambient_tex': 'C_9', 'aut_centralizer_order': 3, 'aut_label': '3.a1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 3, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['9.a1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': False, 'generators': [3], 'hall': 0, 'label': '9.1.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '3.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '3.1', 'proper': True, 'quotient': '3.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 3, 'quotient_solvable': True, 'quotient_tex': 'C_3', 'short_label': '3.a1.a1', 'solvable': True, 'special_labels': ['Phi', 'S', 'C1', '3.a1.a1.N', '3.a1.a1.M'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_fusion': None, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'sylow': 0, 'weyl_group': '1.1'}
69. label: 9.1.9.a1.a1
    {'abelian': True, 'ambient': '9.1', 'ambient_order': 9, 'ambient_tex': 'C_9', 'aut_centralizer_order': 6, 'aut_label': '9.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 6, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': [], 'core': '9.a1.a1', 'coset_action_label': '9T1', 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [], 'hall': 1, 'label': '9.1.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 1, 'mobius_sub': 0, 'nilpotent': True, 'normal': True, 'normal_closure': '9.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, 'projective_image': '9.1', 'proper': False, 'quotient': '9.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 9, 'quotient_solvable': True, 'quotient_tex': 'C_9', 'short_label': '9.a1.a1', 'solvable': True, 'special_labels': ['D', 'PC', 'U1', 'L1', 'D1', 'C2', '9.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_fusion': None, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'sylow': 1, 'weyl_group': '1.1'}
70. label: 9.2.1.a1.a1
    {'abelian': True, 'ambient': '9.2', 'ambient_order': 9, 'ambient_tex': 'C_3^2', 'aut_centralizer_order': 1, 'aut_label': '1.a1', 'aut_weyl_group': '48.29', 'aut_weyl_index': 1, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['9.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['3.a1.a1', '3.a1.d1', '3.a1.b1', '3.a1.c1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': False, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [1, 3], 'hall': 3, 'label': '9.2.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 3, 'mobius_sub': 1, 'nilpotent': True, 'normal': True, 'normal_closure': '1.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '1.1', 'proper': False, 'quotient': '1.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 1, 'quotient_solvable': True, 'quotient_tex': 'C_1', 'short_label': '1.a1.a1', 'solvable': True, 'special_labels': ['Z', 'F', 'R', 'S', 'U0', 'L0', 'D0', 'C0', '1.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_fusion': None, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'sylow': 3, 'weyl_group': '1.1'}
71. label: 9.2.3.a1.d1
    {'abelian': True, 'ambient': '9.2', 'ambient_order': 9, 'ambient_tex': 'C_3^2', 'aut_centralizer_order': 6, 'aut_label': '3.a1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 24, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': False, 'complements': ['3.a1.a1', '3.a1.b1', '3.a1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['9.a1.a1'], 'core': '3.a1.d1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 3667, 'diagramx': [5000, 5000, 3667, 9000], 'direct': True, 'generators': [3], 'hall': 0, 'label': '9.2.3.a1.d1', 'maximal': True, 'maximal_normal': True, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '3.a1.d1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '3.1', 'proper': True, 'quotient': '3.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 3, 'quotient_solvable': True, 'quotient_tex': 'C_3', 'short_label': '3.a1.d1', 'solvable': True, 'special_labels': ['C1', '3.a1.a1.N', '3.a1.b1.N', '3.a1.c1.N', '3.a1.d1.N', '3.a1.a1.M', '3.a1.b1.M', '3.a1.c1.M', '3.a1.d1.M'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_fusion': None, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'sylow': 0, 'weyl_group': '1.1'}
72. label: 9.2.3.a1.c1
    {'abelian': True, 'ambient': '9.2', 'ambient_order': 9, 'ambient_tex': 'C_3^2', 'aut_centralizer_order': 6, 'aut_label': '3.a1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 24, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': False, 'complements': ['3.a1.a1', '3.a1.d1', '3.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['9.a1.a1'], 'core': '3.a1.c1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 9000, 'diagramx': [5000, 5000, 9000, 6333], 'direct': True, 'generators': [4], 'hall': 0, 'label': '9.2.3.a1.c1', 'maximal': True, 'maximal_normal': True, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '3.a1.c1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '3.1', 'proper': True, 'quotient': '3.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 3, 'quotient_solvable': True, 'quotient_tex': 'C_3', 'short_label': '3.a1.c1', 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_fusion': None, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'sylow': 0, 'weyl_group': '1.1'}
73. label: 9.2.3.a1.b1
    {'abelian': True, 'ambient': '9.2', 'ambient_order': 9, 'ambient_tex': 'C_3^2', 'aut_centralizer_order': 6, 'aut_label': '3.a1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 24, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': False, 'complements': ['3.a1.a1', '3.a1.d1', '3.a1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['9.a1.a1'], 'core': '3.a1.b1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 6333, 'diagramx': [5000, 5000, 6333, 3667], 'direct': True, 'generators': [1], 'hall': 0, 'label': '9.2.3.a1.b1', 'maximal': True, 'maximal_normal': True, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '3.a1.b1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '3.1', 'proper': True, 'quotient': '3.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 3, 'quotient_solvable': True, 'quotient_tex': 'C_3', 'short_label': '3.a1.b1', 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_fusion': None, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'sylow': 0, 'weyl_group': '1.1'}
74. label: 9.2.3.a1.a1
    {'abelian': True, 'ambient': '9.2', 'ambient_order': 9, 'ambient_tex': 'C_3^2', 'aut_centralizer_order': 6, 'aut_label': '3.a1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 24, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': False, 'complements': ['3.a1.d1', '3.a1.b1', '3.a1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['9.a1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 1000, 'diagramx': [5000, 5000, 1000, 1000], 'direct': True, 'generators': [7], 'hall': 0, 'label': '9.2.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '3.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '3.1', 'proper': True, 'quotient': '3.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 3, 'quotient_solvable': True, 'quotient_tex': 'C_3', 'short_label': '3.a1.a1', 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_fusion': None, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'sylow': 0, 'weyl_group': '1.1'}
75. label: 9.2.9.a1.a1
    {'abelian': True, 'ambient': '9.2', 'ambient_order': 9, 'ambient_tex': 'C_3^2', 'aut_centralizer_order': 48, 'aut_label': '9.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 48, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.a1.d1', '3.a1.b1', '3.a1.c1'], 'contains': [], 'core': '9.a1.a1', 'coset_action_label': '9T2', 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [], 'hall': 1, 'label': '9.2.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 1, 'mobius_sub': 3, 'nilpotent': True, 'normal': True, 'normal_closure': '9.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, 'projective_image': '9.2', 'proper': False, 'quotient': '9.2', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': False, 'quotient_fusion': None, 'quotient_order': 9, 'quotient_solvable': True, 'quotient_tex': 'C_3^2', 'short_label': '9.a1.a1', 'solvable': True, 'special_labels': ['D', 'Phi', 'PC', 'U1', 'L1', 'D1', 'C2', '9.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_fusion': None, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'sylow': 1, 'weyl_group': '1.1'}
76. label: 10.1.1.a1.a1
    {'abelian': False, 'ambient': '10.1', 'ambient_order': 10, 'ambient_tex': 'D_5', 'aut_centralizer_order': 1, 'aut_label': '1.a1', 'aut_weyl_group': '20.3', 'aut_weyl_index': 1, 'central': False, 'centralizer': '10.a1.a1', 'characteristic': True, 'complements': ['10.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '5.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': False, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [1, 2], 'hall': 10, 'label': '10.1.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 0, 'mobius_sub': 1, 'nilpotent': False, 'normal': True, 'normal_closure': '1.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '10.1', 'proper': False, 'quotient': '1.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 1, 'quotient_solvable': True, 'quotient_tex': 'C_1', 'short_label': '1.a1.a1', 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0', '1.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_fusion': None, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'sylow': 0, 'weyl_group': '10.1'}
77. label: 10.1.2.a1.a1
    {'abelian': True, 'ambient': '10.1', 'ambient_order': 10, 'ambient_tex': 'D_5', 'aut_centralizer_order': 5, 'aut_label': '2.a1', 'aut_weyl_group': '4.1', 'aut_weyl_index': 5, 'central': False, 'centralizer': '2.a1.a1', 'characteristic': True, 'complements': ['5.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 7857, 'diagram_x': 2143, 'diagramx': [7857, 5000, 2143, 5000], 'direct': False, 'generators': [2], 'hall': 5, 'label': '10.1.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '10.1', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.a1.a1', 'solvable': True, 'special_labels': ['D', 'F', 'S', 'L1', 'D1', 'C1', '2.a1.a1.N', '2.a1.a1.M'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_fusion': None, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'sylow': 5, 'weyl_group': '2.1'}
78. label: 10.1.5.a1.a1
    {'abelian': True, 'ambient': '10.1', 'ambient_order': 10, 'ambient_tex': 'D_5', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 20, 'central': False, 'centralizer': '5.a1.a1', 'characteristic': False, 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1'], 'core': '10.a1.a1', 'coset_action_label': '5T2', 'count': 5, 'cyclic': True, 'diagram_aut_x': 2143, 'diagram_x': 7857, 'diagramx': [2143, 7857], 'direct': None, 'generators': [1], 'hall': 2, 'label': '10.1.5.a1.a1', 'maximal': True, 'maximal_normal': False, 'minimal': True, 'minimal_normal': False, 'mobius_quo': None, 'mobius_sub': -1, 'nilpotent': True, 'normal': False, 'normal_closure': '1.a1.a1', 'normalizer': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '10.1', 'proper': True, 'quotient': None, 'quotient_abelian': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': None, 'quotient_fusion': None, 'quotient_order': 5, 'quotient_solvable': None, 'quotient_tex': None, 'short_label': '5.a1.a1', 'solvable': True, 'special_labels': ['5.a1.a1.M'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 2, 'weyl_group': '1.1'}
79. label: 10.1.10.a1.a1
    {'abelian': True, 'ambient': '10.1', 'ambient_order': 10, 'ambient_tex': 'D_5', 'aut_centralizer_order': 20, 'aut_label': '10.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 20, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': [], 'core': '10.a1.a1', 'coset_action_label': '10T2', 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [], 'hall': 1, 'label': '10.1.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 1, 'mobius_sub': 5, 'nilpotent': True, 'normal': True, 'normal_closure': '10.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, 'projective_image': '10.1', 'proper': False, 'quotient': '10.1', 'quotient_abelian': False, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': False, 'quotient_fusion': None, 'quotient_order': 10, 'quotient_solvable': True, 'quotient_tex': 'D_5', 'short_label': '10.a1.a1', 'solvable': True, 'special_labels': ['Z', 'Phi', 'PC', 'U0', 'D2', 'C2', '10.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_fusion': None, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'sylow': 1, 'weyl_group': '1.1'}
80. label: 10.2.1.a1.a1
    {'abelian': True, 'ambient': '10.2', 'ambient_order': 10, 'ambient_tex': 'C_{10}', 'aut_centralizer_order': 1, 'aut_label': '1.a1', 'aut_weyl_group': '4.1', 'aut_weyl_index': 1, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['10.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '5.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [5, 2], 'hall': 10, 'label': '10.2.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 1, 'mobius_sub': 1, 'nilpotent': True, 'normal': True, 'normal_closure': '1.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '1.1', 'proper': False, 'quotient': '1.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 1, 'quotient_solvable': True, 'quotient_tex': 'C_1', 'short_label': '1.a1.a1', 'solvable': True, 'special_labels': ['Z', 'F', 'R', 'S', 'U0', 'L0', 'D0', 'C0', '1.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_fusion': None, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'sylow': 0, 'weyl_group': '1.1'}
81. label: 10.2.2.a1.a1
    {'abelian': True, 'ambient': '10.2', 'ambient_order': 10, 'ambient_tex': 'C_{10}', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_weyl_group': '4.1', 'aut_weyl_index': 1, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['5.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 2143, 'diagram_x': 2143, 'diagramx': [2143, 2143, 2143, 2143], 'direct': True, 'generators': [2], 'hall': 5, 'label': '10.2.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '2.1', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.a1.a1', 'solvable': True, 'special_labels': ['C1', '2.a1.a1.N', '2.a1.a1.M'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_fusion': None, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'sylow': 5, 'weyl_group': '1.1'}
82. label: 10.2.5.a1.a1
    {'abelian': True, 'ambient': '10.2', 'ambient_order': 10, 'ambient_tex': 'C_{10}', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 4, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['2.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1'], 'core': '5.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 7857, 'diagram_x': 7857, 'diagramx': [7857, 7857, 7857, 7857], 'direct': True, 'generators': [5], 'hall': 2, 'label': '10.2.5.a1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '5.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '5.1', 'proper': True, 'quotient': '5.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 5, 'quotient_solvable': True, 'quotient_tex': 'C_5', 'short_label': '5.a1.a1', 'solvable': True, 'special_labels': ['5.a1.a1.N', '5.a1.a1.M'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 2, 'weyl_group': '1.1'}
83. label: 10.2.10.a1.a1
    {'abelian': True, 'ambient': '10.2', 'ambient_order': 10, 'ambient_tex': 'C_{10}', 'aut_centralizer_order': 4, 'aut_label': '10.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 4, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': [], 'core': '10.a1.a1', 'coset_action_label': '10T1', 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [], 'hall': 1, 'label': '10.2.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 1, 'mobius_sub': 1, 'nilpotent': True, 'normal': True, 'normal_closure': '10.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, 'projective_image': '10.2', 'proper': False, 'quotient': '10.2', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 10, 'quotient_solvable': True, 'quotient_tex': 'C_{10}', 'short_label': '10.a1.a1', 'solvable': True, 'special_labels': ['D', 'Phi', 'PC', 'U1', 'L1', 'D1', 'C2', '10.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_fusion': None, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'sylow': 1, 'weyl_group': '1.1'}
84. label: 11.1.1.a1.a1
    {'abelian': True, 'ambient': '11.1', 'ambient_order': 11, 'ambient_tex': 'C_{11}', 'aut_centralizer_order': 1, 'aut_label': '1.a1', 'aut_weyl_group': '10.2', 'aut_weyl_index': 1, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['11.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['11.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [1], 'hall': 11, 'label': '11.1.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': 1, 'nilpotent': True, 'normal': True, 'normal_closure': '1.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '1.1', 'proper': False, 'quotient': '1.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 1, 'quotient_solvable': True, 'quotient_tex': 'C_1', 'short_label': '1.a1.a1', 'solvable': True, 'special_labels': ['Z', 'F', 'R', 'S', 'U0', 'L0', 'D0', 'C0', '1.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_fusion': None, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'sylow': 11, 'weyl_group': '1.1'}
85. label: 11.1.11.a1.a1
    {'abelian': True, 'ambient': '11.1', 'ambient_order': 11, 'ambient_tex': 'C_{11}', 'aut_centralizer_order': 10, 'aut_label': '11.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 10, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': [], 'core': '11.a1.a1', 'coset_action_label': '11T1', 'count': 1, 'cyclic': True, 'diagram_aut_x': 5000, 'diagram_x': 5000, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [], 'hall': 1, 'label': '11.1.11.a1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 1, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '11.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, 'projective_image': '11.1', 'proper': False, 'quotient': '11.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 11, 'quotient_solvable': True, 'quotient_tex': 'C_{11}', 'short_label': '11.a1.a1', 'solvable': True, 'special_labels': ['D', 'Phi', 'PC', 'U1', 'L1', 'D1', 'C1', '11.a1.a1.N', '11.a1.a1.M'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_fusion': None, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'sylow': 1, 'weyl_group': '1.1'}
86. label: 12.1.1.a1.a1
    {'abelian': False, 'ambient': '12.1', 'ambient_order': 12, 'ambient_tex': 'C_3:C_4', 'aut_centralizer_order': 1, 'aut_label': '1.a1', 'aut_weyl_group': '12.4', 'aut_weyl_index': 1, 'central': False, 'centralizer': '6.a1.a1', 'characteristic': True, 'complements': ['12.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': False, 'diagram_aut_x': 6191, 'diagram_x': 6218, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [1, 2, 4], 'hall': 6, 'label': '12.1.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 0, 'mobius_sub': 1, 'nilpotent': False, 'normal': True, 'normal_closure': '1.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '6.1', 'proper': False, 'quotient': '1.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 1, 'quotient_solvable': True, 'quotient_tex': 'C_1', 'short_label': '1.a1.a1', 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0', '1.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_fusion': None, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'sylow': 0, 'weyl_group': '6.1'}
87. label: 12.1.2.a1.a1
    {'abelian': True, 'ambient': '12.1', 'ambient_order': 12, 'ambient_tex': 'C_3:C_4', 'aut_centralizer_order': 6, 'aut_label': '2.a1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 6, 'central': False, 'centralizer': '2.a1.a1', 'characteristic': True, 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 9762, 'diagram_x': 9871, 'diagramx': [7857, 5000, 2143, 5000], 'direct': False, 'generators': [2, 4], 'hall': 0, 'label': '12.1.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 1, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '6.1', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.a1.a1', 'solvable': True, 'special_labels': ['F', 'S', 'C1', '2.a1.a1.N', '2.a1.a1.M'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_fusion': None, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'sylow': 0, 'weyl_group': '2.1'}
88. label: 12.1.3.a1.a1
    {'abelian': True, 'ambient': '12.1', 'ambient_order': 12, 'ambient_tex': 'C_3:C_4', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 6, 'central': False, 'centralizer': '3.a1.a1', 'characteristic': False, 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'cyclic': True, 'diagram_aut_x': 2, 'diagram_x': 2, 'diagramx': [2143, 7857], 'direct': None, 'generators': [1], 'hall': 2, 'label': '12.1.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': None, 'mobius_sub': -1, 'nilpotent': True, 'normal': False, 'normal_closure': '1.a1.a1', 'normalizer': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '6.1', 'proper': True, 'quotient': None, 'quotient_abelian': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': None, 'quotient_fusion': None, 'quotient_order': 3, 'quotient_solvable': None, 'quotient_tex': None, 'short_label': '3.a1.a1', 'solvable': True, 'special_labels': ['3.a1.a1.M'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_fusion': None, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'sylow': 2, 'weyl_group': '1.1'}
89. label: 12.1.4.a1.a1
    {'abelian': True, 'ambient': '12.1', 'ambient_order': 12, 'ambient_tex': 'C_3:C_4', 'aut_centralizer_order': 6, 'aut_label': '4.a1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 6, 'central': False, 'centralizer': '2.a1.a1', 'characteristic': True, 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['12.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 9762, 'diagram_x': 9868, 'diagramx': [7857, 2143, 2143, 2143], 'direct': False, 'generators': [4], 'hall': 3, 'label': '12.1.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': 0, 'nilpotent': True, 'normal': True, 'normal_closure': '4.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '12.1', 'proper': True, 'quotient': '4.1', 'quotient_abelian': True, 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 4, 'quotient_solvable': True, 'quotient_tex': 'C_4', 'short_label': '4.a1.a1', 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C2', '4.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_fusion': None, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'sylow': 3, 'weyl_group': '2.1'}
90. label: 12.1.6.a1.a1
    {'abelian': True, 'ambient': '12.1', 'ambient_order': 12, 'ambient_tex': 'C_3:C_4', 'aut_centralizer_order': 12, 'aut_label': '6.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 12, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 4175, 'diagram_x': 3610, 'diagramx': [2143, 7857, 7857, 7857], 'direct': False, 'generators': [2], 'hall': 0, 'label': '12.1.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': 3, 'nilpotent': True, 'normal': True, 'normal_closure': '6.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '6.1', 'proper': True, 'quotient': '6.1', 'quotient_abelian': False, 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_cyclic': False, 'quotient_fusion': None, 'quotient_order': 6, 'quotient_solvable': True, 'quotient_tex': 'S_3', 'short_label': '6.a1.a1', 'solvable': True, 'special_labels': ['Z', 'Phi', 'U0', '6.a1.a1.N'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 0, 'weyl_group': '1.1'}
91. label: 12.1.12.a1.a1
    {'abelian': True, 'ambient': '12.1', 'ambient_order': 12, 'ambient_tex': 'C_3:C_4', 'aut_centralizer_order': 12, 'aut_label': '12.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 12, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1'], 'contains': [], 'core': '12.a1.a1', 'coset_action_label': '12T5', 'count': 1, 'cyclic': True, 'diagram_aut_x': 6191, 'diagram_x': 6218, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [], 'hall': 1, 'label': '12.1.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 1, 'mobius_sub': 0, 'nilpotent': True, 'normal': True, 'normal_closure': '12.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, 'projective_image': '12.1', 'proper': False, 'quotient': '12.1', 'quotient_abelian': False, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': False, 'quotient_fusion': None, 'quotient_order': 12, 'quotient_solvable': True, 'quotient_tex': 'C_3:C_4', 'short_label': '12.a1.a1', 'solvable': True, 'special_labels': ['PC', 'U1', 'D2', 'C3', '12.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_fusion': None, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'sylow': 1, 'weyl_group': '1.1'}
92. label: 12.2.1.a1.a1
    {'abelian': True, 'ambient': '12.2', 'ambient_order': 12, 'ambient_tex': 'C_{12}', 'aut_centralizer_order': 1, 'aut_label': '1.a1', 'aut_weyl_group': '4.2', 'aut_weyl_index': 1, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['12.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 6207, 'diagram_x': 6257, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [3, 4, 6], 'hall': 6, 'label': '12.2.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 0, 'mobius_sub': 1, 'nilpotent': True, 'normal': True, 'normal_closure': '1.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '1.1', 'proper': False, 'quotient': '1.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 1, 'quotient_solvable': True, 'quotient_tex': 'C_1', 'short_label': '1.a1.a1', 'solvable': True, 'special_labels': ['Z', 'F', 'R', 'U0', 'L0', 'D0', 'C0', '1.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_fusion': None, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'sylow': 0, 'weyl_group': '1.1'}
93. label: 12.2.2.a1.a1
    {'abelian': True, 'ambient': '12.2', 'ambient_order': 12, 'ambient_tex': 'C_{12}', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 2, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 10000, 'diagram_x': 10000, 'diagramx': [7857, 7857, 2143, 2143], 'direct': False, 'generators': [6, 4], 'hall': 0, 'label': '12.2.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 1, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '2.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '2.1', 'proper': True, 'quotient': '2.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 2, 'quotient_solvable': True, 'quotient_tex': 'C_2', 'short_label': '2.a1.a1', 'solvable': True, 'special_labels': ['S', 'C1', '2.a1.a1.N', '2.a1.a1.M'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_fusion': None, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'sylow': 0, 'weyl_group': '1.1'}
94. label: 12.2.3.a1.a1
    {'abelian': True, 'ambient': '12.2', 'ambient_order': 12, 'ambient_tex': 'C_{12}', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 2, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['4.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 2, 'diagram_x': 43, 'diagramx': [2143, 2143, 7857, 7857], 'direct': True, 'generators': [3], 'hall': 2, 'label': '12.2.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 0, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '3.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '3.1', 'proper': True, 'quotient': '3.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 3, 'quotient_solvable': True, 'quotient_tex': 'C_3', 'short_label': '3.a1.a1', 'solvable': True, 'special_labels': ['3.a1.a1.N', '3.a1.a1.M'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_fusion': None, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'sylow': 2, 'weyl_group': '1.1'}
95. label: 12.2.4.a1.a1
    {'abelian': True, 'ambient': '12.2', 'ambient_order': 12, 'ambient_tex': 'C_{12}', 'aut_centralizer_order': 2, 'aut_label': '4.a1', 'aut_weyl_group': '2.1', 'aut_weyl_index': 2, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['12.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 10047, 'diagram_x': 9984, 'diagramx': [7857, 7857, 2143, 2143], 'direct': True, 'generators': [4], 'hall': 3, 'label': '12.2.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': 0, 'nilpotent': True, 'normal': True, 'normal_closure': '4.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '4.1', 'proper': True, 'quotient': '4.1', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 4, 'quotient_solvable': True, 'quotient_tex': 'C_4', 'short_label': '4.a1.a1', 'solvable': True, 'special_labels': ['C2', '4.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_fusion': None, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'sylow': 3, 'weyl_group': '1.1'}
96. label: 12.2.6.a1.a1
    {'abelian': True, 'ambient': '12.2', 'ambient_order': 12, 'ambient_tex': 'C_{12}', 'aut_centralizer_order': 4, 'aut_label': '6.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 4, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': True, 'diagram_aut_x': 3812, 'diagram_x': 3896, 'diagramx': [2143, 2143, 7857, 7857], 'direct': False, 'generators': [6], 'hall': 0, 'label': '12.2.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': True, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': 1, 'nilpotent': True, 'normal': True, 'normal_closure': '6.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '6.2', 'proper': True, 'quotient': '6.2', 'quotient_abelian': True, 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 6, 'quotient_solvable': True, 'quotient_tex': 'C_6', 'short_label': '6.a1.a1', 'solvable': True, 'special_labels': ['Phi', '6.a1.a1.N'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_fusion': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'sylow': 0, 'weyl_group': '1.1'}
97. label: 12.2.12.a1.a1
    {'abelian': True, 'ambient': '12.2', 'ambient_order': 12, 'ambient_tex': 'C_{12}', 'aut_centralizer_order': 4, 'aut_label': '12.a1', 'aut_weyl_group': '1.1', 'aut_weyl_index': 4, 'central': True, 'centralizer': '1.a1.a1', 'characteristic': True, 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1'], 'contains': [], 'core': '12.a1.a1', 'coset_action_label': '12T1', 'count': 1, 'cyclic': True, 'diagram_aut_x': 6207, 'diagram_x': 6257, 'diagramx': [5000, 5000, 5000, 5000], 'direct': True, 'generators': [], 'hall': 1, 'label': '12.2.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 1, 'mobius_sub': 0, 'nilpotent': True, 'normal': True, 'normal_closure': '12.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, 'projective_image': '12.2', 'proper': False, 'quotient': '12.2', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 12, 'quotient_solvable': True, 'quotient_tex': 'C_{12}', 'short_label': '12.a1.a1', 'solvable': True, 'special_labels': ['D', 'PC', 'U1', 'L1', 'D1', 'C3', '12.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_fusion': None, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'sylow': 1, 'weyl_group': '1.1'}
98. label: 12.3.1.a1.a1
    {'abelian': False, 'ambient': '12.3', 'ambient_order': 12, 'ambient_tex': 'A_4', 'aut_centralizer_order': 1, 'aut_label': '1.a1', 'aut_weyl_group': '24.12', 'aut_weyl_index': 1, 'central': False, 'centralizer': '12.a1.a1', 'characteristic': True, 'complements': ['12.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['3.a1.a1', '4.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': False, 'diagram_aut_x': 4922, 'diagram_x': 5078, 'diagramx': [4922, 5000, 5078, 5000], 'direct': True, 'generators': [1, 9, 6], 'hall': 6, 'label': '12.3.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'minimal': False, 'minimal_normal': False, 'mobius_quo': 0, 'mobius_sub': 1, 'nilpotent': False, 'normal': True, 'normal_closure': '1.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '12.3', 'proper': False, 'quotient': '1.1', 'quotient_abelian': True, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 1, 'quotient_solvable': True, 'quotient_tex': 'C_1', 'short_label': '1.a1.a1', 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0', '1.a1.a1.N'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_fusion': None, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'sylow': 0, 'weyl_group': '12.3'}
99. label: 12.3.3.a1.a1
    {'abelian': True, 'ambient': '12.3', 'ambient_order': 12, 'ambient_tex': 'A_4', 'aut_centralizer_order': 4, 'aut_label': '3.a1', 'aut_weyl_group': '6.1', 'aut_weyl_index': 4, 'central': False, 'centralizer': '3.a1.a1', 'characteristic': True, 'complements': ['4.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'cyclic': False, 'diagram_aut_x': 7500, 'diagram_x': 2500, 'diagramx': [7500, 5000, 2500, 5000], 'direct': False, 'generators': [3, 6], 'hall': 2, 'label': '12.3.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'minimal': False, 'minimal_normal': True, 'mobius_quo': -1, 'mobius_sub': -1, 'nilpotent': True, 'normal': True, 'normal_closure': '3.a1.a1', 'normalizer': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'projective_image': '12.3', 'proper': True, 'quotient': '3.1', 'quotient_abelian': True, 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_cyclic': True, 'quotient_fusion': None, 'quotient_order': 3, 'quotient_solvable': True, 'quotient_tex': 'C_3', 'short_label': '3.a1.a1', 'solvable': True, 'special_labels': ['D', 'F', 'S', 'L1', 'D1', 'C1', '3.a1.a1.N', '3.a1.a1.M'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_fusion': None, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'sylow': 2, 'weyl_group': '3.1'}