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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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Parity: |
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Primitive: | yes |
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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 5: None
Low degree siblings
15T17 x 2, 30T71 x 2Siblings 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 | |||||
4A1 | |||||
4A-1 | |||||
5A | |||||
5B | |||||
6A |
Character table
1A | 2A | 3A | 4A1 | 4A-1 | 5A | 5B | 6A | ||
Size | 1 | 25 | 50 | 75 | 75 | 12 | 12 | 50 | |
2 P | 1A | 1A | 3A | 2A | 2A | 5A | 5B | 3A | |
3 P | 1A | 2A | 1A | 4A-1 | 4A1 | 5A | 5B | 2A | |
5 P | 1A | 2A | 3A | 4A1 | 4A-1 | 1A | 1A | 6A | |
Type | |||||||||
300.23.1a | R | ||||||||
300.23.1b | R | ||||||||
300.23.1c1 | C | ||||||||
300.23.1c2 | C | ||||||||
300.23.2a | R | ||||||||
300.23.2b | S | ||||||||
300.23.12a | R | ||||||||
300.23.12b | R |
Regular extensions
Data not computed