metacyclic, supersoluble, monomial, A-group
Aliases: C39⋊3C12, C78.1C6, Dic39⋊C3, C6.(C13⋊C6), C26.(C3×S3), C3⋊(C26.C6), C2.(D39⋊C3), C13⋊C3⋊2Dic3, C13⋊2(C3×Dic3), (C3×C13⋊C3)⋊3C4, (C2×C13⋊C3).S3, (C6×C13⋊C3).1C2, SmallGroup(468,21)
Series: Derived ►Chief ►Lower central ►Upper central
| C39 — C39⋊3C12 |
Generators and relations for C39⋊3C12
G = < a,b | a39=b12=1, bab-1=a17 >
Character table of C39⋊3C12
| class | 1 | 2 | 3A | 3B | 3C | 3D | 3E | 4A | 4B | 6A | 6B | 6C | 6D | 6E | 12A | 12B | 12C | 12D | 13A | 13B | 26A | 26B | 39A | 39B | 39C | 39D | 78A | 78B | 78C | 78D | |
| size | 1 | 1 | 2 | 13 | 13 | 26 | 26 | 39 | 39 | 2 | 13 | 13 | 26 | 26 | 39 | 39 | 39 | 39 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | |
| ρ1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | trivial |
| ρ2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 2 |
| ρ3 | 1 | 1 | 1 | ζ32 | ζ3 | ζ32 | ζ3 | -1 | -1 | 1 | ζ3 | ζ32 | ζ32 | ζ3 | ζ65 | ζ6 | ζ65 | ζ6 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 6 |
| ρ4 | 1 | 1 | 1 | ζ32 | ζ3 | ζ32 | ζ3 | 1 | 1 | 1 | ζ3 | ζ32 | ζ32 | ζ3 | ζ3 | ζ32 | ζ3 | ζ32 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 3 |
| ρ5 | 1 | 1 | 1 | ζ3 | ζ32 | ζ3 | ζ32 | -1 | -1 | 1 | ζ32 | ζ3 | ζ3 | ζ32 | ζ6 | ζ65 | ζ6 | ζ65 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 6 |
| ρ6 | 1 | 1 | 1 | ζ3 | ζ32 | ζ3 | ζ32 | 1 | 1 | 1 | ζ32 | ζ3 | ζ3 | ζ32 | ζ32 | ζ3 | ζ32 | ζ3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 3 |
| ρ7 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | i | -i | -1 | -1 | -1 | -1 | -1 | i | i | -i | -i | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | linear of order 4 |
| ρ8 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | -i | i | -1 | -1 | -1 | -1 | -1 | -i | -i | i | i | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | linear of order 4 |
| ρ9 | 1 | -1 | 1 | ζ32 | ζ3 | ζ32 | ζ3 | -i | i | -1 | ζ65 | ζ6 | ζ6 | ζ65 | ζ43ζ3 | ζ43ζ32 | ζ4ζ3 | ζ4ζ32 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | linear of order 12 |
| ρ10 | 1 | -1 | 1 | ζ32 | ζ3 | ζ32 | ζ3 | i | -i | -1 | ζ65 | ζ6 | ζ6 | ζ65 | ζ4ζ3 | ζ4ζ32 | ζ43ζ3 | ζ43ζ32 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | linear of order 12 |
| ρ11 | 1 | -1 | 1 | ζ3 | ζ32 | ζ3 | ζ32 | -i | i | -1 | ζ6 | ζ65 | ζ65 | ζ6 | ζ43ζ32 | ζ43ζ3 | ζ4ζ32 | ζ4ζ3 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | linear of order 12 |
| ρ12 | 1 | -1 | 1 | ζ3 | ζ32 | ζ3 | ζ32 | i | -i | -1 | ζ6 | ζ65 | ζ65 | ζ6 | ζ4ζ32 | ζ4ζ3 | ζ43ζ32 | ζ43ζ3 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | linear of order 12 |
| ρ13 | 2 | 2 | -1 | 2 | 2 | -1 | -1 | 0 | 0 | -1 | 2 | 2 | -1 | -1 | 0 | 0 | 0 | 0 | 2 | 2 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | orthogonal lifted from S3 |
| ρ14 | 2 | -2 | -1 | 2 | 2 | -1 | -1 | 0 | 0 | 1 | -2 | -2 | 1 | 1 | 0 | 0 | 0 | 0 | 2 | 2 | -2 | -2 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | symplectic lifted from Dic3, Schur index 2 |
| ρ15 | 2 | -2 | -1 | -1-√-3 | -1+√-3 | ζ6 | ζ65 | 0 | 0 | 1 | 1-√-3 | 1+√-3 | ζ32 | ζ3 | 0 | 0 | 0 | 0 | 2 | 2 | -2 | -2 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | complex lifted from C3×Dic3 |
| ρ16 | 2 | 2 | -1 | -1+√-3 | -1-√-3 | ζ65 | ζ6 | 0 | 0 | -1 | -1-√-3 | -1+√-3 | ζ65 | ζ6 | 0 | 0 | 0 | 0 | 2 | 2 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | complex lifted from C3×S3 |
| ρ17 | 2 | -2 | -1 | -1+√-3 | -1-√-3 | ζ65 | ζ6 | 0 | 0 | 1 | 1+√-3 | 1-√-3 | ζ3 | ζ32 | 0 | 0 | 0 | 0 | 2 | 2 | -2 | -2 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | complex lifted from C3×Dic3 |
| ρ18 | 2 | 2 | -1 | -1-√-3 | -1+√-3 | ζ6 | ζ65 | 0 | 0 | -1 | -1+√-3 | -1-√-3 | ζ6 | ζ65 | 0 | 0 | 0 | 0 | 2 | 2 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | complex lifted from C3×S3 |
| ρ19 | 6 | 6 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1+√13/2 | -1-√13/2 | -1+√13/2 | -1-√13/2 | -1+√13/2 | -1-√13/2 | -1+√13/2 | -1-√13/2 | -1+√13/2 | -1-√13/2 | -1+√13/2 | -1-√13/2 | orthogonal lifted from C13⋊C6 |
| ρ20 | 6 | 6 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1+√13/2 | -1-√13/2 | -1+√13/2 | -1-√13/2 | ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13-ζ139-ζ133-ζ13 | -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132-ζ1311-ζ138-ζ137 | -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13-ζ1312-ζ1310-ζ134 | ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132-ζ136-ζ135-ζ132 | ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13-ζ139-ζ133-ζ13 | -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132-ζ1311-ζ138-ζ137 | -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13-ζ1312-ζ1310-ζ134 | ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132-ζ136-ζ135-ζ132 | orthogonal lifted from D39⋊C3 |
| ρ21 | 6 | 6 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1-√13/2 | -1+√13/2 | -1-√13/2 | -1+√13/2 | -1-√13/2 | -1+√13/2 | -1-√13/2 | -1+√13/2 | -1-√13/2 | -1+√13/2 | -1-√13/2 | -1+√13/2 | orthogonal lifted from C13⋊C6 |
| ρ22 | 6 | 6 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1-√13/2 | -1+√13/2 | -1-√13/2 | -1+√13/2 | -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132-ζ1311-ζ138-ζ137 | -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13-ζ1312-ζ1310-ζ134 | ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132-ζ136-ζ135-ζ132 | ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13-ζ139-ζ133-ζ13 | -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132-ζ1311-ζ138-ζ137 | -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13-ζ1312-ζ1310-ζ134 | ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132-ζ136-ζ135-ζ132 | ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13-ζ139-ζ133-ζ13 | orthogonal lifted from D39⋊C3 |
| ρ23 | 6 | 6 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1-√13/2 | -1+√13/2 | -1-√13/2 | -1+√13/2 | ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132-ζ136-ζ135-ζ132 | ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13-ζ139-ζ133-ζ13 | -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132-ζ1311-ζ138-ζ137 | -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13-ζ1312-ζ1310-ζ134 | ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132-ζ136-ζ135-ζ132 | ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13-ζ139-ζ133-ζ13 | -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132-ζ1311-ζ138-ζ137 | -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13-ζ1312-ζ1310-ζ134 | orthogonal lifted from D39⋊C3 |
| ρ24 | 6 | 6 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1+√13/2 | -1-√13/2 | -1+√13/2 | -1-√13/2 | -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13-ζ1312-ζ1310-ζ134 | ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132-ζ136-ζ135-ζ132 | ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13-ζ139-ζ133-ζ13 | -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132-ζ1311-ζ138-ζ137 | -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13-ζ1312-ζ1310-ζ134 | ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132-ζ136-ζ135-ζ132 | ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13-ζ139-ζ133-ζ13 | -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132-ζ1311-ζ138-ζ137 | orthogonal lifted from D39⋊C3 |
| ρ25 | 6 | -6 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1+√13/2 | -1-√13/2 | 1-√13/2 | 1+√13/2 | ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13-ζ139-ζ133-ζ13 | -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132-ζ1311-ζ138-ζ137 | -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13-ζ1312-ζ1310-ζ134 | ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132-ζ136-ζ135-ζ132 | -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13+ζ139+ζ133+ζ13 | ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132+ζ1311+ζ138+ζ137 | ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13+ζ1312+ζ1310+ζ134 | -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132+ζ136+ζ135+ζ132 | symplectic faithful, Schur index 2 |
| ρ26 | 6 | -6 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | -6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1-√13/2 | -1+√13/2 | 1+√13/2 | 1-√13/2 | -1-√13/2 | -1+√13/2 | -1-√13/2 | -1+√13/2 | 1+√13/2 | 1-√13/2 | 1+√13/2 | 1-√13/2 | symplectic lifted from C26.C6, Schur index 2 |
| ρ27 | 6 | -6 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | -6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1+√13/2 | -1-√13/2 | 1-√13/2 | 1+√13/2 | -1+√13/2 | -1-√13/2 | -1+√13/2 | -1-√13/2 | 1-√13/2 | 1+√13/2 | 1-√13/2 | 1+√13/2 | symplectic lifted from C26.C6, Schur index 2 |
| ρ28 | 6 | -6 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1+√13/2 | -1-√13/2 | 1-√13/2 | 1+√13/2 | -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13-ζ1312-ζ1310-ζ134 | ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132-ζ136-ζ135-ζ132 | ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13-ζ139-ζ133-ζ13 | -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132-ζ1311-ζ138-ζ137 | ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13+ζ1312+ζ1310+ζ134 | -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132+ζ136+ζ135+ζ132 | -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13+ζ139+ζ133+ζ13 | ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132+ζ1311+ζ138+ζ137 | symplectic faithful, Schur index 2 |
| ρ29 | 6 | -6 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1-√13/2 | -1+√13/2 | 1+√13/2 | 1-√13/2 | ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132-ζ136-ζ135-ζ132 | ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13-ζ139-ζ133-ζ13 | -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132-ζ1311-ζ138-ζ137 | -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13-ζ1312-ζ1310-ζ134 | -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132+ζ136+ζ135+ζ132 | -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13+ζ139+ζ133+ζ13 | ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132+ζ1311+ζ138+ζ137 | ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13+ζ1312+ζ1310+ζ134 | symplectic faithful, Schur index 2 |
| ρ30 | 6 | -6 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1-√13/2 | -1+√13/2 | 1+√13/2 | 1-√13/2 | -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132-ζ1311-ζ138-ζ137 | -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13-ζ1312-ζ1310-ζ134 | ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132-ζ136-ζ135-ζ132 | ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13-ζ139-ζ133-ζ13 | ζ3ζ1311+ζ3ζ138+ζ3ζ137-ζ3ζ136-ζ3ζ135-ζ3ζ132+ζ1311+ζ138+ζ137 | ζ32ζ1312+ζ32ζ1310-ζ32ζ139+ζ32ζ134-ζ32ζ133-ζ32ζ13+ζ1312+ζ1310+ζ134 | -ζ3ζ1311-ζ3ζ138-ζ3ζ137+ζ3ζ136+ζ3ζ135+ζ3ζ132+ζ136+ζ135+ζ132 | -ζ32ζ1312-ζ32ζ1310+ζ32ζ139-ζ32ζ134+ζ32ζ133+ζ32ζ13+ζ139+ζ133+ζ13 | symplectic faithful, Schur index 2 |
►On 156 points
Generators in S156
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39)(40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78)(79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117)(118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156)
(1 137 49 104)(2 121 71 103 17 154 50 88 23 136 65 82)(3 144 54 102 33 132 51 111 6 135 42 99)(4 128 76 101 10 149 52 95 28 134 58 116)(5 151 59 100 26 127 53 79 11 133 74 94)(7 119 64 98 19 122 55 86 16 131 67 89)(8 142 47 97 35 139 56 109 38 130 44 106)(9 126 69 96 12 156 57 93 21 129 60 84)(13 140 40 92 37 146 61 107 31 125 46 113)(14 124 62 91)(15 147 45 90 30 141 63 114 36 123 78 108)(18 138 72 87 39 153 66 105 24 120 48 81)(20 145 77 85 32 148 68 112 29 118 41 115)(22 152 43 83 25 143 70 80 34 155 73 110)(27 150 75 117)
G:=sub<Sym(156)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39)(40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78)(79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117)(118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156), (1,137,49,104)(2,121,71,103,17,154,50,88,23,136,65,82)(3,144,54,102,33,132,51,111,6,135,42,99)(4,128,76,101,10,149,52,95,28,134,58,116)(5,151,59,100,26,127,53,79,11,133,74,94)(7,119,64,98,19,122,55,86,16,131,67,89)(8,142,47,97,35,139,56,109,38,130,44,106)(9,126,69,96,12,156,57,93,21,129,60,84)(13,140,40,92,37,146,61,107,31,125,46,113)(14,124,62,91)(15,147,45,90,30,141,63,114,36,123,78,108)(18,138,72,87,39,153,66,105,24,120,48,81)(20,145,77,85,32,148,68,112,29,118,41,115)(22,152,43,83,25,143,70,80,34,155,73,110)(27,150,75,117)>;
G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39)(40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78)(79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117)(118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156), (1,137,49,104)(2,121,71,103,17,154,50,88,23,136,65,82)(3,144,54,102,33,132,51,111,6,135,42,99)(4,128,76,101,10,149,52,95,28,134,58,116)(5,151,59,100,26,127,53,79,11,133,74,94)(7,119,64,98,19,122,55,86,16,131,67,89)(8,142,47,97,35,139,56,109,38,130,44,106)(9,126,69,96,12,156,57,93,21,129,60,84)(13,140,40,92,37,146,61,107,31,125,46,113)(14,124,62,91)(15,147,45,90,30,141,63,114,36,123,78,108)(18,138,72,87,39,153,66,105,24,120,48,81)(20,145,77,85,32,148,68,112,29,118,41,115)(22,152,43,83,25,143,70,80,34,155,73,110)(27,150,75,117) );
G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39),(40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78),(79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117),(118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156)], [(1,137,49,104),(2,121,71,103,17,154,50,88,23,136,65,82),(3,144,54,102,33,132,51,111,6,135,42,99),(4,128,76,101,10,149,52,95,28,134,58,116),(5,151,59,100,26,127,53,79,11,133,74,94),(7,119,64,98,19,122,55,86,16,131,67,89),(8,142,47,97,35,139,56,109,38,130,44,106),(9,126,69,96,12,156,57,93,21,129,60,84),(13,140,40,92,37,146,61,107,31,125,46,113),(14,124,62,91),(15,147,45,90,30,141,63,114,36,123,78,108),(18,138,72,87,39,153,66,105,24,120,48,81),(20,145,77,85,32,148,68,112,29,118,41,115),(22,152,43,83,25,143,70,80,34,155,73,110),(27,150,75,117)]])
Matrix representation of C39⋊3C12 ►in GL8(𝔽157)
| 130 | 52 | 0 | 0 | 0 | 0 | 0 | 0 |
| 68 | 26 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 70 | 138 | 69 | 69 | 138 | 70 |
| 0 | 0 | 87 | 20 | 155 | 89 | 86 | 88 |
| 0 | 0 | 69 | 69 | 1 | 68 | 70 | 68 |
| 0 | 0 | 89 | 155 | 90 | 155 | 89 | 156 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 50 | 99 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 107 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 148 | 113 | 35 | 69 | 35 |
| 0 | 0 | 113 | 35 | 34 | 79 | 88 | 35 |
| 0 | 0 | 146 | 73 | 8 | 40 | 154 | 92 |
| 0 | 0 | 96 | 93 | 150 | 49 | 140 | 147 |
| 0 | 0 | 44 | 122 | 44 | 19 | 44 | 44 |
| 0 | 0 | 36 | 30 | 149 | 19 | 55 | 11 |
G:=sub<GL(8,GF(157))| [130,68,0,0,0,0,0,0,52,26,0,0,0,0,0,0,0,0,70,87,69,89,1,0,0,0,138,20,69,155,0,1,0,0,69,155,1,90,0,0,0,0,69,89,68,155,0,0,0,0,138,86,70,89,0,0,0,0,70,88,68,156,0,0],[50,0,0,0,0,0,0,0,99,107,0,0,0,0,0,0,0,0,10,113,146,96,44,36,0,0,148,35,73,93,122,30,0,0,113,34,8,150,44,149,0,0,35,79,40,49,19,19,0,0,69,88,154,140,44,55,0,0,35,35,92,147,44,11] >;
C39⋊3C12 in GAP, Magma, Sage, TeX
C_{39}\rtimes_3C_{12} % in TeX
G:=Group("C39:3C12"); // GroupNames label
G:=SmallGroup(468,21);
// by ID
G=gap.SmallGroup(468,21);
# by ID
G:=PCGroup([5,-2,-3,-2,-3,-13,30,483,10804,1359]);
// Polycyclic
G:=Group<a,b|a^39=b^12=1,b*a*b^-1=a^17>;
// generators/relations
Export
Subgroup lattice of C39⋊3C12 in TeX
Character table of C39⋊3C12 in TeX