Properties

Label 21T35
21T35 1 5 1->5 12 1->12 2 6 2->6 8 2->8 3 7 3->7 11 3->11 4 4->1 14 4->14 5->2 10 5->10 6->3 13 6->13 7->4 9 7->9 8->11 19 8->19 9->12 20 9->20 10->13 21 10->21 11->14 15 11->15 12->8 16 12->16 13->9 17 13->17 14->10 18 14->18 15->6 15->16 16->5 16->17 17->4 17->18 18->3 18->19 19->2 19->20 20->1 20->21 21->7 21->15
Degree 2121
Order 30873087
Cyclic no
Abelian no
Solvable yes
Primitive no
pp-group no
Group: C73:C9C_7^3:C_9

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Copy content magma:G := TransitiveGroup(21, 35);
 

Group invariants

Abstract group:  C73:C9C_7^3:C_9
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Order:  3087=32733087=3^{2} \cdot 7^{3}
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Cyclic:  no
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Abelian:  no
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Solvable:  yes
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Nilpotency class:   not nilpotent
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Group action invariants

Degree nn:  2121
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number tt:  3535
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Parity:  11
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Primitive:  no
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#Aut(F/K)\card{\Aut(F/K)}:  11
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Generators:  (1,12,16,5,10,21,7,9,20)(2,8,19)(3,11,15,6,13,17,4,14,18)(1,12,16,5,10,21,7,9,20)(2,8,19)(3,11,15,6,13,17,4,14,18), (1,5,2,6,3,7,4)(8,11,14,10,13,9,12)(15,16,17,18,19,20,21)(1,5,2,6,3,7,4)(8,11,14,10,13,9,12)(15,16,17,18,19,20,21)
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Low degree resolvents

#(G/N)\card{(G/N)}Galois groups for stem field(s)
33C3C_3
99C9C_9

Resolvents shown for degrees 47\leq 47

Subfields

Degree 3: C3C_3

Degree 7: None

Low degree siblings

21T35 x 18

Siblings are shown with degree 47\leq 47

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

LabelCycle TypeSizeOrderIndexRepresentative
1A 1211^{21} 11 11 00 ()()
3A1 36,133^{6},1^{3} 343343 33 1212 (1,7,5)(3,4,6)(8,12,13)(9,14,10)(15,20,16)(18,19,21)( 1, 7, 5)( 3, 4, 6)( 8,12,13)( 9,14,10)(15,20,16)(18,19,21)
3A-1 36,133^{6},1^{3} 343343 33 1212 (1,5,7)(3,6,4)(8,13,12)(9,10,14)(15,16,20)(18,21,19)( 1, 5, 7)( 3, 6, 4)( 8,13,12)( 9,10,14)(15,16,20)(18,21,19)
7A1 737^{3} 99 77 1818 (1,5,2,6,3,7,4)(8,13,11,9,14,12,10)(15,21,20,19,18,17,16)( 1, 5, 2, 6, 3, 7, 4)( 8,13,11, 9,14,12,10)(15,21,20,19,18,17,16)
7A-1 737^{3} 99 77 1818 (1,6,4,2,7,5,3)(8,9,10,11,12,13,14)(15,19,16,20,17,21,18)( 1, 6, 4, 2, 7, 5, 3)( 8, 9,10,11,12,13,14)(15,19,16,20,17,21,18)
7B1 737^{3} 99 77 1818 (1,4,7,3,6,2,5)(8,11,14,10,13,9,12)(15,17,19,21,16,18,20)( 1, 4, 7, 3, 6, 2, 5)( 8,11,14,10,13, 9,12)(15,17,19,21,16,18,20)
7B-1 737^{3} 99 77 1818 (1,3,5,7,2,4,6)(8,10,12,14,9,11,13)(15,21,20,19,18,17,16)( 1, 3, 5, 7, 2, 4, 6)( 8,10,12,14, 9,11,13)(15,21,20,19,18,17,16)
7C1 72,177^{2},1^{7} 99 77 1212 (1,5,2,6,3,7,4)(15,17,19,21,16,18,20)( 1, 5, 2, 6, 3, 7, 4)(15,17,19,21,16,18,20)
7C-1 72,177^{2},1^{7} 99 77 1212 (1,6,4,2,7,5,3)(15,21,20,19,18,17,16)( 1, 6, 4, 2, 7, 5, 3)(15,21,20,19,18,17,16)
7D1 72,177^{2},1^{7} 99 77 1212 (8,9,10,11,12,13,14)(15,16,17,18,19,20,21)( 8, 9,10,11,12,13,14)(15,16,17,18,19,20,21)
7D-1 72,177^{2},1^{7} 99 77 1212 (8,11,14,10,13,9,12)(15,18,21,17,20,16,19)( 8,11,14,10,13, 9,12)(15,18,21,17,20,16,19)
7E1 737^{3} 99 77 1818 (1,2,3,4,5,6,7)(8,13,11,9,14,12,10)(15,16,17,18,19,20,21)( 1, 2, 3, 4, 5, 6, 7)( 8,13,11, 9,14,12,10)(15,16,17,18,19,20,21)
7E-1 737^{3} 99 77 1818 (1,4,7,3,6,2,5)(8,9,10,11,12,13,14)(15,18,21,17,20,16,19)( 1, 4, 7, 3, 6, 2, 5)( 8, 9,10,11,12,13,14)(15,18,21,17,20,16,19)
7F1 72,177^{2},1^{7} 99 77 1212 (8,11,14,10,13,9,12)(15,19,16,20,17,21,18)( 8,11,14,10,13, 9,12)(15,19,16,20,17,21,18)
7F-1 72,177^{2},1^{7} 99 77 1212 (8,10,12,14,9,11,13)(15,20,18,16,21,19,17)( 8,10,12,14, 9,11,13)(15,20,18,16,21,19,17)
7G1 72,177^{2},1^{7} 99 77 1212 (1,5,2,6,3,7,4)(8,14,13,12,11,10,9)( 1, 5, 2, 6, 3, 7, 4)( 8,14,13,12,11,10, 9)
7G-1 72,177^{2},1^{7} 99 77 1212 (1,7,6,5,4,3,2)(8,10,12,14,9,11,13)( 1, 7, 6, 5, 4, 3, 2)( 8,10,12,14, 9,11,13)
7H1 737^{3} 99 77 1818 (1,4,7,3,6,2,5)(8,12,9,13,10,14,11)(15,18,21,17,20,16,19)( 1, 4, 7, 3, 6, 2, 5)( 8,12, 9,13,10,14,11)(15,18,21,17,20,16,19)
7H-1 737^{3} 99 77 1818 (1,3,5,7,2,4,6)(8,9,10,11,12,13,14)(15,21,20,19,18,17,16)( 1, 3, 5, 7, 2, 4, 6)( 8, 9,10,11,12,13,14)(15,21,20,19,18,17,16)
7I1 72,177^{2},1^{7} 99 77 1212 (1,6,4,2,7,5,3)(8,11,14,10,13,9,12)( 1, 6, 4, 2, 7, 5, 3)( 8,11,14,10,13, 9,12)
7I-1 72,177^{2},1^{7} 99 77 1212 (1,7,6,5,4,3,2)(15,20,18,16,21,19,17)( 1, 7, 6, 5, 4, 3, 2)(15,20,18,16,21,19,17)
7J1 737^{3} 99 77 1818 (1,4,7,3,6,2,5)(8,14,13,12,11,10,9)(15,21,20,19,18,17,16)( 1, 4, 7, 3, 6, 2, 5)( 8,14,13,12,11,10, 9)(15,21,20,19,18,17,16)
7J-1 737^{3} 99 77 1818 (1,2,3,4,5,6,7)(8,10,12,14,9,11,13)(15,17,19,21,16,18,20)( 1, 2, 3, 4, 5, 6, 7)( 8,10,12,14, 9,11,13)(15,17,19,21,16,18,20)
7K1 737^{3} 99 77 1818 (1,6,4,2,7,5,3)(8,13,11,9,14,12,10)(15,18,21,17,20,16,19)( 1, 6, 4, 2, 7, 5, 3)( 8,13,11, 9,14,12,10)(15,18,21,17,20,16,19)
7K-1 737^{3} 99 77 1818 (1,5,2,6,3,7,4)(8,12,9,13,10,14,11)(15,16,17,18,19,20,21)( 1, 5, 2, 6, 3, 7, 4)( 8,12, 9,13,10,14,11)(15,16,17,18,19,20,21)
7L1 737^{3} 99 77 1818 (1,5,2,6,3,7,4)(8,11,14,10,13,9,12)(15,21,20,19,18,17,16)( 1, 5, 2, 6, 3, 7, 4)( 8,11,14,10,13, 9,12)(15,21,20,19,18,17,16)
7L-1 737^{3} 99 77 1818 (1,7,6,5,4,3,2)(8,9,10,11,12,13,14)(15,17,19,21,16,18,20)( 1, 7, 6, 5, 4, 3, 2)( 8, 9,10,11,12,13,14)(15,17,19,21,16,18,20)
7M1 737^{3} 99 77 1818 (1,2,3,4,5,6,7)(8,12,9,13,10,14,11)(15,21,20,19,18,17,16)( 1, 2, 3, 4, 5, 6, 7)( 8,12, 9,13,10,14,11)(15,21,20,19,18,17,16)
7M-1 737^{3} 99 77 1818 (1,4,7,3,6,2,5)(8,13,11,9,14,12,10)(15,19,16,20,17,21,18)( 1, 4, 7, 3, 6, 2, 5)( 8,13,11, 9,14,12,10)(15,19,16,20,17,21,18)
7N1 737^{3} 99 77 1818 (1,3,5,7,2,4,6)(8,13,11,9,14,12,10)(15,20,18,16,21,19,17)( 1, 3, 5, 7, 2, 4, 6)( 8,13,11, 9,14,12,10)(15,20,18,16,21,19,17)
7N-1 737^{3} 99 77 1818 (1,7,6,5,4,3,2)(8,9,10,11,12,13,14)(15,16,17,18,19,20,21)( 1, 7, 6, 5, 4, 3, 2)( 8, 9,10,11,12,13,14)(15,16,17,18,19,20,21)
7O1 737^{3} 99 77 1818 (1,2,3,4,5,6,7)(8,11,14,10,13,9,12)(15,16,17,18,19,20,21)( 1, 2, 3, 4, 5, 6, 7)( 8,11,14,10,13, 9,12)(15,16,17,18,19,20,21)
7O-1 737^{3} 99 77 1818 (1,4,7,3,6,2,5)(8,10,12,14,9,11,13)(15,18,21,17,20,16,19)( 1, 4, 7, 3, 6, 2, 5)( 8,10,12,14, 9,11,13)(15,18,21,17,20,16,19)
7P1 737^{3} 99 77 1818 (1,2,3,4,5,6,7)(8,9,10,11,12,13,14)(15,20,18,16,21,19,17)( 1, 2, 3, 4, 5, 6, 7)( 8, 9,10,11,12,13,14)(15,20,18,16,21,19,17)
7P-1 737^{3} 99 77 1818 (1,2,3,4,5,6,7)(8,9,10,11,12,13,14)(15,19,16,20,17,21,18)( 1, 2, 3, 4, 5, 6, 7)( 8, 9,10,11,12,13,14)(15,19,16,20,17,21,18)
7Q1 7,1147,1^{14} 99 77 66 (1,4,7,3,6,2,5)(1,4,7,3,6,2,5)
7Q-1 7,1147,1^{14} 99 77 66 (8,14,13,12,11,10,9)( 8,14,13,12,11,10, 9)
7R1 737^{3} 99 77 1818 (1,6,4,2,7,5,3)(8,14,13,12,11,10,9)(15,19,16,20,17,21,18)( 1, 6, 4, 2, 7, 5, 3)( 8,14,13,12,11,10, 9)(15,19,16,20,17,21,18)
7R-1 737^{3} 99 77 1818 (1,4,7,3,6,2,5)(8,14,13,12,11,10,9)(15,18,21,17,20,16,19)( 1, 4, 7, 3, 6, 2, 5)( 8,14,13,12,11,10, 9)(15,18,21,17,20,16,19)
7S1 72,177^{2},1^{7} 99 77 1212 (1,2,3,4,5,6,7)(15,18,21,17,20,16,19)( 1, 2, 3, 4, 5, 6, 7)(15,18,21,17,20,16,19)
7S-1 72,177^{2},1^{7} 99 77 1212 (1,4,7,3,6,2,5)(8,12,9,13,10,14,11)( 1, 4, 7, 3, 6, 2, 5)( 8,12, 9,13,10,14,11)
9A1 92,39^{2},3 343343 99 1818 (1,19,8,7,21,12,5,18,13)(2,17,11)(3,15,14,4,20,10,6,16,9)( 1,19, 8, 7,21,12, 5,18,13)( 2,17,11)( 3,15,14, 4,20,10, 6,16, 9)
9A-1 92,39^{2},3 343343 99 1818 (1,13,18,5,12,21,7,8,19)(2,11,17)(3,9,16,6,10,20,4,14,15)( 1,13,18, 5,12,21, 7, 8,19)( 2,11,17)( 3, 9,16, 6,10,20, 4,14,15)
9A2 92,39^{2},3 343343 99 1818 (1,8,21,5,13,19,7,12,18)(2,11,17)(3,14,20,6,9,15,4,10,16)( 1, 8,21, 5,13,19, 7,12,18)( 2,11,17)( 3,14,20, 6, 9,15, 4,10,16)
9A-2 92,39^{2},3 343343 99 1818 (1,18,12,7,19,13,5,21,8)(2,17,11)(3,16,10,4,15,9,6,20,14)( 1,18,12, 7,19,13, 5,21, 8)( 2,17,11)( 3,16,10, 4,15, 9, 6,20,14)
9A4 92,39^{2},3 343343 99 1818 (1,21,13,7,18,8,5,19,12)(2,17,11)(3,20,9,4,16,14,6,15,10)( 1,21,13, 7,18, 8, 5,19,12)( 2,17,11)( 3,20, 9, 4,16,14, 6,15,10)
9A-4 92,39^{2},3 343343 99 1818 (1,12,19,5,8,18,7,13,21)(2,11,17)(3,10,15,6,14,16,4,9,20)( 1,12,19, 5, 8,18, 7,13,21)( 2,11,17)( 3,10,15, 6,14,16, 4, 9,20)

Malle's constant a(G)a(G):     1/61/6

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Character table

47 x 47 character table

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Regular extensions

Data not computed