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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 2: None
Low degree siblings
16T1081, 20T172, 20T177, 30T214, 30T217, 40T888, 40T889, 40T932, 40T942, 40T944, 40T945Siblings 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 | |||||
2B | |||||
2C | |||||
3A | |||||
4A | |||||
4B | |||||
5A1 | |||||
5A2 | |||||
6A | |||||
6B1 | |||||
6B-1 |
Character table
1A | 2A | 2B | 2C | 3A | 4A | 4B | 5A1 | 5A2 | 6A | 6B1 | 6B-1 | ||
Size | 1 | 5 | 10 | 60 | 80 | 60 | 120 | 192 | 192 | 80 | 80 | 80 | |
2 P | 1A | 1A | 1A | 1A | 3A | 2A | 2B | 5A2 | 5A1 | 3A | 3A | 3A | |
3 P | 1A | 2A | 2B | 2C | 1A | 4A | 4B | 5A2 | 5A1 | 2B | 2A | 2A | |
5 P | 1A | 2A | 2B | 2C | 3A | 4A | 4B | 1A | 1A | 6A | 6B-1 | 6B1 | |
Type | |||||||||||||
960.11358.1a | R | ||||||||||||
960.11358.3a1 | R | ||||||||||||
960.11358.3a2 | R | ||||||||||||
960.11358.4a | R | ||||||||||||
960.11358.5a | R | ||||||||||||
960.11358.5b | R | ||||||||||||
960.11358.5c1 | C | ||||||||||||
960.11358.5c2 | C | ||||||||||||
960.11358.10a | R | ||||||||||||
960.11358.10b | R | ||||||||||||
960.11358.15a | R | ||||||||||||
960.11358.20a | R |
Regular extensions
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