metacyclic, supersoluble, monomial, 2-hyperelementary
Aliases: Dic26, C13⋊Q8, C4.D13, C52.1C2, C2.3D26, C26.1C22, Dic13.1C2, SmallGroup(104,4)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic26
G = < a,b | a52=1, b2=a26, bab-1=a-1 >
Character table of Dic26
| class | 1 | 2 | 4A | 4B | 4C | 13A | 13B | 13C | 13D | 13E | 13F | 26A | 26B | 26C | 26D | 26E | 26F | 52A | 52B | 52C | 52D | 52E | 52F | 52G | 52H | 52I | 52J | 52K | 52L | |
| size | 1 | 1 | 2 | 26 | 26 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | |
| 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 | 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 | linear of order 2 |
| ρ3 | 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 |
| ρ4 | 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 |
| ρ5 | 2 | 2 | -2 | 0 | 0 | ζ1311+ζ132 | ζ139+ζ134 | ζ138+ζ135 | ζ1310+ζ133 | ζ137+ζ136 | ζ1312+ζ13 | ζ137+ζ136 | ζ1312+ζ13 | ζ139+ζ134 | ζ138+ζ135 | ζ1310+ζ133 | ζ1311+ζ132 | -ζ1311-ζ132 | -ζ137-ζ136 | -ζ1312-ζ13 | -ζ139-ζ134 | -ζ139-ζ134 | -ζ1312-ζ13 | -ζ137-ζ136 | -ζ1311-ζ132 | -ζ1310-ζ133 | -ζ138-ζ135 | -ζ138-ζ135 | -ζ1310-ζ133 | orthogonal lifted from D26 |
| ρ6 | 2 | 2 | 2 | 0 | 0 | ζ139+ζ134 | ζ138+ζ135 | ζ1310+ζ133 | ζ137+ζ136 | ζ1312+ζ13 | ζ1311+ζ132 | ζ1312+ζ13 | ζ1311+ζ132 | ζ138+ζ135 | ζ1310+ζ133 | ζ137+ζ136 | ζ139+ζ134 | ζ139+ζ134 | ζ1312+ζ13 | ζ1311+ζ132 | ζ138+ζ135 | ζ138+ζ135 | ζ1311+ζ132 | ζ1312+ζ13 | ζ139+ζ134 | ζ137+ζ136 | ζ1310+ζ133 | ζ1310+ζ133 | ζ137+ζ136 | orthogonal lifted from D13 |
| ρ7 | 2 | 2 | -2 | 0 | 0 | ζ1310+ζ133 | ζ137+ζ136 | ζ1312+ζ13 | ζ1311+ζ132 | ζ139+ζ134 | ζ138+ζ135 | ζ139+ζ134 | ζ138+ζ135 | ζ137+ζ136 | ζ1312+ζ13 | ζ1311+ζ132 | ζ1310+ζ133 | -ζ1310-ζ133 | -ζ139-ζ134 | -ζ138-ζ135 | -ζ137-ζ136 | -ζ137-ζ136 | -ζ138-ζ135 | -ζ139-ζ134 | -ζ1310-ζ133 | -ζ1311-ζ132 | -ζ1312-ζ13 | -ζ1312-ζ13 | -ζ1311-ζ132 | orthogonal lifted from D26 |
| ρ8 | 2 | 2 | 2 | 0 | 0 | ζ1311+ζ132 | ζ139+ζ134 | ζ138+ζ135 | ζ1310+ζ133 | ζ137+ζ136 | ζ1312+ζ13 | ζ137+ζ136 | ζ1312+ζ13 | ζ139+ζ134 | ζ138+ζ135 | ζ1310+ζ133 | ζ1311+ζ132 | ζ1311+ζ132 | ζ137+ζ136 | ζ1312+ζ13 | ζ139+ζ134 | ζ139+ζ134 | ζ1312+ζ13 | ζ137+ζ136 | ζ1311+ζ132 | ζ1310+ζ133 | ζ138+ζ135 | ζ138+ζ135 | ζ1310+ζ133 | orthogonal lifted from D13 |
| ρ9 | 2 | 2 | -2 | 0 | 0 | ζ139+ζ134 | ζ138+ζ135 | ζ1310+ζ133 | ζ137+ζ136 | ζ1312+ζ13 | ζ1311+ζ132 | ζ1312+ζ13 | ζ1311+ζ132 | ζ138+ζ135 | ζ1310+ζ133 | ζ137+ζ136 | ζ139+ζ134 | -ζ139-ζ134 | -ζ1312-ζ13 | -ζ1311-ζ132 | -ζ138-ζ135 | -ζ138-ζ135 | -ζ1311-ζ132 | -ζ1312-ζ13 | -ζ139-ζ134 | -ζ137-ζ136 | -ζ1310-ζ133 | -ζ1310-ζ133 | -ζ137-ζ136 | orthogonal lifted from D26 |
| ρ10 | 2 | 2 | -2 | 0 | 0 | ζ1312+ζ13 | ζ1311+ζ132 | ζ139+ζ134 | ζ138+ζ135 | ζ1310+ζ133 | ζ137+ζ136 | ζ1310+ζ133 | ζ137+ζ136 | ζ1311+ζ132 | ζ139+ζ134 | ζ138+ζ135 | ζ1312+ζ13 | -ζ1312-ζ13 | -ζ1310-ζ133 | -ζ137-ζ136 | -ζ1311-ζ132 | -ζ1311-ζ132 | -ζ137-ζ136 | -ζ1310-ζ133 | -ζ1312-ζ13 | -ζ138-ζ135 | -ζ139-ζ134 | -ζ139-ζ134 | -ζ138-ζ135 | orthogonal lifted from D26 |
| ρ11 | 2 | 2 | -2 | 0 | 0 | ζ137+ζ136 | ζ1312+ζ13 | ζ1311+ζ132 | ζ139+ζ134 | ζ138+ζ135 | ζ1310+ζ133 | ζ138+ζ135 | ζ1310+ζ133 | ζ1312+ζ13 | ζ1311+ζ132 | ζ139+ζ134 | ζ137+ζ136 | -ζ137-ζ136 | -ζ138-ζ135 | -ζ1310-ζ133 | -ζ1312-ζ13 | -ζ1312-ζ13 | -ζ1310-ζ133 | -ζ138-ζ135 | -ζ137-ζ136 | -ζ139-ζ134 | -ζ1311-ζ132 | -ζ1311-ζ132 | -ζ139-ζ134 | orthogonal lifted from D26 |
| ρ12 | 2 | 2 | 2 | 0 | 0 | ζ1312+ζ13 | ζ1311+ζ132 | ζ139+ζ134 | ζ138+ζ135 | ζ1310+ζ133 | ζ137+ζ136 | ζ1310+ζ133 | ζ137+ζ136 | ζ1311+ζ132 | ζ139+ζ134 | ζ138+ζ135 | ζ1312+ζ13 | ζ1312+ζ13 | ζ1310+ζ133 | ζ137+ζ136 | ζ1311+ζ132 | ζ1311+ζ132 | ζ137+ζ136 | ζ1310+ζ133 | ζ1312+ζ13 | ζ138+ζ135 | ζ139+ζ134 | ζ139+ζ134 | ζ138+ζ135 | orthogonal lifted from D13 |
| ρ13 | 2 | 2 | 2 | 0 | 0 | ζ137+ζ136 | ζ1312+ζ13 | ζ1311+ζ132 | ζ139+ζ134 | ζ138+ζ135 | ζ1310+ζ133 | ζ138+ζ135 | ζ1310+ζ133 | ζ1312+ζ13 | ζ1311+ζ132 | ζ139+ζ134 | ζ137+ζ136 | ζ137+ζ136 | ζ138+ζ135 | ζ1310+ζ133 | ζ1312+ζ13 | ζ1312+ζ13 | ζ1310+ζ133 | ζ138+ζ135 | ζ137+ζ136 | ζ139+ζ134 | ζ1311+ζ132 | ζ1311+ζ132 | ζ139+ζ134 | orthogonal lifted from D13 |
| ρ14 | 2 | 2 | 2 | 0 | 0 | ζ138+ζ135 | ζ1310+ζ133 | ζ137+ζ136 | ζ1312+ζ13 | ζ1311+ζ132 | ζ139+ζ134 | ζ1311+ζ132 | ζ139+ζ134 | ζ1310+ζ133 | ζ137+ζ136 | ζ1312+ζ13 | ζ138+ζ135 | ζ138+ζ135 | ζ1311+ζ132 | ζ139+ζ134 | ζ1310+ζ133 | ζ1310+ζ133 | ζ139+ζ134 | ζ1311+ζ132 | ζ138+ζ135 | ζ1312+ζ13 | ζ137+ζ136 | ζ137+ζ136 | ζ1312+ζ13 | orthogonal lifted from D13 |
| ρ15 | 2 | 2 | 2 | 0 | 0 | ζ1310+ζ133 | ζ137+ζ136 | ζ1312+ζ13 | ζ1311+ζ132 | ζ139+ζ134 | ζ138+ζ135 | ζ139+ζ134 | ζ138+ζ135 | ζ137+ζ136 | ζ1312+ζ13 | ζ1311+ζ132 | ζ1310+ζ133 | ζ1310+ζ133 | ζ139+ζ134 | ζ138+ζ135 | ζ137+ζ136 | ζ137+ζ136 | ζ138+ζ135 | ζ139+ζ134 | ζ1310+ζ133 | ζ1311+ζ132 | ζ1312+ζ13 | ζ1312+ζ13 | ζ1311+ζ132 | orthogonal lifted from D13 |
| ρ16 | 2 | 2 | -2 | 0 | 0 | ζ138+ζ135 | ζ1310+ζ133 | ζ137+ζ136 | ζ1312+ζ13 | ζ1311+ζ132 | ζ139+ζ134 | ζ1311+ζ132 | ζ139+ζ134 | ζ1310+ζ133 | ζ137+ζ136 | ζ1312+ζ13 | ζ138+ζ135 | -ζ138-ζ135 | -ζ1311-ζ132 | -ζ139-ζ134 | -ζ1310-ζ133 | -ζ1310-ζ133 | -ζ139-ζ134 | -ζ1311-ζ132 | -ζ138-ζ135 | -ζ1312-ζ13 | -ζ137-ζ136 | -ζ137-ζ136 | -ζ1312-ζ13 | orthogonal lifted from D26 |
| ρ17 | 2 | -2 | 0 | 0 | 0 | 2 | 2 | 2 | 2 | 2 | 2 | -2 | -2 | -2 | -2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from Q8, Schur index 2 |
| ρ18 | 2 | -2 | 0 | 0 | 0 | ζ1310+ζ133 | ζ137+ζ136 | ζ1312+ζ13 | ζ1311+ζ132 | ζ139+ζ134 | ζ138+ζ135 | -ζ139-ζ134 | -ζ138-ζ135 | -ζ137-ζ136 | -ζ1312-ζ13 | -ζ1311-ζ132 | -ζ1310-ζ133 | -ζ4ζ1310+ζ4ζ133 | ζ43ζ139-ζ43ζ134 | ζ43ζ138-ζ43ζ135 | ζ43ζ137-ζ43ζ136 | -ζ43ζ137+ζ43ζ136 | -ζ43ζ138+ζ43ζ135 | -ζ43ζ139+ζ43ζ134 | ζ4ζ1310-ζ4ζ133 | ζ4ζ1311-ζ4ζ132 | ζ4ζ1312-ζ4ζ13 | -ζ4ζ1312+ζ4ζ13 | -ζ4ζ1311+ζ4ζ132 | symplectic faithful, Schur index 2 |
| ρ19 | 2 | -2 | 0 | 0 | 0 | ζ139+ζ134 | ζ138+ζ135 | ζ1310+ζ133 | ζ137+ζ136 | ζ1312+ζ13 | ζ1311+ζ132 | -ζ1312-ζ13 | -ζ1311-ζ132 | -ζ138-ζ135 | -ζ1310-ζ133 | -ζ137-ζ136 | -ζ139-ζ134 | ζ43ζ139-ζ43ζ134 | -ζ4ζ1312+ζ4ζ13 | ζ4ζ1311-ζ4ζ132 | -ζ43ζ138+ζ43ζ135 | ζ43ζ138-ζ43ζ135 | -ζ4ζ1311+ζ4ζ132 | ζ4ζ1312-ζ4ζ13 | -ζ43ζ139+ζ43ζ134 | ζ43ζ137-ζ43ζ136 | -ζ4ζ1310+ζ4ζ133 | ζ4ζ1310-ζ4ζ133 | -ζ43ζ137+ζ43ζ136 | symplectic faithful, Schur index 2 |
| ρ20 | 2 | -2 | 0 | 0 | 0 | ζ138+ζ135 | ζ1310+ζ133 | ζ137+ζ136 | ζ1312+ζ13 | ζ1311+ζ132 | ζ139+ζ134 | -ζ1311-ζ132 | -ζ139-ζ134 | -ζ1310-ζ133 | -ζ137-ζ136 | -ζ1312-ζ13 | -ζ138-ζ135 | -ζ43ζ138+ζ43ζ135 | -ζ4ζ1311+ζ4ζ132 | -ζ43ζ139+ζ43ζ134 | -ζ4ζ1310+ζ4ζ133 | ζ4ζ1310-ζ4ζ133 | ζ43ζ139-ζ43ζ134 | ζ4ζ1311-ζ4ζ132 | ζ43ζ138-ζ43ζ135 | ζ4ζ1312-ζ4ζ13 | ζ43ζ137-ζ43ζ136 | -ζ43ζ137+ζ43ζ136 | -ζ4ζ1312+ζ4ζ13 | symplectic faithful, Schur index 2 |
| ρ21 | 2 | -2 | 0 | 0 | 0 | ζ1311+ζ132 | ζ139+ζ134 | ζ138+ζ135 | ζ1310+ζ133 | ζ137+ζ136 | ζ1312+ζ13 | -ζ137-ζ136 | -ζ1312-ζ13 | -ζ139-ζ134 | -ζ138-ζ135 | -ζ1310-ζ133 | -ζ1311-ζ132 | ζ4ζ1311-ζ4ζ132 | ζ43ζ137-ζ43ζ136 | -ζ4ζ1312+ζ4ζ13 | -ζ43ζ139+ζ43ζ134 | ζ43ζ139-ζ43ζ134 | ζ4ζ1312-ζ4ζ13 | -ζ43ζ137+ζ43ζ136 | -ζ4ζ1311+ζ4ζ132 | ζ4ζ1310-ζ4ζ133 | ζ43ζ138-ζ43ζ135 | -ζ43ζ138+ζ43ζ135 | -ζ4ζ1310+ζ4ζ133 | symplectic faithful, Schur index 2 |
| ρ22 | 2 | -2 | 0 | 0 | 0 | ζ1311+ζ132 | ζ139+ζ134 | ζ138+ζ135 | ζ1310+ζ133 | ζ137+ζ136 | ζ1312+ζ13 | -ζ137-ζ136 | -ζ1312-ζ13 | -ζ139-ζ134 | -ζ138-ζ135 | -ζ1310-ζ133 | -ζ1311-ζ132 | -ζ4ζ1311+ζ4ζ132 | -ζ43ζ137+ζ43ζ136 | ζ4ζ1312-ζ4ζ13 | ζ43ζ139-ζ43ζ134 | -ζ43ζ139+ζ43ζ134 | -ζ4ζ1312+ζ4ζ13 | ζ43ζ137-ζ43ζ136 | ζ4ζ1311-ζ4ζ132 | -ζ4ζ1310+ζ4ζ133 | -ζ43ζ138+ζ43ζ135 | ζ43ζ138-ζ43ζ135 | ζ4ζ1310-ζ4ζ133 | symplectic faithful, Schur index 2 |
| ρ23 | 2 | -2 | 0 | 0 | 0 | ζ1310+ζ133 | ζ137+ζ136 | ζ1312+ζ13 | ζ1311+ζ132 | ζ139+ζ134 | ζ138+ζ135 | -ζ139-ζ134 | -ζ138-ζ135 | -ζ137-ζ136 | -ζ1312-ζ13 | -ζ1311-ζ132 | -ζ1310-ζ133 | ζ4ζ1310-ζ4ζ133 | -ζ43ζ139+ζ43ζ134 | -ζ43ζ138+ζ43ζ135 | -ζ43ζ137+ζ43ζ136 | ζ43ζ137-ζ43ζ136 | ζ43ζ138-ζ43ζ135 | ζ43ζ139-ζ43ζ134 | -ζ4ζ1310+ζ4ζ133 | -ζ4ζ1311+ζ4ζ132 | -ζ4ζ1312+ζ4ζ13 | ζ4ζ1312-ζ4ζ13 | ζ4ζ1311-ζ4ζ132 | symplectic faithful, Schur index 2 |
| ρ24 | 2 | -2 | 0 | 0 | 0 | ζ137+ζ136 | ζ1312+ζ13 | ζ1311+ζ132 | ζ139+ζ134 | ζ138+ζ135 | ζ1310+ζ133 | -ζ138-ζ135 | -ζ1310-ζ133 | -ζ1312-ζ13 | -ζ1311-ζ132 | -ζ139-ζ134 | -ζ137-ζ136 | ζ43ζ137-ζ43ζ136 | -ζ43ζ138+ζ43ζ135 | ζ4ζ1310-ζ4ζ133 | ζ4ζ1312-ζ4ζ13 | -ζ4ζ1312+ζ4ζ13 | -ζ4ζ1310+ζ4ζ133 | ζ43ζ138-ζ43ζ135 | -ζ43ζ137+ζ43ζ136 | -ζ43ζ139+ζ43ζ134 | ζ4ζ1311-ζ4ζ132 | -ζ4ζ1311+ζ4ζ132 | ζ43ζ139-ζ43ζ134 | symplectic faithful, Schur index 2 |
| ρ25 | 2 | -2 | 0 | 0 | 0 | ζ1312+ζ13 | ζ1311+ζ132 | ζ139+ζ134 | ζ138+ζ135 | ζ1310+ζ133 | ζ137+ζ136 | -ζ1310-ζ133 | -ζ137-ζ136 | -ζ1311-ζ132 | -ζ139-ζ134 | -ζ138-ζ135 | -ζ1312-ζ13 | -ζ4ζ1312+ζ4ζ13 | ζ4ζ1310-ζ4ζ133 | ζ43ζ137-ζ43ζ136 | -ζ4ζ1311+ζ4ζ132 | ζ4ζ1311-ζ4ζ132 | -ζ43ζ137+ζ43ζ136 | -ζ4ζ1310+ζ4ζ133 | ζ4ζ1312-ζ4ζ13 | -ζ43ζ138+ζ43ζ135 | ζ43ζ139-ζ43ζ134 | -ζ43ζ139+ζ43ζ134 | ζ43ζ138-ζ43ζ135 | symplectic faithful, Schur index 2 |
| ρ26 | 2 | -2 | 0 | 0 | 0 | ζ1312+ζ13 | ζ1311+ζ132 | ζ139+ζ134 | ζ138+ζ135 | ζ1310+ζ133 | ζ137+ζ136 | -ζ1310-ζ133 | -ζ137-ζ136 | -ζ1311-ζ132 | -ζ139-ζ134 | -ζ138-ζ135 | -ζ1312-ζ13 | ζ4ζ1312-ζ4ζ13 | -ζ4ζ1310+ζ4ζ133 | -ζ43ζ137+ζ43ζ136 | ζ4ζ1311-ζ4ζ132 | -ζ4ζ1311+ζ4ζ132 | ζ43ζ137-ζ43ζ136 | ζ4ζ1310-ζ4ζ133 | -ζ4ζ1312+ζ4ζ13 | ζ43ζ138-ζ43ζ135 | -ζ43ζ139+ζ43ζ134 | ζ43ζ139-ζ43ζ134 | -ζ43ζ138+ζ43ζ135 | symplectic faithful, Schur index 2 |
| ρ27 | 2 | -2 | 0 | 0 | 0 | ζ137+ζ136 | ζ1312+ζ13 | ζ1311+ζ132 | ζ139+ζ134 | ζ138+ζ135 | ζ1310+ζ133 | -ζ138-ζ135 | -ζ1310-ζ133 | -ζ1312-ζ13 | -ζ1311-ζ132 | -ζ139-ζ134 | -ζ137-ζ136 | -ζ43ζ137+ζ43ζ136 | ζ43ζ138-ζ43ζ135 | -ζ4ζ1310+ζ4ζ133 | -ζ4ζ1312+ζ4ζ13 | ζ4ζ1312-ζ4ζ13 | ζ4ζ1310-ζ4ζ133 | -ζ43ζ138+ζ43ζ135 | ζ43ζ137-ζ43ζ136 | ζ43ζ139-ζ43ζ134 | -ζ4ζ1311+ζ4ζ132 | ζ4ζ1311-ζ4ζ132 | -ζ43ζ139+ζ43ζ134 | symplectic faithful, Schur index 2 |
| ρ28 | 2 | -2 | 0 | 0 | 0 | ζ138+ζ135 | ζ1310+ζ133 | ζ137+ζ136 | ζ1312+ζ13 | ζ1311+ζ132 | ζ139+ζ134 | -ζ1311-ζ132 | -ζ139-ζ134 | -ζ1310-ζ133 | -ζ137-ζ136 | -ζ1312-ζ13 | -ζ138-ζ135 | ζ43ζ138-ζ43ζ135 | ζ4ζ1311-ζ4ζ132 | ζ43ζ139-ζ43ζ134 | ζ4ζ1310-ζ4ζ133 | -ζ4ζ1310+ζ4ζ133 | -ζ43ζ139+ζ43ζ134 | -ζ4ζ1311+ζ4ζ132 | -ζ43ζ138+ζ43ζ135 | -ζ4ζ1312+ζ4ζ13 | -ζ43ζ137+ζ43ζ136 | ζ43ζ137-ζ43ζ136 | ζ4ζ1312-ζ4ζ13 | symplectic faithful, Schur index 2 |
| ρ29 | 2 | -2 | 0 | 0 | 0 | ζ139+ζ134 | ζ138+ζ135 | ζ1310+ζ133 | ζ137+ζ136 | ζ1312+ζ13 | ζ1311+ζ132 | -ζ1312-ζ13 | -ζ1311-ζ132 | -ζ138-ζ135 | -ζ1310-ζ133 | -ζ137-ζ136 | -ζ139-ζ134 | -ζ43ζ139+ζ43ζ134 | ζ4ζ1312-ζ4ζ13 | -ζ4ζ1311+ζ4ζ132 | ζ43ζ138-ζ43ζ135 | -ζ43ζ138+ζ43ζ135 | ζ4ζ1311-ζ4ζ132 | -ζ4ζ1312+ζ4ζ13 | ζ43ζ139-ζ43ζ134 | -ζ43ζ137+ζ43ζ136 | ζ4ζ1310-ζ4ζ133 | -ζ4ζ1310+ζ4ζ133 | ζ43ζ137-ζ43ζ136 | symplectic faithful, Schur index 2 |
►Regular action on 104 points
Generators in S104
(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)
(1 76 27 102)(2 75 28 101)(3 74 29 100)(4 73 30 99)(5 72 31 98)(6 71 32 97)(7 70 33 96)(8 69 34 95)(9 68 35 94)(10 67 36 93)(11 66 37 92)(12 65 38 91)(13 64 39 90)(14 63 40 89)(15 62 41 88)(16 61 42 87)(17 60 43 86)(18 59 44 85)(19 58 45 84)(20 57 46 83)(21 56 47 82)(22 55 48 81)(23 54 49 80)(24 53 50 79)(25 104 51 78)(26 103 52 77)
G:=sub<Sym(104)| (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), (1,76,27,102)(2,75,28,101)(3,74,29,100)(4,73,30,99)(5,72,31,98)(6,71,32,97)(7,70,33,96)(8,69,34,95)(9,68,35,94)(10,67,36,93)(11,66,37,92)(12,65,38,91)(13,64,39,90)(14,63,40,89)(15,62,41,88)(16,61,42,87)(17,60,43,86)(18,59,44,85)(19,58,45,84)(20,57,46,83)(21,56,47,82)(22,55,48,81)(23,54,49,80)(24,53,50,79)(25,104,51,78)(26,103,52,77)>;
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), (1,76,27,102)(2,75,28,101)(3,74,29,100)(4,73,30,99)(5,72,31,98)(6,71,32,97)(7,70,33,96)(8,69,34,95)(9,68,35,94)(10,67,36,93)(11,66,37,92)(12,65,38,91)(13,64,39,90)(14,63,40,89)(15,62,41,88)(16,61,42,87)(17,60,43,86)(18,59,44,85)(19,58,45,84)(20,57,46,83)(21,56,47,82)(22,55,48,81)(23,54,49,80)(24,53,50,79)(25,104,51,78)(26,103,52,77) );
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)], [(1,76,27,102),(2,75,28,101),(3,74,29,100),(4,73,30,99),(5,72,31,98),(6,71,32,97),(7,70,33,96),(8,69,34,95),(9,68,35,94),(10,67,36,93),(11,66,37,92),(12,65,38,91),(13,64,39,90),(14,63,40,89),(15,62,41,88),(16,61,42,87),(17,60,43,86),(18,59,44,85),(19,58,45,84),(20,57,46,83),(21,56,47,82),(22,55,48,81),(23,54,49,80),(24,53,50,79),(25,104,51,78),(26,103,52,77)]])
Dic26 is a maximal subgroup of
C104⋊C2 Dic52 D4.D13 C13⋊Q16 D52⋊5C2 D4⋊2D13 Q8×D13 Dic26⋊C3 C39⋊Q8 Dic78
Dic26 is a maximal quotient of
C26.D4 C52⋊3C4 C39⋊Q8 Dic78
Matrix representation of Dic26 ►in GL2(𝔽53) generated by
| 21 | 9 |
| 0 | 48 |
| 43 | 44 |
| 23 | 10 |
G:=sub<GL(2,GF(53))| [21,0,9,48],[43,23,44,10] >;
Dic26 in GAP, Magma, Sage, TeX
{\rm Dic}_{26} % in TeX
G:=Group("Dic26"); // GroupNames label
G:=SmallGroup(104,4);
// by ID
G=gap.SmallGroup(104,4);
# by ID
G:=PCGroup([4,-2,-2,-2,-13,16,49,21,1539]);
// Polycyclic
G:=Group<a,b|a^52=1,b^2=a^26,b*a*b^-1=a^-1>;
// generators/relations
Export
Subgroup lattice of Dic26 in TeX
Character table of Dic26 in TeX