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Group invariants
Abstract group: |
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Order: |
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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 : |
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Transitive number : |
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CHM label: | |||
Parity: |
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Primitive: | no |
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: |
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Generators: | , , , |
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Low degree resolvents
Galois groups for stem field(s) : x 3 : : Resolvents shown for degrees
Subfields
Degree 3: None
Degree 6: None
Low degree siblings
9T14, 18T35 x 3, 24T82, 36T55Siblings are shown with degree
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
Label | Cycle Type | Size | Order | Index | Representative |
1A | |||||
2A | |||||
3A | |||||
4A | |||||
4B | |||||
4C |
Character table
1A | 2A | 3A | 4A | 4B | 4C | ||
Size | 1 | 9 | 8 | 18 | 18 | 18 | |
2 P | 1A | 1A | 3A | 2A | 2A | 2A | |
3 P | 1A | 2A | 1A | 4A | 4B | 4C | |
Type | |||||||
72.41.1a | R | ||||||
72.41.1b | R | ||||||
72.41.1c | R | ||||||
72.41.1d | R | ||||||
72.41.2a | S | ||||||
72.41.8a | R |
Regular extensions
Data not computed
Additional information
This is an elusive group.