metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D26.2D4, Dic26⋊1C4, Dic13.21D4, C13⋊1C4≀C2, D4⋊2(C13⋊C4), (D4×C13)⋊2C4, C52.2(C2×C4), C52.C4⋊1C2, D4⋊2D13.2C2, C26.6(C22⋊C4), (C4×D13).8C22, C2.7(D13.D4), (C4×C13⋊C4)⋊1C2, C4.2(C2×C13⋊C4), SmallGroup(416,83)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic26⋊C4
G = < a,b,c | a52=c4=1, b2=a26, bab-1=a-1, cac-1=a21, cbc-1=a39b >
4C2
26C2
2C22
13C4
13C22
26C4
26C4
26C4
2D13
4C26
13Q8
13C2×C4
26D4
26C2×C4
26C2×C4
26C8
13C4○D4
13C42
13M4(2)
13C4≀C2
Character table of Dic26⋊C4
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 8A | 8B | 13A | 13B | 13C | 26A | 26B | 26C | 26D | 26E | 26F | 26G | 26H | 26I | 52A | 52B | 52C | |
| size | 1 | 1 | 4 | 26 | 2 | 13 | 13 | 26 | 26 | 26 | 26 | 52 | 52 | 52 | 4 | 4 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | |
| 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 | 1 | 1 | 1 | -1 | 1 | -1 | -1 | -i | i | i | -i | -1 | i | -i | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 4 |
| ρ6 | 1 | 1 | -1 | -1 | 1 | -1 | -1 | -i | i | i | -i | 1 | -i | i | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | linear of order 4 |
| ρ7 | 1 | 1 | 1 | -1 | 1 | -1 | -1 | i | -i | -i | i | -1 | -i | i | 1 | 1 | 1 | 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 | -i | i | 1 | i | -i | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | linear of order 4 |
| ρ9 | 2 | 2 | 0 | 2 | -2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 2 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | -2 | -2 | orthogonal lifted from D4 |
| ρ10 | 2 | 2 | 0 | -2 | -2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 2 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | -2 | -2 | orthogonal lifted from D4 |
| ρ11 | 2 | -2 | 0 | 0 | 0 | -2i | 2i | 1-i | 1+i | -1-i | -1+i | 0 | 0 | 0 | 2 | 2 | 2 | -2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from C4≀C2 |
| ρ12 | 2 | -2 | 0 | 0 | 0 | 2i | -2i | 1+i | 1-i | -1+i | -1-i | 0 | 0 | 0 | 2 | 2 | 2 | -2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from C4≀C2 |
| ρ13 | 2 | -2 | 0 | 0 | 0 | -2i | 2i | -1+i | -1-i | 1+i | 1-i | 0 | 0 | 0 | 2 | 2 | 2 | -2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from C4≀C2 |
| ρ14 | 2 | -2 | 0 | 0 | 0 | 2i | -2i | -1-i | -1+i | 1-i | 1+i | 0 | 0 | 0 | 2 | 2 | 2 | -2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from C4≀C2 |
| ρ15 | 4 | 4 | 0 | 0 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ1311-ζ1310-ζ133+ζ132 | -ζ139+ζ137+ζ136-ζ134 | -ζ1311+ζ1310+ζ133-ζ132 | ζ139-ζ137-ζ136+ζ134 | -ζ1312+ζ138+ζ135-ζ13 | ζ1312-ζ138-ζ135+ζ13 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ1312-ζ138-ζ135-ζ13 | -ζ139-ζ137-ζ136-ζ134 | orthogonal lifted from D13.D4 |
| ρ16 | 4 | 4 | 4 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | orthogonal lifted from C13⋊C4 |
| ρ17 | 4 | 4 | 0 | 0 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | -ζ139+ζ137+ζ136-ζ134 | -ζ1312+ζ138+ζ135-ζ13 | ζ139-ζ137-ζ136+ζ134 | ζ1312-ζ138-ζ135+ζ13 | ζ1311-ζ1310-ζ133+ζ132 | -ζ1311+ζ1310+ζ133-ζ132 | -ζ139-ζ137-ζ136-ζ134 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ1312-ζ138-ζ135-ζ13 | orthogonal lifted from D13.D4 |
| ρ18 | 4 | 4 | 0 | 0 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | -ζ1312+ζ138+ζ135-ζ13 | ζ1311-ζ1310-ζ133+ζ132 | ζ1312-ζ138-ζ135+ζ13 | -ζ1311+ζ1310+ζ133-ζ132 | -ζ139+ζ137+ζ136-ζ134 | ζ139-ζ137-ζ136+ζ134 | -ζ1312-ζ138-ζ135-ζ13 | -ζ139-ζ137-ζ136-ζ134 | -ζ1311-ζ1310-ζ133-ζ132 | orthogonal lifted from D13.D4 |
| ρ19 | 4 | 4 | 4 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | orthogonal lifted from C13⋊C4 |
| ρ20 | 4 | 4 | -4 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | -ζ1312-ζ138-ζ135-ζ13 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ1312-ζ138-ζ135-ζ13 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ139-ζ137-ζ136-ζ134 | -ζ139-ζ137-ζ136-ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | orthogonal lifted from C2×C13⋊C4 |
| ρ21 | 4 | 4 | 0 | 0 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ139-ζ137-ζ136+ζ134 | ζ1312-ζ138-ζ135+ζ13 | -ζ139+ζ137+ζ136-ζ134 | -ζ1312+ζ138+ζ135-ζ13 | -ζ1311+ζ1310+ζ133-ζ132 | ζ1311-ζ1310-ζ133+ζ132 | -ζ139-ζ137-ζ136-ζ134 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ1312-ζ138-ζ135-ζ13 | orthogonal lifted from D13.D4 |
| ρ22 | 4 | 4 | 4 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | orthogonal lifted from C13⋊C4 |
| ρ23 | 4 | 4 | -4 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | -ζ139-ζ137-ζ136-ζ134 | -ζ1312-ζ138-ζ135-ζ13 | -ζ139-ζ137-ζ136-ζ134 | -ζ1312-ζ138-ζ135-ζ13 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ1311-ζ1310-ζ133-ζ132 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | orthogonal lifted from C2×C13⋊C4 |
| ρ24 | 4 | 4 | 0 | 0 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | -ζ1311+ζ1310+ζ133-ζ132 | ζ139-ζ137-ζ136+ζ134 | ζ1311-ζ1310-ζ133+ζ132 | -ζ139+ζ137+ζ136-ζ134 | ζ1312-ζ138-ζ135+ζ13 | -ζ1312+ζ138+ζ135-ζ13 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ1312-ζ138-ζ135-ζ13 | -ζ139-ζ137-ζ136-ζ134 | orthogonal lifted from D13.D4 |
| ρ25 | 4 | 4 | -4 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ139+ζ137+ζ136+ζ134 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ139-ζ137-ζ136-ζ134 | -ζ1311-ζ1310-ζ133-ζ132 | -ζ139-ζ137-ζ136-ζ134 | -ζ1312-ζ138-ζ135-ζ13 | -ζ1312-ζ138-ζ135-ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | orthogonal lifted from C2×C13⋊C4 |
| ρ26 | 4 | 4 | 0 | 0 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ139+ζ137+ζ136+ζ134 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312+ζ138+ζ135+ζ13 | ζ139+ζ137+ζ136+ζ134 | ζ1312+ζ138+ζ135+ζ13 | ζ1311+ζ1310+ζ133+ζ132 | ζ1312-ζ138-ζ135+ζ13 | -ζ1311+ζ1310+ζ133-ζ132 | -ζ1312+ζ138+ζ135-ζ13 | ζ1311-ζ1310-ζ133+ζ132 | ζ139-ζ137-ζ136+ζ134 | -ζ139+ζ137+ζ136-ζ134 | -ζ1312-ζ138-ζ135-ζ13 | -ζ139-ζ137-ζ136-ζ134 | -ζ1311-ζ1310-ζ133-ζ132 | orthogonal lifted from D13.D4 |
| ρ27 | 8 | -8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2ζ139+2ζ137+2ζ136+2ζ134 | 2ζ1311+2ζ1310+2ζ133+2ζ132 | 2ζ1312+2ζ138+2ζ135+2ζ13 | -2ζ139-2ζ137-2ζ136-2ζ134 | -2ζ1312-2ζ138-2ζ135-2ζ13 | -2ζ1311-2ζ1310-2ζ133-2ζ132 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic faithful, Schur index 2 |
| ρ28 | 8 | -8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2ζ1311+2ζ1310+2ζ133+2ζ132 | 2ζ1312+2ζ138+2ζ135+2ζ13 | 2ζ139+2ζ137+2ζ136+2ζ134 | -2ζ1311-2ζ1310-2ζ133-2ζ132 | -2ζ139-2ζ137-2ζ136-2ζ134 | -2ζ1312-2ζ138-2ζ135-2ζ13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic faithful, Schur index 2 |
| ρ29 | 8 | -8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2ζ1312+2ζ138+2ζ135+2ζ13 | 2ζ139+2ζ137+2ζ136+2ζ134 | 2ζ1311+2ζ1310+2ζ133+2ζ132 | -2ζ1312-2ζ138-2ζ135-2ζ13 | -2ζ1311-2ζ1310-2ζ133-2ζ132 | -2ζ139-2ζ137-2ζ136-2ζ134 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic faithful, Schur index 2 |
►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)
(1 101 27 75)(2 100 28 74)(3 99 29 73)(4 98 30 72)(5 97 31 71)(6 96 32 70)(7 95 33 69)(8 94 34 68)(9 93 35 67)(10 92 36 66)(11 91 37 65)(12 90 38 64)(13 89 39 63)(14 88 40 62)(15 87 41 61)(16 86 42 60)(17 85 43 59)(18 84 44 58)(19 83 45 57)(20 82 46 56)(21 81 47 55)(22 80 48 54)(23 79 49 53)(24 78 50 104)(25 77 51 103)(26 76 52 102)
(1 27)(2 32 26 48)(3 37 51 17)(4 42 24 38)(5 47 49 7)(6 52 22 28)(8 10 20 18)(9 15 45 39)(11 25 43 29)(12 30 16 50)(13 35 41 19)(14 40)(21 23 33 31)(34 36 46 44)(53 82 71 68)(54 87 96 89)(55 92 69 58)(56 97 94 79)(57 102 67 100)(59 60 65 90)(61 70 63 80)(62 75 88 101)(64 85 86 91)(66 95 84 81)(72 73 78 103)(74 83 76 93)(77 98 99 104)
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), (1,101,27,75)(2,100,28,74)(3,99,29,73)(4,98,30,72)(5,97,31,71)(6,96,32,70)(7,95,33,69)(8,94,34,68)(9,93,35,67)(10,92,36,66)(11,91,37,65)(12,90,38,64)(13,89,39,63)(14,88,40,62)(15,87,41,61)(16,86,42,60)(17,85,43,59)(18,84,44,58)(19,83,45,57)(20,82,46,56)(21,81,47,55)(22,80,48,54)(23,79,49,53)(24,78,50,104)(25,77,51,103)(26,76,52,102), (1,27)(2,32,26,48)(3,37,51,17)(4,42,24,38)(5,47,49,7)(6,52,22,28)(8,10,20,18)(9,15,45,39)(11,25,43,29)(12,30,16,50)(13,35,41,19)(14,40)(21,23,33,31)(34,36,46,44)(53,82,71,68)(54,87,96,89)(55,92,69,58)(56,97,94,79)(57,102,67,100)(59,60,65,90)(61,70,63,80)(62,75,88,101)(64,85,86,91)(66,95,84,81)(72,73,78,103)(74,83,76,93)(77,98,99,104)>;
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), (1,101,27,75)(2,100,28,74)(3,99,29,73)(4,98,30,72)(5,97,31,71)(6,96,32,70)(7,95,33,69)(8,94,34,68)(9,93,35,67)(10,92,36,66)(11,91,37,65)(12,90,38,64)(13,89,39,63)(14,88,40,62)(15,87,41,61)(16,86,42,60)(17,85,43,59)(18,84,44,58)(19,83,45,57)(20,82,46,56)(21,81,47,55)(22,80,48,54)(23,79,49,53)(24,78,50,104)(25,77,51,103)(26,76,52,102), (1,27)(2,32,26,48)(3,37,51,17)(4,42,24,38)(5,47,49,7)(6,52,22,28)(8,10,20,18)(9,15,45,39)(11,25,43,29)(12,30,16,50)(13,35,41,19)(14,40)(21,23,33,31)(34,36,46,44)(53,82,71,68)(54,87,96,89)(55,92,69,58)(56,97,94,79)(57,102,67,100)(59,60,65,90)(61,70,63,80)(62,75,88,101)(64,85,86,91)(66,95,84,81)(72,73,78,103)(74,83,76,93)(77,98,99,104) );
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)], [(1,101,27,75),(2,100,28,74),(3,99,29,73),(4,98,30,72),(5,97,31,71),(6,96,32,70),(7,95,33,69),(8,94,34,68),(9,93,35,67),(10,92,36,66),(11,91,37,65),(12,90,38,64),(13,89,39,63),(14,88,40,62),(15,87,41,61),(16,86,42,60),(17,85,43,59),(18,84,44,58),(19,83,45,57),(20,82,46,56),(21,81,47,55),(22,80,48,54),(23,79,49,53),(24,78,50,104),(25,77,51,103),(26,76,52,102)], [(1,27),(2,32,26,48),(3,37,51,17),(4,42,24,38),(5,47,49,7),(6,52,22,28),(8,10,20,18),(9,15,45,39),(11,25,43,29),(12,30,16,50),(13,35,41,19),(14,40),(21,23,33,31),(34,36,46,44),(53,82,71,68),(54,87,96,89),(55,92,69,58),(56,97,94,79),(57,102,67,100),(59,60,65,90),(61,70,63,80),(62,75,88,101),(64,85,86,91),(66,95,84,81),(72,73,78,103),(74,83,76,93),(77,98,99,104)]])
Matrix representation of Dic26⋊C4 ►in GL6(𝔽313)
| 25 | 0 | 0 | 0 | 0 | 0 |
| 0 | 288 | 0 | 0 | 0 | 0 |
| 0 | 0 | 29 | 1 | 0 | 0 |
| 0 | 0 | 311 | 0 | 1 | 0 |
| 0 | 0 | 241 | 0 | 0 | 1 |
| 0 | 0 | 139 | 103 | 240 | 72 |
| 0 | 288 | 0 | 0 | 0 | 0 |
| 288 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 284 | 99 | 212 | 101 |
| 0 | 0 | 75 | 297 | 286 | 100 |
| 0 | 0 | 217 | 62 | 147 | 29 |
| 0 | 0 | 36 | 134 | 36 | 211 |
| 312 | 0 | 0 | 0 | 0 | 0 |
| 0 | 288 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 270 | 285 | 283 |
| 0 | 0 | 181 | 70 | 141 | 3 |
| 0 | 0 | 169 | 104 | 138 | 43 |
| 0 | 0 | 208 | 43 | 269 | 103 |
G:=sub<GL(6,GF(313))| [25,0,0,0,0,0,0,288,0,0,0,0,0,0,29,311,241,139,0,0,1,0,0,103,0,0,0,1,0,240,0,0,0,0,1,72],[0,288,0,0,0,0,288,0,0,0,0,0,0,0,284,75,217,36,0,0,99,297,62,134,0,0,212,286,147,36,0,0,101,100,29,211],[312,0,0,0,0,0,0,288,0,0,0,0,0,0,2,181,169,208,0,0,270,70,104,43,0,0,285,141,138,269,0,0,283,3,43,103] >;
Dic26⋊C4 in GAP, Magma, Sage, TeX
{\rm Dic}_{26}\rtimes C_4 % in TeX
G:=Group("Dic26:C4"); // GroupNames label
G:=SmallGroup(416,83);
// by ID
G=gap.SmallGroup(416,83);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-13,24,121,86,579,297,69,9221,3473]);
// Polycyclic
G:=Group<a,b,c|a^52=c^4=1,b^2=a^26,b*a*b^-1=a^-1,c*a*c^-1=a^21,c*b*c^-1=a^39*b>;
// generators/relations
Export
Subgroup lattice of Dic26⋊C4 in TeX
Character table of Dic26⋊C4 in TeX