metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C13⋊2D4, C22⋊D13, D26⋊2C2, Dic13⋊C2, C2.5D26, C26.5C22, (C2×C26)⋊2C2, SmallGroup(104,8)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C13⋊D4
G = < a,b,c | a13=b4=c2=1, bab-1=cac=a-1, cbc=b-1 >
Character table of C13⋊D4
| class | 1 | 2A | 2B | 2C | 4 | 13A | 13B | 13C | 13D | 13E | 13F | 26A | 26B | 26C | 26D | 26E | 26F | 26G | 26H | 26I | 26J | 26K | 26L | 26M | 26N | 26O | 26P | 26Q | 26R | |
| 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 | 0 | 0 | 0 | 2 | 2 | 2 | 2 | 2 | 2 | -2 | -2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | -2 | orthogonal lifted from D4 |
| ρ6 | 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 | ζ137+ζ136 | ζ1312+ζ13 | ζ138+ζ135 | ζ1311+ζ132 | ζ139+ζ134 | ζ1310+ζ133 | ζ1310+ζ133 | ζ139+ζ134 | ζ1311+ζ132 | ζ138+ζ135 | ζ1312+ζ13 | ζ137+ζ136 | ζ1312+ζ13 | ζ138+ζ135 | orthogonal lifted from D13 |
| ρ7 | 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 | ζ138+ζ135 | ζ1310+ζ133 | ζ1311+ζ132 | ζ137+ζ136 | ζ1312+ζ13 | ζ139+ζ134 | ζ139+ζ134 | ζ1312+ζ13 | ζ137+ζ136 | ζ1311+ζ132 | ζ1310+ζ133 | ζ138+ζ135 | ζ1310+ζ133 | ζ1311+ζ132 | orthogonal lifted from D13 |
| ρ8 | 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 | -ζ1312-ζ13 | -ζ1311-ζ132 | -ζ1310-ζ133 | -ζ139-ζ134 | -ζ138-ζ135 | -ζ137-ζ136 | -ζ137-ζ136 | -ζ138-ζ135 | -ζ139-ζ134 | -ζ1310-ζ133 | -ζ1311-ζ132 | -ζ1312-ζ13 | ζ1311+ζ132 | ζ1310+ζ133 | orthogonal lifted from D26 |
| ρ9 | 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 | -ζ137-ζ136 | -ζ1312-ζ13 | -ζ138-ζ135 | -ζ1311-ζ132 | -ζ139-ζ134 | -ζ1310-ζ133 | -ζ1310-ζ133 | -ζ139-ζ134 | -ζ1311-ζ132 | -ζ138-ζ135 | -ζ1312-ζ13 | -ζ137-ζ136 | ζ1312+ζ13 | ζ138+ζ135 | orthogonal lifted from D26 |
| ρ10 | 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 | ζ1310+ζ133 | ζ137+ζ136 | ζ139+ζ134 | ζ1312+ζ13 | ζ1311+ζ132 | ζ138+ζ135 | ζ138+ζ135 | ζ1311+ζ132 | ζ1312+ζ13 | ζ139+ζ134 | ζ137+ζ136 | ζ1310+ζ133 | ζ137+ζ136 | ζ139+ζ134 | orthogonal lifted from D13 |
| ρ11 | 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 | ζ139+ζ134 | ζ138+ζ135 | ζ1312+ζ13 | ζ1310+ζ133 | ζ137+ζ136 | ζ1311+ζ132 | ζ1311+ζ132 | ζ137+ζ136 | ζ1310+ζ133 | ζ1312+ζ13 | ζ138+ζ135 | ζ139+ζ134 | ζ138+ζ135 | ζ1312+ζ13 | orthogonal lifted from D13 |
| 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 | -ζ139-ζ134 | -ζ138-ζ135 | -ζ1312-ζ13 | -ζ1310-ζ133 | -ζ137-ζ136 | -ζ1311-ζ132 | -ζ1311-ζ132 | -ζ137-ζ136 | -ζ1310-ζ133 | -ζ1312-ζ13 | -ζ138-ζ135 | -ζ139-ζ134 | ζ138+ζ135 | ζ1312+ζ13 | orthogonal lifted from D26 |
| 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 | -ζ1311-ζ132 | -ζ139-ζ134 | -ζ137-ζ136 | -ζ138-ζ135 | -ζ1310-ζ133 | -ζ1312-ζ13 | -ζ1312-ζ13 | -ζ1310-ζ133 | -ζ138-ζ135 | -ζ137-ζ136 | -ζ139-ζ134 | -ζ1311-ζ132 | ζ139+ζ134 | ζ137+ζ136 | orthogonal lifted from D26 |
| ρ14 | 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 | -ζ138-ζ135 | -ζ1310-ζ133 | -ζ1311-ζ132 | -ζ137-ζ136 | -ζ1312-ζ13 | -ζ139-ζ134 | -ζ139-ζ134 | -ζ1312-ζ13 | -ζ137-ζ136 | -ζ1311-ζ132 | -ζ1310-ζ133 | -ζ138-ζ135 | ζ1310+ζ133 | ζ1311+ζ132 | orthogonal lifted from D26 |
| ρ15 | 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 | ζ1311+ζ132 | ζ139+ζ134 | ζ137+ζ136 | ζ138+ζ135 | ζ1310+ζ133 | ζ1312+ζ13 | ζ1312+ζ13 | ζ1310+ζ133 | ζ138+ζ135 | ζ137+ζ136 | ζ139+ζ134 | ζ1311+ζ132 | ζ139+ζ134 | ζ137+ζ136 | orthogonal lifted from D13 |
| ρ16 | 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 | -ζ1310-ζ133 | -ζ137-ζ136 | -ζ139-ζ134 | -ζ1312-ζ13 | -ζ1311-ζ132 | -ζ138-ζ135 | -ζ138-ζ135 | -ζ1311-ζ132 | -ζ1312-ζ13 | -ζ139-ζ134 | -ζ137-ζ136 | -ζ1310-ζ133 | ζ137+ζ136 | ζ139+ζ134 | orthogonal lifted from D26 |
| ρ17 | 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 | ζ1312+ζ13 | ζ1311+ζ132 | ζ1310+ζ133 | ζ139+ζ134 | ζ138+ζ135 | ζ137+ζ136 | ζ137+ζ136 | ζ138+ζ135 | ζ139+ζ134 | ζ1310+ζ133 | ζ1311+ζ132 | ζ1312+ζ13 | ζ1311+ζ132 | ζ1310+ζ133 | orthogonal lifted from D13 |
| ρ18 | 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 | -ζ137+ζ136 | ζ1312-ζ13 | -ζ138+ζ135 | ζ1311-ζ132 | -ζ139+ζ134 | ζ1310-ζ133 | -ζ1310+ζ133 | ζ139-ζ134 | -ζ1311+ζ132 | ζ138-ζ135 | -ζ1312+ζ13 | ζ137-ζ136 | -ζ1312-ζ13 | -ζ138-ζ135 | complex faithful |
| ρ19 | 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 | ζ138-ζ135 | -ζ1310+ζ133 | ζ1311-ζ132 | -ζ137+ζ136 | -ζ1312+ζ13 | ζ139-ζ134 | -ζ139+ζ134 | ζ1312-ζ13 | ζ137-ζ136 | -ζ1311+ζ132 | ζ1310-ζ133 | -ζ138+ζ135 | -ζ1310-ζ133 | -ζ1311-ζ132 | complex faithful |
| 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 | ζ137-ζ136 | -ζ1312+ζ13 | ζ138-ζ135 | -ζ1311+ζ132 | ζ139-ζ134 | -ζ1310+ζ133 | ζ1310-ζ133 | -ζ139+ζ134 | ζ1311-ζ132 | -ζ138+ζ135 | ζ1312-ζ13 | -ζ137+ζ136 | -ζ1312-ζ13 | -ζ138-ζ135 | complex faithful |
| ρ21 | 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 | -ζ139+ζ134 | ζ138-ζ135 | ζ1312-ζ13 | -ζ1310+ζ133 | ζ137-ζ136 | ζ1311-ζ132 | -ζ1311+ζ132 | -ζ137+ζ136 | ζ1310-ζ133 | -ζ1312+ζ13 | -ζ138+ζ135 | ζ139-ζ134 | -ζ138-ζ135 | -ζ1312-ζ13 | complex faithful |
| ρ22 | 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 | ζ1311-ζ132 | ζ139-ζ134 | ζ137-ζ136 | -ζ138+ζ135 | -ζ1310+ζ133 | -ζ1312+ζ13 | ζ1312-ζ13 | ζ1310-ζ133 | ζ138-ζ135 | -ζ137+ζ136 | -ζ139+ζ134 | -ζ1311+ζ132 | -ζ139-ζ134 | -ζ137-ζ136 | complex faithful |
| ρ23 | 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 | ζ1310-ζ133 | ζ137-ζ136 | -ζ139+ζ134 | -ζ1312+ζ13 | ζ1311-ζ132 | ζ138-ζ135 | -ζ138+ζ135 | -ζ1311+ζ132 | ζ1312-ζ13 | ζ139-ζ134 | -ζ137+ζ136 | -ζ1310+ζ133 | -ζ137-ζ136 | -ζ139-ζ134 | complex faithful |
| ρ24 | 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 | -ζ138+ζ135 | ζ1310-ζ133 | -ζ1311+ζ132 | ζ137-ζ136 | ζ1312-ζ13 | -ζ139+ζ134 | ζ139-ζ134 | -ζ1312+ζ13 | -ζ137+ζ136 | ζ1311-ζ132 | -ζ1310+ζ133 | ζ138-ζ135 | -ζ1310-ζ133 | -ζ1311-ζ132 | complex faithful |
| ρ25 | 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 | ζ1312-ζ13 | ζ1311-ζ132 | ζ1310-ζ133 | ζ139-ζ134 | ζ138-ζ135 | ζ137-ζ136 | -ζ137+ζ136 | -ζ138+ζ135 | -ζ139+ζ134 | -ζ1310+ζ133 | -ζ1311+ζ132 | -ζ1312+ζ13 | -ζ1311-ζ132 | -ζ1310-ζ133 | complex faithful |
| 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 | ζ139-ζ134 | -ζ138+ζ135 | -ζ1312+ζ13 | ζ1310-ζ133 | -ζ137+ζ136 | -ζ1311+ζ132 | ζ1311-ζ132 | ζ137-ζ136 | -ζ1310+ζ133 | ζ1312-ζ13 | ζ138-ζ135 | -ζ139+ζ134 | -ζ138-ζ135 | -ζ1312-ζ13 | complex faithful |
| 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 | -ζ1311+ζ132 | -ζ139+ζ134 | -ζ137+ζ136 | ζ138-ζ135 | ζ1310-ζ133 | ζ1312-ζ13 | -ζ1312+ζ13 | -ζ1310+ζ133 | -ζ138+ζ135 | ζ137-ζ136 | ζ139-ζ134 | ζ1311-ζ132 | -ζ139-ζ134 | -ζ137-ζ136 | complex faithful |
| ρ28 | 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 | -ζ1310+ζ133 | -ζ137+ζ136 | ζ139-ζ134 | ζ1312-ζ13 | -ζ1311+ζ132 | -ζ138+ζ135 | ζ138-ζ135 | ζ1311-ζ132 | -ζ1312+ζ13 | -ζ139+ζ134 | ζ137-ζ136 | ζ1310-ζ133 | -ζ137-ζ136 | -ζ139-ζ134 | complex faithful |
| ρ29 | 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 | -ζ1312+ζ13 | -ζ1311+ζ132 | -ζ1310+ζ133 | -ζ139+ζ134 | -ζ138+ζ135 | -ζ137+ζ136 | ζ137-ζ136 | ζ138-ζ135 | ζ139-ζ134 | ζ1310-ζ133 | ζ1311-ζ132 | ζ1312-ζ13 | -ζ1311-ζ132 | -ζ1310-ζ133 | complex faithful |
►On 52 points
Generators in S52
(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)
(1 28 14 49)(2 27 15 48)(3 39 16 47)(4 38 17 46)(5 37 18 45)(6 36 19 44)(7 35 20 43)(8 34 21 42)(9 33 22 41)(10 32 23 40)(11 31 24 52)(12 30 25 51)(13 29 26 50)
(2 13)(3 12)(4 11)(5 10)(6 9)(7 8)(15 26)(16 25)(17 24)(18 23)(19 22)(20 21)(27 50)(28 49)(29 48)(30 47)(31 46)(32 45)(33 44)(34 43)(35 42)(36 41)(37 40)(38 52)(39 51)
G:=sub<Sym(52)| (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), (1,28,14,49)(2,27,15,48)(3,39,16,47)(4,38,17,46)(5,37,18,45)(6,36,19,44)(7,35,20,43)(8,34,21,42)(9,33,22,41)(10,32,23,40)(11,31,24,52)(12,30,25,51)(13,29,26,50), (2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(27,50)(28,49)(29,48)(30,47)(31,46)(32,45)(33,44)(34,43)(35,42)(36,41)(37,40)(38,52)(39,51)>;
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), (1,28,14,49)(2,27,15,48)(3,39,16,47)(4,38,17,46)(5,37,18,45)(6,36,19,44)(7,35,20,43)(8,34,21,42)(9,33,22,41)(10,32,23,40)(11,31,24,52)(12,30,25,51)(13,29,26,50), (2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(27,50)(28,49)(29,48)(30,47)(31,46)(32,45)(33,44)(34,43)(35,42)(36,41)(37,40)(38,52)(39,51) );
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)], [(1,28,14,49),(2,27,15,48),(3,39,16,47),(4,38,17,46),(5,37,18,45),(6,36,19,44),(7,35,20,43),(8,34,21,42),(9,33,22,41),(10,32,23,40),(11,31,24,52),(12,30,25,51),(13,29,26,50)], [(2,13),(3,12),(4,11),(5,10),(6,9),(7,8),(15,26),(16,25),(17,24),(18,23),(19,22),(20,21),(27,50),(28,49),(29,48),(30,47),(31,46),(32,45),(33,44),(34,43),(35,42),(36,41),(37,40),(38,52),(39,51)]])
C13⋊D4 is a maximal subgroup of
D52⋊5C2 D4×D13 D4⋊2D13 D26⋊C6 C39⋊D4 C13⋊D12 C39⋊7D4 C13⋊S4
C13⋊D4 is a maximal quotient of
C26.D4 D26⋊C4 D4⋊D13 D4.D13 Q8⋊D13 C13⋊Q16 C23.D13 C39⋊D4 C13⋊D12 C39⋊7D4
Matrix representation of C13⋊D4 ►in GL2(𝔽53) generated by
| 0 | 1 |
| 52 | 26 |
| 31 | 18 |
| 29 | 22 |
| 1 | 0 |
| 26 | 52 |
G:=sub<GL(2,GF(53))| [0,52,1,26],[31,29,18,22],[1,26,0,52] >;
C13⋊D4 in GAP, Magma, Sage, TeX
C_{13}\rtimes D_4 % in TeX
G:=Group("C13:D4"); // GroupNames label
G:=SmallGroup(104,8);
// by ID
G=gap.SmallGroup(104,8);
# by ID
G:=PCGroup([4,-2,-2,-2,-13,49,1539]);
// Polycyclic
G:=Group<a,b,c|a^13=b^4=c^2=1,b*a*b^-1=c*a*c=a^-1,c*b*c=b^-1>;
// generators/relations
Export
Subgroup lattice of C13⋊D4 in TeX
Character table of C13⋊D4 in TeX