non-abelian, soluble, monomial
Aliases: (S32)⋊C4, C2.1S3≀C2, C3⋊S3.2D4, (C3×C6).1D4, C32⋊(C22⋊C4), C6.D6⋊4C2, (C2×S32).C2, C3⋊S3.2(C2×C4), (C2×C32⋊C4)⋊1C2, (C2×C3⋊S3).1C22, SmallGroup(144,115)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (S32)⋊C4
G = < a,b,c,d,e | a3=b2=c3=d2=e4=1, bab=ece-1=a-1, ac=ca, ad=da, eae-1=dcd=c-1, bc=cb, bd=db, ebe-1=d, ede-1=b >
Subgroups: 278 in 58 conjugacy classes, 13 normal (11 characteristic)
C1, C2, C2 [×4], C3 [×2], C4 [×2], C22 [×5], S3 [×6], C6 [×4], C2×C4 [×2], C23, C32, Dic3, C12, D6 [×7], C2×C6, C22⋊C4, C3×S3 [×2], C3⋊S3 [×2], C3×C6, C4×S3, C22×S3, C3×Dic3, C32⋊C4, S32 [×2], S32, S3×C6, C2×C3⋊S3, C6.D6, C2×C32⋊C4, C2×S32, (S32)⋊C4
Quotients: C1, C2 [×3], C4 [×2], C22, C2×C4, D4 [×2], C22⋊C4, S3≀C2, (S32)⋊C4
Character table of (S32)⋊C4
| class | 1 | 2A | 2B | 2C | 2D | 2E | 3A | 3B | 4A | 4B | 4C | 4D | 6A | 6B | 6C | 6D | 12A | 12B | |
| size | 1 | 1 | 6 | 6 | 9 | 9 | 4 | 4 | 6 | 6 | 18 | 18 | 4 | 4 | 12 | 12 | 12 | 12 | |
| ρ1 | 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 | linear of order 2 |
| ρ3 | 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 | linear of order 2 |
| ρ5 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | 1 | -i | i | -i | i | -1 | -1 | 1 | -1 | -i | i | linear of order 4 |
| ρ6 | 1 | -1 | -1 | 1 | 1 | -1 | 1 | 1 | i | -i | -i | i | -1 | -1 | -1 | 1 | i | -i | linear of order 4 |
| ρ7 | 1 | -1 | -1 | 1 | 1 | -1 | 1 | 1 | -i | i | i | -i | -1 | -1 | -1 | 1 | -i | i | linear of order 4 |
| ρ8 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | 1 | i | -i | i | -i | -1 | -1 | 1 | -1 | i | -i | linear of order 4 |
| ρ9 | 2 | 2 | 0 | 0 | -2 | -2 | 2 | 2 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ10 | 2 | -2 | 0 | 0 | -2 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ11 | 4 | -4 | 2 | -2 | 0 | 0 | 1 | -2 | 0 | 0 | 0 | 0 | 2 | -1 | -1 | 1 | 0 | 0 | orthogonal faithful |
| ρ12 | 4 | -4 | -2 | 2 | 0 | 0 | 1 | -2 | 0 | 0 | 0 | 0 | 2 | -1 | 1 | -1 | 0 | 0 | orthogonal faithful |
| ρ13 | 4 | 4 | 0 | 0 | 0 | 0 | -2 | 1 | -2 | -2 | 0 | 0 | 1 | -2 | 0 | 0 | 1 | 1 | orthogonal lifted from S3≀C2 |
| ρ14 | 4 | 4 | 2 | 2 | 0 | 0 | 1 | -2 | 0 | 0 | 0 | 0 | -2 | 1 | -1 | -1 | 0 | 0 | orthogonal lifted from S3≀C2 |
| ρ15 | 4 | 4 | 0 | 0 | 0 | 0 | -2 | 1 | 2 | 2 | 0 | 0 | 1 | -2 | 0 | 0 | -1 | -1 | orthogonal lifted from S3≀C2 |
| ρ16 | 4 | 4 | -2 | -2 | 0 | 0 | 1 | -2 | 0 | 0 | 0 | 0 | -2 | 1 | 1 | 1 | 0 | 0 | orthogonal lifted from S3≀C2 |
| ρ17 | 4 | -4 | 0 | 0 | 0 | 0 | -2 | 1 | 2i | -2i | 0 | 0 | -1 | 2 | 0 | 0 | -i | i | complex faithful |
| ρ18 | 4 | -4 | 0 | 0 | 0 | 0 | -2 | 1 | -2i | 2i | 0 | 0 | -1 | 2 | 0 | 0 | i | -i | complex faithful |
►On 12 points - transitive group 12T79
Generators in S12
(2 5 10)(4 7 12)
(5 10)(7 12)
(1 9 8)(3 11 6)
(6 11)(8 9)
(1 2 3 4)(5 6 7 8)(9 10 11 12)
G:=sub<Sym(12)| (2,5,10)(4,7,12), (5,10)(7,12), (1,9,8)(3,11,6), (6,11)(8,9), (1,2,3,4)(5,6,7,8)(9,10,11,12)>;
G:=Group( (2,5,10)(4,7,12), (5,10)(7,12), (1,9,8)(3,11,6), (6,11)(8,9), (1,2,3,4)(5,6,7,8)(9,10,11,12) );
G=PermutationGroup([(2,5,10),(4,7,12)], [(5,10),(7,12)], [(1,9,8),(3,11,6)], [(6,11),(8,9)], [(1,2,3,4),(5,6,7,8),(9,10,11,12)])
G:=TransitiveGroup(12,79);
►On 12 points - transitive group 12T80
Generators in S12
(1 8 9)(3 6 11)
(2 4)(5 7)(6 11)(8 9)(10 12)
(2 10 5)(4 12 7)
(1 3)(5 10)(6 8)(7 12)(9 11)
(1 2 3 4)(5 6 7 8)(9 10 11 12)
G:=sub<Sym(12)| (1,8,9)(3,6,11), (2,4)(5,7)(6,11)(8,9)(10,12), (2,10,5)(4,12,7), (1,3)(5,10)(6,8)(7,12)(9,11), (1,2,3,4)(5,6,7,8)(9,10,11,12)>;
G:=Group( (1,8,9)(3,6,11), (2,4)(5,7)(6,11)(8,9)(10,12), (2,10,5)(4,12,7), (1,3)(5,10)(6,8)(7,12)(9,11), (1,2,3,4)(5,6,7,8)(9,10,11,12) );
G=PermutationGroup([(1,8,9),(3,6,11)], [(2,4),(5,7),(6,11),(8,9),(10,12)], [(2,10,5),(4,12,7)], [(1,3),(5,10),(6,8),(7,12),(9,11)], [(1,2,3,4),(5,6,7,8),(9,10,11,12)])
G:=TransitiveGroup(12,80);
►On 24 points - transitive group 24T213
Generators in S24
(1 15 20)(2 16 17)(3 13 18)(4 14 19)(5 23 10)(6 11 24)(7 21 12)(8 9 22)
(1 22)(2 23)(3 24)(4 21)(5 16)(6 18)(7 14)(8 20)(9 15)(10 17)(11 13)(12 19)
(1 20 15)(2 17 16)(3 18 13)(4 19 14)(5 23 10)(6 11 24)(7 21 12)(8 9 22)
(1 22)(2 23)(3 24)(4 21)(5 17)(6 13)(7 19)(8 15)(9 20)(10 16)(11 18)(12 14)
(1 2 3 4)(5 6 7 8)(9 10 11 12)(13 14 15 16)(17 18 19 20)(21 22 23 24)
G:=sub<Sym(24)| (1,15,20)(2,16,17)(3,13,18)(4,14,19)(5,23,10)(6,11,24)(7,21,12)(8,9,22), (1,22)(2,23)(3,24)(4,21)(5,16)(6,18)(7,14)(8,20)(9,15)(10,17)(11,13)(12,19), (1,20,15)(2,17,16)(3,18,13)(4,19,14)(5,23,10)(6,11,24)(7,21,12)(8,9,22), (1,22)(2,23)(3,24)(4,21)(5,17)(6,13)(7,19)(8,15)(9,20)(10,16)(11,18)(12,14), (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)>;
G:=Group( (1,15,20)(2,16,17)(3,13,18)(4,14,19)(5,23,10)(6,11,24)(7,21,12)(8,9,22), (1,22)(2,23)(3,24)(4,21)(5,16)(6,18)(7,14)(8,20)(9,15)(10,17)(11,13)(12,19), (1,20,15)(2,17,16)(3,18,13)(4,19,14)(5,23,10)(6,11,24)(7,21,12)(8,9,22), (1,22)(2,23)(3,24)(4,21)(5,17)(6,13)(7,19)(8,15)(9,20)(10,16)(11,18)(12,14), (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24) );
G=PermutationGroup([(1,15,20),(2,16,17),(3,13,18),(4,14,19),(5,23,10),(6,11,24),(7,21,12),(8,9,22)], [(1,22),(2,23),(3,24),(4,21),(5,16),(6,18),(7,14),(8,20),(9,15),(10,17),(11,13),(12,19)], [(1,20,15),(2,17,16),(3,18,13),(4,19,14),(5,23,10),(6,11,24),(7,21,12),(8,9,22)], [(1,22),(2,23),(3,24),(4,21),(5,17),(6,13),(7,19),(8,15),(9,20),(10,16),(11,18),(12,14)], [(1,2,3,4),(5,6,7,8),(9,10,11,12),(13,14,15,16),(17,18,19,20),(21,22,23,24)])
G:=TransitiveGroup(24,213);
►On 24 points - transitive group 24T215
Generators in S24
(1 18 13)(2 19 14)(3 20 15)(4 17 16)(5 21 10)(6 11 22)(7 23 12)(8 9 24)
(1 22)(2 21)(3 24)(4 23)(5 19)(6 13)(7 17)(8 15)(9 20)(10 14)(11 18)(12 16)
(1 13 18)(2 14 19)(3 15 20)(4 16 17)(5 21 10)(6 11 22)(7 23 12)(8 9 24)
(1 24)(2 23)(3 22)(4 21)(5 16)(6 20)(7 14)(8 18)(9 13)(10 17)(11 15)(12 19)
(1 2 3 4)(5 6 7 8)(9 10 11 12)(13 14 15 16)(17 18 19 20)(21 22 23 24)
G:=sub<Sym(24)| (1,18,13)(2,19,14)(3,20,15)(4,17,16)(5,21,10)(6,11,22)(7,23,12)(8,9,24), (1,22)(2,21)(3,24)(4,23)(5,19)(6,13)(7,17)(8,15)(9,20)(10,14)(11,18)(12,16), (1,13,18)(2,14,19)(3,15,20)(4,16,17)(5,21,10)(6,11,22)(7,23,12)(8,9,24), (1,24)(2,23)(3,22)(4,21)(5,16)(6,20)(7,14)(8,18)(9,13)(10,17)(11,15)(12,19), (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)>;
G:=Group( (1,18,13)(2,19,14)(3,20,15)(4,17,16)(5,21,10)(6,11,22)(7,23,12)(8,9,24), (1,22)(2,21)(3,24)(4,23)(5,19)(6,13)(7,17)(8,15)(9,20)(10,14)(11,18)(12,16), (1,13,18)(2,14,19)(3,15,20)(4,16,17)(5,21,10)(6,11,22)(7,23,12)(8,9,24), (1,24)(2,23)(3,22)(4,21)(5,16)(6,20)(7,14)(8,18)(9,13)(10,17)(11,15)(12,19), (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24) );
G=PermutationGroup([(1,18,13),(2,19,14),(3,20,15),(4,17,16),(5,21,10),(6,11,22),(7,23,12),(8,9,24)], [(1,22),(2,21),(3,24),(4,23),(5,19),(6,13),(7,17),(8,15),(9,20),(10,14),(11,18),(12,16)], [(1,13,18),(2,14,19),(3,15,20),(4,16,17),(5,21,10),(6,11,22),(7,23,12),(8,9,24)], [(1,24),(2,23),(3,22),(4,21),(5,16),(6,20),(7,14),(8,18),(9,13),(10,17),(11,15),(12,19)], [(1,2,3,4),(5,6,7,8),(9,10,11,12),(13,14,15,16),(17,18,19,20),(21,22,23,24)])
G:=TransitiveGroup(24,215);
►On 24 points - transitive group 24T265
Generators in S24
(2 10 6)(4 12 8)(14 24 20)(16 22 18)
(1 3)(2 20)(4 18)(5 7)(6 14)(8 16)(9 11)(10 24)(12 22)(13 15)(17 19)(21 23)
(1 5 9)(3 7 11)(13 19 23)(15 17 21)
(1 19)(2 4)(3 17)(5 13)(6 8)(7 15)(9 23)(10 12)(11 21)(14 16)(18 20)(22 24)
(1 2 3 4)(5 6 7 8)(9 10 11 12)(13 14 15 16)(17 18 19 20)(21 22 23 24)
G:=sub<Sym(24)| (2,10,6)(4,12,8)(14,24,20)(16,22,18), (1,3)(2,20)(4,18)(5,7)(6,14)(8,16)(9,11)(10,24)(12,22)(13,15)(17,19)(21,23), (1,5,9)(3,7,11)(13,19,23)(15,17,21), (1,19)(2,4)(3,17)(5,13)(6,8)(7,15)(9,23)(10,12)(11,21)(14,16)(18,20)(22,24), (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)>;
G:=Group( (2,10,6)(4,12,8)(14,24,20)(16,22,18), (1,3)(2,20)(4,18)(5,7)(6,14)(8,16)(9,11)(10,24)(12,22)(13,15)(17,19)(21,23), (1,5,9)(3,7,11)(13,19,23)(15,17,21), (1,19)(2,4)(3,17)(5,13)(6,8)(7,15)(9,23)(10,12)(11,21)(14,16)(18,20)(22,24), (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24) );
G=PermutationGroup([(2,10,6),(4,12,8),(14,24,20),(16,22,18)], [(1,3),(2,20),(4,18),(5,7),(6,14),(8,16),(9,11),(10,24),(12,22),(13,15),(17,19),(21,23)], [(1,5,9),(3,7,11),(13,19,23),(15,17,21)], [(1,19),(2,4),(3,17),(5,13),(6,8),(7,15),(9,23),(10,12),(11,21),(14,16),(18,20),(22,24)], [(1,2,3,4),(5,6,7,8),(9,10,11,12),(13,14,15,16),(17,18,19,20),(21,22,23,24)])
G:=TransitiveGroup(24,265);
►On 24 points - transitive group 24T266
Generators in S24
(1 9 5)(3 11 7)(13 23 19)(15 21 17)
(2 18)(4 20)(5 9)(6 22)(7 11)(8 24)(10 16)(12 14)(13 23)(15 21)
(2 6 10)(4 8 12)(14 20 24)(16 18 22)
(1 17)(3 19)(5 21)(6 10)(7 23)(8 12)(9 15)(11 13)(14 24)(16 22)
(1 2 3 4)(5 6 7 8)(9 10 11 12)(13 14 15 16)(17 18 19 20)(21 22 23 24)
G:=sub<Sym(24)| (1,9,5)(3,11,7)(13,23,19)(15,21,17), (2,18)(4,20)(5,9)(6,22)(7,11)(8,24)(10,16)(12,14)(13,23)(15,21), (2,6,10)(4,8,12)(14,20,24)(16,18,22), (1,17)(3,19)(5,21)(6,10)(7,23)(8,12)(9,15)(11,13)(14,24)(16,22), (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)>;
G:=Group( (1,9,5)(3,11,7)(13,23,19)(15,21,17), (2,18)(4,20)(5,9)(6,22)(7,11)(8,24)(10,16)(12,14)(13,23)(15,21), (2,6,10)(4,8,12)(14,20,24)(16,18,22), (1,17)(3,19)(5,21)(6,10)(7,23)(8,12)(9,15)(11,13)(14,24)(16,22), (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24) );
G=PermutationGroup([(1,9,5),(3,11,7),(13,23,19),(15,21,17)], [(2,18),(4,20),(5,9),(6,22),(7,11),(8,24),(10,16),(12,14),(13,23),(15,21)], [(2,6,10),(4,8,12),(14,20,24),(16,18,22)], [(1,17),(3,19),(5,21),(6,10),(7,23),(8,12),(9,15),(11,13),(14,24),(16,22)], [(1,2,3,4),(5,6,7,8),(9,10,11,12),(13,14,15,16),(17,18,19,20),(21,22,23,24)])
G:=TransitiveGroup(24,266);
►On 24 points - transitive group 24T267
Generators in S24
(2 16 17)(4 14 19)(5 23 10)(7 21 12)
(1 22)(2 23)(3 24)(4 21)(5 16)(6 18)(7 14)(8 20)(9 15)(10 17)(11 13)(12 19)
(1 20 15)(3 18 13)(6 11 24)(8 9 22)
(1 22)(2 23)(3 24)(4 21)(5 17)(6 13)(7 19)(8 15)(9 20)(10 16)(11 18)(12 14)
(1 2 3 4)(5 6 7 8)(9 10 11 12)(13 14 15 16)(17 18 19 20)(21 22 23 24)
G:=sub<Sym(24)| (2,16,17)(4,14,19)(5,23,10)(7,21,12), (1,22)(2,23)(3,24)(4,21)(5,16)(6,18)(7,14)(8,20)(9,15)(10,17)(11,13)(12,19), (1,20,15)(3,18,13)(6,11,24)(8,9,22), (1,22)(2,23)(3,24)(4,21)(5,17)(6,13)(7,19)(8,15)(9,20)(10,16)(11,18)(12,14), (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)>;
G:=Group( (2,16,17)(4,14,19)(5,23,10)(7,21,12), (1,22)(2,23)(3,24)(4,21)(5,16)(6,18)(7,14)(8,20)(9,15)(10,17)(11,13)(12,19), (1,20,15)(3,18,13)(6,11,24)(8,9,22), (1,22)(2,23)(3,24)(4,21)(5,17)(6,13)(7,19)(8,15)(9,20)(10,16)(11,18)(12,14), (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24) );
G=PermutationGroup([(2,16,17),(4,14,19),(5,23,10),(7,21,12)], [(1,22),(2,23),(3,24),(4,21),(5,16),(6,18),(7,14),(8,20),(9,15),(10,17),(11,13),(12,19)], [(1,20,15),(3,18,13),(6,11,24),(8,9,22)], [(1,22),(2,23),(3,24),(4,21),(5,17),(6,13),(7,19),(8,15),(9,20),(10,16),(11,18),(12,14)], [(1,2,3,4),(5,6,7,8),(9,10,11,12),(13,14,15,16),(17,18,19,20),(21,22,23,24)])
G:=TransitiveGroup(24,267);
►On 24 points - transitive group 24T268
Generators in S24
(2 19 14)(4 17 16)(5 21 10)(7 23 12)
(1 22)(2 21)(3 24)(4 23)(5 19)(6 13)(7 17)(8 15)(9 20)(10 14)(11 18)(12 16)
(1 13 18)(3 15 20)(6 11 22)(8 9 24)
(1 24)(2 23)(3 22)(4 21)(5 16)(6 20)(7 14)(8 18)(9 13)(10 17)(11 15)(12 19)
(1 2 3 4)(5 6 7 8)(9 10 11 12)(13 14 15 16)(17 18 19 20)(21 22 23 24)
G:=sub<Sym(24)| (2,19,14)(4,17,16)(5,21,10)(7,23,12), (1,22)(2,21)(3,24)(4,23)(5,19)(6,13)(7,17)(8,15)(9,20)(10,14)(11,18)(12,16), (1,13,18)(3,15,20)(6,11,22)(8,9,24), (1,24)(2,23)(3,22)(4,21)(5,16)(6,20)(7,14)(8,18)(9,13)(10,17)(11,15)(12,19), (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)>;
G:=Group( (2,19,14)(4,17,16)(5,21,10)(7,23,12), (1,22)(2,21)(3,24)(4,23)(5,19)(6,13)(7,17)(8,15)(9,20)(10,14)(11,18)(12,16), (1,13,18)(3,15,20)(6,11,22)(8,9,24), (1,24)(2,23)(3,22)(4,21)(5,16)(6,20)(7,14)(8,18)(9,13)(10,17)(11,15)(12,19), (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24) );
G=PermutationGroup([(2,19,14),(4,17,16),(5,21,10),(7,23,12)], [(1,22),(2,21),(3,24),(4,23),(5,19),(6,13),(7,17),(8,15),(9,20),(10,14),(11,18),(12,16)], [(1,13,18),(3,15,20),(6,11,22),(8,9,24)], [(1,24),(2,23),(3,22),(4,21),(5,16),(6,20),(7,14),(8,18),(9,13),(10,17),(11,15),(12,19)], [(1,2,3,4),(5,6,7,8),(9,10,11,12),(13,14,15,16),(17,18,19,20),(21,22,23,24)])
G:=TransitiveGroup(24,268);
Polynomial with Galois group (S32)⋊C4 over ℚ
| action | f(x) | Disc(f) |
|---|---|---|
| 12T79 | x12-16x10+96x8-260x6+288x4-64x2+2 | 235·1032·1912 |
| 12T80 | x12-16x9-36x8-24x7-136x6+210x4-128x3-72x2+96x-8 | -251·324·5692·2578672 |
Matrix representation of (S32)⋊C4 ►in GL4(ℤ) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | -1 | -1 |
| 0 | 0 | 1 | 0 |
| -1 | 0 | 0 | 0 |
| 0 | -1 | 0 | 0 |
| 0 | 0 | -1 | 0 |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 0 |
| -1 | -1 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| -1 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 |
| 0 | 0 | -1 | 0 |
| 0 | 0 | 0 | -1 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| -1 | 0 | 0 | 0 |
| 0 | -1 | 0 | 0 |
G:=sub<GL(4,Integers())| [1,0,0,0,0,1,0,0,0,0,-1,1,0,0,-1,0],[-1,0,0,0,0,-1,0,0,0,0,-1,1,0,0,0,1],[0,-1,0,0,1,-1,0,0,0,0,1,0,0,0,0,1],[-1,1,0,0,0,1,0,0,0,0,-1,0,0,0,0,-1],[0,0,-1,0,0,0,0,-1,1,0,0,0,0,1,0,0] >;
(S32)⋊C4 in GAP, Magma, Sage, TeX
(S_3^2)\rtimes C_4
% in TeX
G:=Group("(S3^2):C4"); // GroupNames label
G:=SmallGroup(144,115);
// by ID
G=gap.SmallGroup(144,115);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-3,3,73,55,964,730,256,299,881]);
// Polycyclic
G:=Group<a,b,c,d,e|a^3=b^2=c^3=d^2=e^4=1,b*a*b=e*c*e^-1=a^-1,a*c=c*a,a*d=d*a,e*a*e^-1=d*c*d=c^-1,b*c=c*b,b*d=d*b,e*b*e^-1=d,e*d*e^-1=b>;
// generators/relations