direct product, metabelian, soluble, monomial, A-group
Aliases: A4×C13⋊C3, C13⋊A4⋊C3, (A4×C13)⋊C3, C13⋊1(C3×A4), (C2×C26)⋊C32, (C22×C13⋊C3)⋊C3, C22⋊1(C3×C13⋊C3), SmallGroup(468,32)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C13 — C2×C26 — C22×C13⋊C3 — A4×C13⋊C3 |
| C2×C26 — A4×C13⋊C3 |
Generators and relations for A4×C13⋊C3
G = < a,b,c,d,e | a2=b2=c3=d13=e3=1, cac-1=ab=ba, ad=da, ae=ea, cbc-1=a, bd=db, be=eb, cd=dc, ce=ec, ede-1=d9 >
Character table of A4×C13⋊C3
| class | 1 | 2 | 3A | 3B | 3C | 3D | 3E | 3F | 3G | 3H | 6A | 6B | 13A | 13B | 13C | 13D | 26A | 26B | 26C | 26D | 39A | 39B | 39C | 39D | 39E | 39F | 39G | 39H | |
| size | 1 | 3 | 4 | 4 | 13 | 13 | 52 | 52 | 52 | 52 | 39 | 39 | 3 | 3 | 3 | 3 | 9 | 9 | 9 | 9 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | |
| 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 | trivial |
| ρ2 | 1 | 1 | ζ3 | ζ32 | 1 | 1 | ζ3 | ζ32 | ζ32 | ζ3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ζ32 | ζ32 | ζ32 | ζ32 | ζ3 | ζ3 | ζ3 | ζ3 | linear of order 3 |
| ρ3 | 1 | 1 | 1 | 1 | ζ3 | ζ32 | ζ32 | ζ3 | ζ32 | ζ3 | ζ32 | ζ3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 3 |
| ρ4 | 1 | 1 | ζ32 | ζ3 | 1 | 1 | ζ32 | ζ3 | ζ3 | ζ32 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ζ3 | ζ3 | ζ3 | ζ3 | ζ32 | ζ32 | ζ32 | ζ32 | linear of order 3 |
| ρ5 | 1 | 1 | 1 | 1 | ζ32 | ζ3 | ζ3 | ζ32 | ζ3 | ζ32 | ζ3 | ζ32 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 3 |
| ρ6 | 1 | 1 | ζ3 | ζ32 | ζ32 | ζ3 | ζ32 | ζ3 | 1 | 1 | ζ3 | ζ32 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ζ32 | ζ32 | ζ32 | ζ32 | ζ3 | ζ3 | ζ3 | ζ3 | linear of order 3 |
| ρ7 | 1 | 1 | ζ3 | ζ32 | ζ3 | ζ32 | 1 | 1 | ζ3 | ζ32 | ζ32 | ζ3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ζ32 | ζ32 | ζ32 | ζ32 | ζ3 | ζ3 | ζ3 | ζ3 | linear of order 3 |
| ρ8 | 1 | 1 | ζ32 | ζ3 | ζ3 | ζ32 | ζ3 | ζ32 | 1 | 1 | ζ32 | ζ3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ζ3 | ζ3 | ζ3 | ζ3 | ζ32 | ζ32 | ζ32 | ζ32 | linear of order 3 |
| ρ9 | 1 | 1 | ζ32 | ζ3 | ζ32 | ζ3 | 1 | 1 | ζ32 | ζ3 | ζ3 | ζ32 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ζ3 | ζ3 | ζ3 | ζ3 | ζ32 | ζ32 | ζ32 | ζ32 | linear of order 3 |
| ρ10 | 3 | -1 | 0 | 0 | 3 | 3 | 0 | 0 | 0 | 0 | -1 | -1 | 3 | 3 | 3 | 3 | -1 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from A4 |
| ρ11 | 3 | -1 | 0 | 0 | -3+3√-3/2 | -3-3√-3/2 | 0 | 0 | 0 | 0 | ζ6 | ζ65 | 3 | 3 | 3 | 3 | -1 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from C3×A4 |
| ρ12 | 3 | -1 | 0 | 0 | -3-3√-3/2 | -3+3√-3/2 | 0 | 0 | 0 | 0 | ζ65 | ζ6 | 3 | 3 | 3 | 3 | -1 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from C3×A4 |
| ρ13 | 3 | 3 | 3 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1311+ζ138+ζ137 | ζ1312+ζ1310+ζ134 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | ζ1312+ζ1310+ζ134 | ζ136+ζ135+ζ132 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | complex lifted from C13⋊C3 |
| ρ14 | 3 | 3 | 3 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1312+ζ1310+ζ134 | ζ136+ζ135+ζ132 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | ζ136+ζ135+ζ132 | ζ139+ζ133+ζ13 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | complex lifted from C13⋊C3 |
| ρ15 | 3 | 3 | 3 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ139+ζ133+ζ13 | ζ1311+ζ138+ζ137 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | ζ1311+ζ138+ζ137 | ζ1312+ζ1310+ζ134 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | complex lifted from C13⋊C3 |
| ρ16 | 3 | 3 | 3 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ136+ζ135+ζ132 | ζ139+ζ133+ζ13 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | ζ139+ζ133+ζ13 | ζ1311+ζ138+ζ137 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | complex lifted from C13⋊C3 |
| ρ17 | 3 | 3 | -3+3√-3/2 | -3-3√-3/2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ136+ζ135+ζ132 | ζ139+ζ133+ζ13 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | ζ139+ζ133+ζ13 | ζ1311+ζ138+ζ137 | ζ32ζ1311+ζ32ζ138+ζ32ζ137 | ζ32ζ139+ζ32ζ133+ζ32ζ13 | ζ32ζ136+ζ32ζ135+ζ32ζ132 | ζ32ζ1312+ζ32ζ1310+ζ32ζ134 | ζ3ζ1312+ζ3ζ1310+ζ3ζ134 | ζ3ζ1311+ζ3ζ138+ζ3ζ137 | ζ3ζ139+ζ3ζ133+ζ3ζ13 | ζ3ζ136+ζ3ζ135+ζ3ζ132 | complex lifted from C3×C13⋊C3 |
| ρ18 | 3 | 3 | -3+3√-3/2 | -3-3√-3/2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ139+ζ133+ζ13 | ζ1311+ζ138+ζ137 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | ζ1311+ζ138+ζ137 | ζ1312+ζ1310+ζ134 | ζ32ζ1312+ζ32ζ1310+ζ32ζ134 | ζ32ζ1311+ζ32ζ138+ζ32ζ137 | ζ32ζ139+ζ32ζ133+ζ32ζ13 | ζ32ζ136+ζ32ζ135+ζ32ζ132 | ζ3ζ136+ζ3ζ135+ζ3ζ132 | ζ3ζ1312+ζ3ζ1310+ζ3ζ134 | ζ3ζ1311+ζ3ζ138+ζ3ζ137 | ζ3ζ139+ζ3ζ133+ζ3ζ13 | complex lifted from C3×C13⋊C3 |
| ρ19 | 3 | 3 | -3-3√-3/2 | -3+3√-3/2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ139+ζ133+ζ13 | ζ1311+ζ138+ζ137 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | ζ1311+ζ138+ζ137 | ζ1312+ζ1310+ζ134 | ζ3ζ1312+ζ3ζ1310+ζ3ζ134 | ζ3ζ1311+ζ3ζ138+ζ3ζ137 | ζ3ζ139+ζ3ζ133+ζ3ζ13 | ζ3ζ136+ζ3ζ135+ζ3ζ132 | ζ32ζ136+ζ32ζ135+ζ32ζ132 | ζ32ζ1312+ζ32ζ1310+ζ32ζ134 | ζ32ζ1311+ζ32ζ138+ζ32ζ137 | ζ32ζ139+ζ32ζ133+ζ32ζ13 | complex lifted from C3×C13⋊C3 |
| ρ20 | 3 | 3 | -3-3√-3/2 | -3+3√-3/2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1311+ζ138+ζ137 | ζ1312+ζ1310+ζ134 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | ζ1312+ζ1310+ζ134 | ζ136+ζ135+ζ132 | ζ3ζ136+ζ3ζ135+ζ3ζ132 | ζ3ζ1312+ζ3ζ1310+ζ3ζ134 | ζ3ζ1311+ζ3ζ138+ζ3ζ137 | ζ3ζ139+ζ3ζ133+ζ3ζ13 | ζ32ζ139+ζ32ζ133+ζ32ζ13 | ζ32ζ136+ζ32ζ135+ζ32ζ132 | ζ32ζ1312+ζ32ζ1310+ζ32ζ134 | ζ32ζ1311+ζ32ζ138+ζ32ζ137 | complex lifted from C3×C13⋊C3 |
| ρ21 | 3 | 3 | -3+3√-3/2 | -3-3√-3/2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1312+ζ1310+ζ134 | ζ136+ζ135+ζ132 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | ζ136+ζ135+ζ132 | ζ139+ζ133+ζ13 | ζ32ζ139+ζ32ζ133+ζ32ζ13 | ζ32ζ136+ζ32ζ135+ζ32ζ132 | ζ32ζ1312+ζ32ζ1310+ζ32ζ134 | ζ32ζ1311+ζ32ζ138+ζ32ζ137 | ζ3ζ1311+ζ3ζ138+ζ3ζ137 | ζ3ζ139+ζ3ζ133+ζ3ζ13 | ζ3ζ136+ζ3ζ135+ζ3ζ132 | ζ3ζ1312+ζ3ζ1310+ζ3ζ134 | complex lifted from C3×C13⋊C3 |
| ρ22 | 3 | 3 | -3-3√-3/2 | -3+3√-3/2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ136+ζ135+ζ132 | ζ139+ζ133+ζ13 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | ζ136+ζ135+ζ132 | ζ1312+ζ1310+ζ134 | ζ139+ζ133+ζ13 | ζ1311+ζ138+ζ137 | ζ3ζ1311+ζ3ζ138+ζ3ζ137 | ζ3ζ139+ζ3ζ133+ζ3ζ13 | ζ3ζ136+ζ3ζ135+ζ3ζ132 | ζ3ζ1312+ζ3ζ1310+ζ3ζ134 | ζ32ζ1312+ζ32ζ1310+ζ32ζ134 | ζ32ζ1311+ζ32ζ138+ζ32ζ137 | ζ32ζ139+ζ32ζ133+ζ32ζ13 | ζ32ζ136+ζ32ζ135+ζ32ζ132 | complex lifted from C3×C13⋊C3 |
| ρ23 | 3 | 3 | -3+3√-3/2 | -3-3√-3/2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1311+ζ138+ζ137 | ζ1312+ζ1310+ζ134 | ζ139+ζ133+ζ13 | ζ136+ζ135+ζ132 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | ζ1312+ζ1310+ζ134 | ζ136+ζ135+ζ132 | ζ32ζ136+ζ32ζ135+ζ32ζ132 | ζ32ζ1312+ζ32ζ1310+ζ32ζ134 | ζ32ζ1311+ζ32ζ138+ζ32ζ137 | ζ32ζ139+ζ32ζ133+ζ32ζ13 | ζ3ζ139+ζ3ζ133+ζ3ζ13 | ζ3ζ136+ζ3ζ135+ζ3ζ132 | ζ3ζ1312+ζ3ζ1310+ζ3ζ134 | ζ3ζ1311+ζ3ζ138+ζ3ζ137 | complex lifted from C3×C13⋊C3 |
| ρ24 | 3 | 3 | -3-3√-3/2 | -3+3√-3/2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ1312+ζ1310+ζ134 | ζ136+ζ135+ζ132 | ζ1311+ζ138+ζ137 | ζ139+ζ133+ζ13 | ζ1312+ζ1310+ζ134 | ζ1311+ζ138+ζ137 | ζ136+ζ135+ζ132 | ζ139+ζ133+ζ13 | ζ3ζ139+ζ3ζ133+ζ3ζ13 | ζ3ζ136+ζ3ζ135+ζ3ζ132 | ζ3ζ1312+ζ3ζ1310+ζ3ζ134 | ζ3ζ1311+ζ3ζ138+ζ3ζ137 | ζ32ζ1311+ζ32ζ138+ζ32ζ137 | ζ32ζ139+ζ32ζ133+ζ32ζ13 | ζ32ζ136+ζ32ζ135+ζ32ζ132 | ζ32ζ1312+ζ32ζ1310+ζ32ζ134 | complex lifted from C3×C13⋊C3 |
| ρ25 | 9 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 3ζ139+3ζ133+3ζ13 | 3ζ1311+3ζ138+3ζ137 | 3ζ136+3ζ135+3ζ132 | 3ζ1312+3ζ1310+3ζ134 | -ζ139-ζ133-ζ13 | -ζ136-ζ135-ζ132 | -ζ1311-ζ138-ζ137 | -ζ1312-ζ1310-ζ134 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex faithful |
| ρ26 | 9 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 3ζ1311+3ζ138+3ζ137 | 3ζ1312+3ζ1310+3ζ134 | 3ζ139+3ζ133+3ζ13 | 3ζ136+3ζ135+3ζ132 | -ζ1311-ζ138-ζ137 | -ζ139-ζ133-ζ13 | -ζ1312-ζ1310-ζ134 | -ζ136-ζ135-ζ132 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex faithful |
| ρ27 | 9 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 3ζ1312+3ζ1310+3ζ134 | 3ζ136+3ζ135+3ζ132 | 3ζ1311+3ζ138+3ζ137 | 3ζ139+3ζ133+3ζ13 | -ζ1312-ζ1310-ζ134 | -ζ1311-ζ138-ζ137 | -ζ136-ζ135-ζ132 | -ζ139-ζ133-ζ13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex faithful |
| ρ28 | 9 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 3ζ136+3ζ135+3ζ132 | 3ζ139+3ζ133+3ζ13 | 3ζ1312+3ζ1310+3ζ134 | 3ζ1311+3ζ138+3ζ137 | -ζ136-ζ135-ζ132 | -ζ1312-ζ1310-ζ134 | -ζ139-ζ133-ζ13 | -ζ1311-ζ138-ζ137 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex faithful |
►On 52 points
Generators in S52
(1 14)(2 15)(3 16)(4 17)(5 18)(6 19)(7 20)(8 21)(9 22)(10 23)(11 24)(12 25)(13 26)(27 40)(28 41)(29 42)(30 43)(31 44)(32 45)(33 46)(34 47)(35 48)(36 49)(37 50)(38 51)(39 52)
(1 27)(2 28)(3 29)(4 30)(5 31)(6 32)(7 33)(8 34)(9 35)(10 36)(11 37)(12 38)(13 39)(14 40)(15 41)(16 42)(17 43)(18 44)(19 45)(20 46)(21 47)(22 48)(23 49)(24 50)(25 51)(26 52)
(14 27 40)(15 28 41)(16 29 42)(17 30 43)(18 31 44)(19 32 45)(20 33 46)(21 34 47)(22 35 48)(23 36 49)(24 37 50)(25 38 51)(26 39 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)
(2 4 10)(3 7 6)(5 13 11)(8 9 12)(15 17 23)(16 20 19)(18 26 24)(21 22 25)(28 30 36)(29 33 32)(31 39 37)(34 35 38)(41 43 49)(42 46 45)(44 52 50)(47 48 51)
G:=sub<Sym(52)| (1,14)(2,15)(3,16)(4,17)(5,18)(6,19)(7,20)(8,21)(9,22)(10,23)(11,24)(12,25)(13,26)(27,40)(28,41)(29,42)(30,43)(31,44)(32,45)(33,46)(34,47)(35,48)(36,49)(37,50)(38,51)(39,52), (1,27)(2,28)(3,29)(4,30)(5,31)(6,32)(7,33)(8,34)(9,35)(10,36)(11,37)(12,38)(13,39)(14,40)(15,41)(16,42)(17,43)(18,44)(19,45)(20,46)(21,47)(22,48)(23,49)(24,50)(25,51)(26,52), (14,27,40)(15,28,41)(16,29,42)(17,30,43)(18,31,44)(19,32,45)(20,33,46)(21,34,47)(22,35,48)(23,36,49)(24,37,50)(25,38,51)(26,39,52), (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), (2,4,10)(3,7,6)(5,13,11)(8,9,12)(15,17,23)(16,20,19)(18,26,24)(21,22,25)(28,30,36)(29,33,32)(31,39,37)(34,35,38)(41,43,49)(42,46,45)(44,52,50)(47,48,51)>;
G:=Group( (1,14)(2,15)(3,16)(4,17)(5,18)(6,19)(7,20)(8,21)(9,22)(10,23)(11,24)(12,25)(13,26)(27,40)(28,41)(29,42)(30,43)(31,44)(32,45)(33,46)(34,47)(35,48)(36,49)(37,50)(38,51)(39,52), (1,27)(2,28)(3,29)(4,30)(5,31)(6,32)(7,33)(8,34)(9,35)(10,36)(11,37)(12,38)(13,39)(14,40)(15,41)(16,42)(17,43)(18,44)(19,45)(20,46)(21,47)(22,48)(23,49)(24,50)(25,51)(26,52), (14,27,40)(15,28,41)(16,29,42)(17,30,43)(18,31,44)(19,32,45)(20,33,46)(21,34,47)(22,35,48)(23,36,49)(24,37,50)(25,38,51)(26,39,52), (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), (2,4,10)(3,7,6)(5,13,11)(8,9,12)(15,17,23)(16,20,19)(18,26,24)(21,22,25)(28,30,36)(29,33,32)(31,39,37)(34,35,38)(41,43,49)(42,46,45)(44,52,50)(47,48,51) );
G=PermutationGroup([[(1,14),(2,15),(3,16),(4,17),(5,18),(6,19),(7,20),(8,21),(9,22),(10,23),(11,24),(12,25),(13,26),(27,40),(28,41),(29,42),(30,43),(31,44),(32,45),(33,46),(34,47),(35,48),(36,49),(37,50),(38,51),(39,52)], [(1,27),(2,28),(3,29),(4,30),(5,31),(6,32),(7,33),(8,34),(9,35),(10,36),(11,37),(12,38),(13,39),(14,40),(15,41),(16,42),(17,43),(18,44),(19,45),(20,46),(21,47),(22,48),(23,49),(24,50),(25,51),(26,52)], [(14,27,40),(15,28,41),(16,29,42),(17,30,43),(18,31,44),(19,32,45),(20,33,46),(21,34,47),(22,35,48),(23,36,49),(24,37,50),(25,38,51),(26,39,52)], [(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)], [(2,4,10),(3,7,6),(5,13,11),(8,9,12),(15,17,23),(16,20,19),(18,26,24),(21,22,25),(28,30,36),(29,33,32),(31,39,37),(34,35,38),(41,43,49),(42,46,45),(44,52,50),(47,48,51)]])
Matrix representation of A4×C13⋊C3 ►in GL6(𝔽79)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 42 | 0 |
| 0 | 0 | 0 | 0 | 78 | 0 |
| 0 | 0 | 0 | 30 | 77 | 78 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 42 |
| 0 | 0 | 0 | 30 | 78 | 77 |
| 0 | 0 | 0 | 0 | 0 | 78 |
| 23 | 0 | 0 | 0 | 0 | 0 |
| 0 | 23 | 0 | 0 | 0 | 0 |
| 0 | 0 | 23 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 30 | 78 | 78 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 50 | 66 | 1 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 23 | 0 | 0 | 0 | 0 | 0 |
| 39 | 21 | 17 | 0 | 0 | 0 |
| 51 | 40 | 35 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
G:=sub<GL(6,GF(79))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,30,0,0,0,42,78,77,0,0,0,0,0,78],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,30,0,0,0,0,0,78,0,0,0,0,42,77,78],[23,0,0,0,0,0,0,23,0,0,0,0,0,0,23,0,0,0,0,0,0,1,30,0,0,0,0,0,78,1,0,0,0,0,78,0],[50,1,0,0,0,0,66,0,1,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[23,39,51,0,0,0,0,21,40,0,0,0,0,17,35,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1] >;
A4×C13⋊C3 in GAP, Magma, Sage, TeX
A_4\times C_{13}\rtimes C_3 % in TeX
G:=Group("A4xC13:C3"); // GroupNames label
G:=SmallGroup(468,32);
// by ID
G=gap.SmallGroup(468,32);
# by ID
G:=PCGroup([5,-3,-3,-2,2,-13,142,68,2704]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^3=d^13=e^3=1,c*a*c^-1=a*b=b*a,a*d=d*a,a*e=e*a,c*b*c^-1=a,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=d^9>;
// generators/relations
Export
Subgroup lattice of A4×C13⋊C3 in TeX
Character table of A4×C13⋊C3 in TeX