direct product, metabelian, soluble, monomial
Aliases: C3×C23.A4, (C4×C12)⋊5C6, C42⋊C3⋊3C6, C4⋊1D4⋊C32, C42⋊2(C3×C6), C23.2(C3×A4), C22.4(C6×A4), (C22×C6).6A4, (C3×C4⋊1D4)⋊C3, (C3×C42⋊C3)⋊7C2, (C2×C6).12(C2×A4), SmallGroup(288,636)
Series: Derived ►Chief ►Lower central ►Upper central
| C42 — C3×C23.A4 |
Generators and relations for C3×C23.A4
G = < a,b,c,d,e,f,g | a3=b2=c2=d2=g3=1, e2=dc=gcg-1=cd, f2=gdg-1=c, ab=ba, ac=ca, ad=da, ae=ea, af=fa, ag=ga, fbf-1=bc=cb, bd=db, ebe-1=bcd, bg=gb, ce=ec, cf=fc, gfg-1=de=ed, df=fd, ef=fe, geg-1=cef >
Subgroups: 348 in 68 conjugacy classes, 18 normal (12 characteristic)
C1, C2, C3, C3, C4, C22, C22, C6, C2×C4, D4, C23, C23, C32, C12, A4, C2×C6, C2×C6, C42, C2×D4, C3×C6, C2×C12, C3×D4, C2×A4, C22×C6, C22×C6, C4⋊1D4, C3×A4, C42⋊C3, C4×C12, C6×D4, C6×A4, C23.A4, C3×C4⋊1D4, C3×C42⋊C3, C3×C23.A4
Quotients: C1, C2, C3, C6, C32, A4, C3×C6, C2×A4, C3×A4, C6×A4, C23.A4, C3×C23.A4
Character table of C3×C23.A4
| class | 1 | 2A | 2B | 2C | 3A | 3B | 3C | 3D | 3E | 3F | 3G | 3H | 4A | 4B | 6A | 6B | 6C | 6D | 6E | 6F | 6G | 6H | 6I | 6J | 6K | 6L | 12A | 12B | 12C | 12D | |
| size | 1 | 3 | 4 | 12 | 1 | 1 | 16 | 16 | 16 | 16 | 16 | 16 | 6 | 6 | 3 | 3 | 4 | 4 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | 16 | 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 | -1 | 1 | 1 | ζ3 | ζ32 | ζ3 | ζ3 | ζ32 | ζ32 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | ζ65 | ζ6 | ζ6 | ζ6 | ζ65 | ζ65 | 1 | 1 | 1 | 1 | linear of order 6 |
| ρ4 | 1 | 1 | -1 | -1 | ζ3 | ζ32 | ζ3 | ζ32 | ζ32 | 1 | 1 | ζ3 | 1 | 1 | ζ32 | ζ3 | ζ65 | ζ6 | ζ65 | ζ6 | -1 | ζ6 | -1 | ζ65 | ζ65 | ζ6 | ζ32 | ζ3 | ζ32 | ζ3 | linear of order 6 |
| ρ5 | 1 | 1 | -1 | -1 | ζ32 | ζ3 | ζ32 | ζ3 | ζ3 | 1 | 1 | ζ32 | 1 | 1 | ζ3 | ζ32 | ζ6 | ζ65 | ζ6 | ζ65 | -1 | ζ65 | -1 | ζ6 | ζ6 | ζ65 | ζ3 | ζ32 | ζ3 | ζ32 | linear of order 6 |
| ρ6 | 1 | 1 | 1 | 1 | 1 | 1 | ζ3 | ζ32 | ζ3 | ζ3 | ζ32 | ζ32 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ζ3 | ζ32 | ζ32 | ζ32 | ζ3 | ζ3 | 1 | 1 | 1 | 1 | linear of order 3 |
| ρ7 | 1 | 1 | 1 | 1 | ζ32 | ζ3 | ζ3 | ζ32 | 1 | ζ32 | ζ3 | 1 | 1 | 1 | ζ3 | ζ32 | ζ32 | ζ3 | ζ32 | ζ3 | ζ32 | ζ32 | ζ3 | 1 | ζ3 | 1 | ζ3 | ζ32 | ζ3 | ζ32 | linear of order 3 |
| ρ8 | 1 | 1 | 1 | 1 | ζ3 | ζ32 | ζ3 | ζ32 | ζ32 | 1 | 1 | ζ3 | 1 | 1 | ζ32 | ζ3 | ζ3 | ζ32 | ζ3 | ζ32 | 1 | ζ32 | 1 | ζ3 | ζ3 | ζ32 | ζ32 | ζ3 | ζ32 | ζ3 | linear of order 3 |
| ρ9 | 1 | 1 | 1 | 1 | ζ3 | ζ32 | ζ32 | ζ3 | 1 | ζ3 | ζ32 | 1 | 1 | 1 | ζ32 | ζ3 | ζ3 | ζ32 | ζ3 | ζ32 | ζ3 | ζ3 | ζ32 | 1 | ζ32 | 1 | ζ32 | ζ3 | ζ32 | ζ3 | linear of order 3 |
| ρ10 | 1 | 1 | -1 | -1 | 1 | 1 | ζ32 | ζ3 | ζ32 | ζ32 | ζ3 | ζ3 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | ζ6 | ζ65 | ζ65 | ζ65 | ζ6 | ζ6 | 1 | 1 | 1 | 1 | linear of order 6 |
| ρ11 | 1 | 1 | 1 | 1 | 1 | 1 | ζ32 | ζ3 | ζ32 | ζ32 | ζ3 | ζ3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ζ32 | ζ3 | ζ3 | ζ3 | ζ32 | ζ32 | 1 | 1 | 1 | 1 | linear of order 3 |
| ρ12 | 1 | 1 | -1 | -1 | ζ32 | ζ3 | ζ3 | ζ32 | 1 | ζ32 | ζ3 | 1 | 1 | 1 | ζ3 | ζ32 | ζ6 | ζ65 | ζ6 | ζ65 | ζ6 | ζ6 | ζ65 | -1 | ζ65 | -1 | ζ3 | ζ32 | ζ3 | ζ32 | linear of order 6 |
| ρ13 | 1 | 1 | 1 | 1 | ζ3 | ζ32 | 1 | 1 | ζ3 | ζ32 | ζ3 | ζ32 | 1 | 1 | ζ32 | ζ3 | ζ3 | ζ32 | ζ3 | ζ32 | ζ32 | 1 | ζ3 | ζ32 | 1 | ζ3 | ζ32 | ζ3 | ζ32 | ζ3 | linear of order 3 |
| ρ14 | 1 | 1 | -1 | -1 | ζ3 | ζ32 | 1 | 1 | ζ3 | ζ32 | ζ3 | ζ32 | 1 | 1 | ζ32 | ζ3 | ζ65 | ζ6 | ζ65 | ζ6 | ζ6 | -1 | ζ65 | ζ6 | -1 | ζ65 | ζ32 | ζ3 | ζ32 | ζ3 | linear of order 6 |
| ρ15 | 1 | 1 | 1 | 1 | ζ32 | ζ3 | 1 | 1 | ζ32 | ζ3 | ζ32 | ζ3 | 1 | 1 | ζ3 | ζ32 | ζ32 | ζ3 | ζ32 | ζ3 | ζ3 | 1 | ζ32 | ζ3 | 1 | ζ32 | ζ3 | ζ32 | ζ3 | ζ32 | linear of order 3 |
| ρ16 | 1 | 1 | -1 | -1 | ζ3 | ζ32 | ζ32 | ζ3 | 1 | ζ3 | ζ32 | 1 | 1 | 1 | ζ32 | ζ3 | ζ65 | ζ6 | ζ65 | ζ6 | ζ65 | ζ65 | ζ6 | -1 | ζ6 | -1 | ζ32 | ζ3 | ζ32 | ζ3 | linear of order 6 |
| ρ17 | 1 | 1 | 1 | 1 | ζ32 | ζ3 | ζ32 | ζ3 | ζ3 | 1 | 1 | ζ32 | 1 | 1 | ζ3 | ζ32 | ζ32 | ζ3 | ζ32 | ζ3 | 1 | ζ3 | 1 | ζ32 | ζ32 | ζ3 | ζ3 | ζ32 | ζ3 | ζ32 | linear of order 3 |
| ρ18 | 1 | 1 | -1 | -1 | ζ32 | ζ3 | 1 | 1 | ζ32 | ζ3 | ζ32 | ζ3 | 1 | 1 | ζ3 | ζ32 | ζ6 | ζ65 | ζ6 | ζ65 | ζ65 | -1 | ζ6 | ζ65 | -1 | ζ6 | ζ3 | ζ32 | ζ3 | ζ32 | linear of order 6 |
| ρ19 | 3 | 3 | -3 | 1 | 3 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | -1 | 3 | 3 | -3 | -3 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | -1 | -1 | -1 | orthogonal lifted from C2×A4 |
| ρ20 | 3 | 3 | 3 | -1 | 3 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | -1 | 3 | 3 | 3 | 3 | -1 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | -1 | -1 | -1 | orthogonal lifted from A4 |
| ρ21 | 3 | 3 | 3 | -1 | -3-3√-3/2 | -3+3√-3/2 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | -1 | -3+3√-3/2 | -3-3√-3/2 | -3-3√-3/2 | -3+3√-3/2 | ζ6 | ζ65 | 0 | 0 | 0 | 0 | 0 | 0 | ζ65 | ζ6 | ζ65 | ζ6 | complex lifted from C3×A4 |
| ρ22 | 3 | 3 | -3 | 1 | -3-3√-3/2 | -3+3√-3/2 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | -1 | -3+3√-3/2 | -3-3√-3/2 | 3+3√-3/2 | 3-3√-3/2 | ζ32 | ζ3 | 0 | 0 | 0 | 0 | 0 | 0 | ζ65 | ζ6 | ζ65 | ζ6 | complex lifted from C6×A4 |
| ρ23 | 3 | 3 | -3 | 1 | -3+3√-3/2 | -3-3√-3/2 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | -1 | -3-3√-3/2 | -3+3√-3/2 | 3-3√-3/2 | 3+3√-3/2 | ζ3 | ζ32 | 0 | 0 | 0 | 0 | 0 | 0 | ζ6 | ζ65 | ζ6 | ζ65 | complex lifted from C6×A4 |
| ρ24 | 3 | 3 | 3 | -1 | -3+3√-3/2 | -3-3√-3/2 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | -1 | -3-3√-3/2 | -3+3√-3/2 | -3+3√-3/2 | -3-3√-3/2 | ζ65 | ζ6 | 0 | 0 | 0 | 0 | 0 | 0 | ζ6 | ζ65 | ζ6 | ζ65 | complex lifted from C3×A4 |
| ρ25 | 6 | -2 | 0 | 0 | 6 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | -2 | 2 | 2 | orthogonal lifted from C23.A4 |
| ρ26 | 6 | -2 | 0 | 0 | 6 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | -2 | -2 | orthogonal lifted from C23.A4 |
| ρ27 | 6 | -2 | 0 | 0 | -3+3√-3 | -3-3√-3 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 1+√-3 | 1-√-3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1+√-3 | 1-√-3 | -1-√-3 | -1+√-3 | complex faithful |
| ρ28 | 6 | -2 | 0 | 0 | -3-3√-3 | -3+3√-3 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 1-√-3 | 1+√-3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1-√-3 | 1+√-3 | -1+√-3 | -1-√-3 | complex faithful |
| ρ29 | 6 | -2 | 0 | 0 | -3-3√-3 | -3+3√-3 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 1-√-3 | 1+√-3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1+√-3 | -1-√-3 | 1-√-3 | 1+√-3 | complex faithful |
| ρ30 | 6 | -2 | 0 | 0 | -3+3√-3 | -3-3√-3 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 1+√-3 | 1-√-3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1-√-3 | -1+√-3 | 1+√-3 | 1-√-3 | complex faithful |
►On 36 points
Generators in S36
(1 9 5)(2 8 4)(3 11 7)(6 12 10)(13 18 21)(14 19 22)(15 20 23)(16 17 24)(25 33 29)(26 34 30)(27 35 31)(28 36 32)
(1 12)(2 11)(3 4)(5 6)(7 8)(9 10)(13 14)(15 16)(17 20)(18 19)(21 22)(23 24)(25 28)(26 27)(29 32)(30 31)(33 36)(34 35)
(1 4)(2 9)(3 12)(5 8)(6 7)(10 11)(13 15)(14 16)(17 19)(18 20)(21 23)(22 24)
(1 4)(2 9)(3 12)(5 8)(6 7)(10 11)(25 27)(26 28)(29 31)(30 32)(33 35)(34 36)
(13 14 15 16)(17 18 19 20)(21 22 23 24)(25 26 27 28)(29 30 31 32)(33 34 35 36)
(1 3 4 12)(2 10 9 11)(5 7 8 6)(13 14 15 16)(17 18 19 20)(21 22 23 24)(25 27)(26 28)(29 31)(30 32)(33 35)(34 36)
(1 26 14)(2 36 17)(3 25 15)(4 28 16)(5 30 22)(6 31 21)(7 29 23)(8 32 24)(9 34 19)(10 35 18)(11 33 20)(12 27 13)
G:=sub<Sym(36)| (1,9,5)(2,8,4)(3,11,7)(6,12,10)(13,18,21)(14,19,22)(15,20,23)(16,17,24)(25,33,29)(26,34,30)(27,35,31)(28,36,32), (1,12)(2,11)(3,4)(5,6)(7,8)(9,10)(13,14)(15,16)(17,20)(18,19)(21,22)(23,24)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35), (1,4)(2,9)(3,12)(5,8)(6,7)(10,11)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24), (1,4)(2,9)(3,12)(5,8)(6,7)(10,11)(25,27)(26,28)(29,31)(30,32)(33,35)(34,36), (13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)(29,30,31,32)(33,34,35,36), (1,3,4,12)(2,10,9,11)(5,7,8,6)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,27)(26,28)(29,31)(30,32)(33,35)(34,36), (1,26,14)(2,36,17)(3,25,15)(4,28,16)(5,30,22)(6,31,21)(7,29,23)(8,32,24)(9,34,19)(10,35,18)(11,33,20)(12,27,13)>;
G:=Group( (1,9,5)(2,8,4)(3,11,7)(6,12,10)(13,18,21)(14,19,22)(15,20,23)(16,17,24)(25,33,29)(26,34,30)(27,35,31)(28,36,32), (1,12)(2,11)(3,4)(5,6)(7,8)(9,10)(13,14)(15,16)(17,20)(18,19)(21,22)(23,24)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35), (1,4)(2,9)(3,12)(5,8)(6,7)(10,11)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24), (1,4)(2,9)(3,12)(5,8)(6,7)(10,11)(25,27)(26,28)(29,31)(30,32)(33,35)(34,36), (13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)(29,30,31,32)(33,34,35,36), (1,3,4,12)(2,10,9,11)(5,7,8,6)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,27)(26,28)(29,31)(30,32)(33,35)(34,36), (1,26,14)(2,36,17)(3,25,15)(4,28,16)(5,30,22)(6,31,21)(7,29,23)(8,32,24)(9,34,19)(10,35,18)(11,33,20)(12,27,13) );
G=PermutationGroup([[(1,9,5),(2,8,4),(3,11,7),(6,12,10),(13,18,21),(14,19,22),(15,20,23),(16,17,24),(25,33,29),(26,34,30),(27,35,31),(28,36,32)], [(1,12),(2,11),(3,4),(5,6),(7,8),(9,10),(13,14),(15,16),(17,20),(18,19),(21,22),(23,24),(25,28),(26,27),(29,32),(30,31),(33,36),(34,35)], [(1,4),(2,9),(3,12),(5,8),(6,7),(10,11),(13,15),(14,16),(17,19),(18,20),(21,23),(22,24)], [(1,4),(2,9),(3,12),(5,8),(6,7),(10,11),(25,27),(26,28),(29,31),(30,32),(33,35),(34,36)], [(13,14,15,16),(17,18,19,20),(21,22,23,24),(25,26,27,28),(29,30,31,32),(33,34,35,36)], [(1,3,4,12),(2,10,9,11),(5,7,8,6),(13,14,15,16),(17,18,19,20),(21,22,23,24),(25,27),(26,28),(29,31),(30,32),(33,35),(34,36)], [(1,26,14),(2,36,17),(3,25,15),(4,28,16),(5,30,22),(6,31,21),(7,29,23),(8,32,24),(9,34,19),(10,35,18),(11,33,20),(12,27,13)]])
Matrix representation of C3×C23.A4 ►in GL9(𝔽13)
| 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 3 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 11 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 12 | 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 12 |
| 12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 12 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 2 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 1 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 1 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 12 | 1 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 12 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 12 | 0 | 12 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 2 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 12 | 1 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 12 |
| 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 9 | 4 | 5 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 9 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 11 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 12 | 1 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 12 | 0 |
G:=sub<GL(9,GF(13))| [3,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,11,12,12,12,12,12,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,12,0,0,0,12,12,0,0,0,0,12,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,12],[12,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,12,12,12,12,12,0,0,0,0,2,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,1,0],[1,0,12,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,12,12,0,12,0,0,0,0,0,2,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,12],[0,9,0,0,0,0,0,0,0,4,4,0,0,0,0,0,0,0,0,5,9,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,11,12,12,12,12,12,0,0,0,0,1,0,0,0,0] >;
C3×C23.A4 in GAP, Magma, Sage, TeX
C_3\times C_2^3.A_4
% in TeX
G:=Group("C3xC2^3.A4"); // GroupNames label
G:=SmallGroup(288,636);
// by ID
G=gap.SmallGroup(288,636);
# by ID
G:=PCGroup([7,-2,-3,-3,-2,2,-2,2,6555,514,360,3784,3476,102,3036,5305]);
// Polycyclic
G:=Group<a,b,c,d,e,f,g|a^3=b^2=c^2=d^2=g^3=1,e^2=d*c=g*c*g^-1=c*d,f^2=g*d*g^-1=c,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,a*g=g*a,f*b*f^-1=b*c=c*b,b*d=d*b,e*b*e^-1=b*c*d,b*g=g*b,c*e=e*c,c*f=f*c,g*f*g^-1=d*e=e*d,d*f=f*d,e*f=f*e,g*e*g^-1=c*e*f>;
// generators/relations
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