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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: | no |
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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 3: None
Low degree siblings
15T21, 15T22, 18T146, 30T89, 30T93 x 2, 30T101, 36T554, 45T45Siblings are shown with degree
A number field with this Galois group has exactly one arithmetically equivalent field.
Conjugacy classes
Label | Cycle Type | Size | Order | Index | Representative |
1A | |||||
2A | |||||
2B | |||||
3A | |||||
3B | |||||
3C | |||||
4A | |||||
5A | |||||
6A | |||||
6B | |||||
15A1 | |||||
15A-1 |
Character table
1A | 2A | 2B | 3A | 3B | 3C | 4A | 5A | 6A | 6B | 15A1 | 15A-1 | ||
Size | 1 | 15 | 30 | 2 | 20 | 40 | 90 | 24 | 30 | 60 | 24 | 24 | |
2 P | 1A | 1A | 1A | 3A | 3B | 3C | 2A | 5A | 3A | 3B | 15A1 | 15A-1 | |
3 P | 1A | 2A | 2B | 1A | 1A | 1A | 4A | 5A | 2A | 2B | 5A | 5A | |
5 P | 1A | 2A | 2B | 3A | 3B | 3C | 4A | 1A | 6A | 6B | 3A | 3A | |
Type | |||||||||||||
360.120.1a | R | ||||||||||||
360.120.1b | R | ||||||||||||
360.120.2a | R | ||||||||||||
360.120.4a | R | ||||||||||||
360.120.4b | R | ||||||||||||
360.120.5a | R | ||||||||||||
360.120.5b | R | ||||||||||||
360.120.6a | R | ||||||||||||
360.120.6b1 | C | ||||||||||||
360.120.6b2 | C | ||||||||||||
360.120.8a | R | ||||||||||||
360.120.10a | R |
Regular extensions
Data not computed