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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) : Resolvents shown for degrees
Subfields
Degree 2: None
Low degree siblings
4T4, 6T4Siblings 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 | |||||
3A1 | |||||
3A-1 |
Character table
1A | 2A | 3A1 | 3A-1 | ||
Size | 1 | 3 | 4 | 4 | |
2 P | 1A | 1A | 3A-1 | 3A1 | |
3 P | 1A | 2A | 1A | 1A | |
Type | |||||
12.3.1a | R | ||||
12.3.1b1 | C | ||||
12.3.1b2 | C | ||||
12.3.3a | R |
Regular extensions
Data not computed