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## G = C24.2A4order 192 = 26·3

### 2nd non-split extension by C24 of A4 acting faithfully

Aliases: C24.2A4, C23.2SL2(𝔽3), C23.Q8⋊C3, C23.17(C2×A4), C2.C421C6, C23.3A42C2, C2.2(C42⋊C6), C22.3(C2×SL2(𝔽3)), SmallGroup(192,197)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2 — C2.C42 — C24.2A4
 Chief series C1 — C2 — C23 — C2.C42 — C23.3A4 — C24.2A4
 Lower central C2.C42 — C24.2A4
 Upper central C1 — C2

Generators and relations for C24.2A4
G = < a,b,c,d,e,f,g | a2=b2=c2=d2=g3=1, e2=gbg-1=bcd, f2=gcg-1=b, ab=ba, ac=ca, ad=da, eae-1=abd, faf-1=acd, ag=ga, bc=cb, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, fef-1=de=ed, df=fd, dg=gd, geg-1=bef, gfg-1=cde >

Character table of C24.2A4

 class 1 2A 2B 2C 2D 2E 3A 3B 4A 4B 4C 4D 6A 6B 6C 6D 6E 6F size 1 1 3 3 4 4 16 16 12 12 12 12 16 16 16 16 16 16 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 ζ3 ζ32 1 1 1 1 ζ32 ζ32 ζ3 ζ3 ζ32 ζ3 linear of order 3 ρ4 1 1 1 1 -1 -1 ζ32 ζ3 1 1 -1 -1 ζ65 ζ3 ζ6 ζ6 ζ65 ζ32 linear of order 6 ρ5 1 1 1 1 1 1 ζ32 ζ3 1 1 1 1 ζ3 ζ3 ζ32 ζ32 ζ3 ζ32 linear of order 3 ρ6 1 1 1 1 -1 -1 ζ3 ζ32 1 1 -1 -1 ζ6 ζ32 ζ65 ζ65 ζ6 ζ3 linear of order 6 ρ7 2 -2 2 -2 2 -2 -1 -1 0 0 0 0 -1 1 1 -1 1 1 symplectic lifted from SL2(𝔽3), Schur index 2 ρ8 2 -2 2 -2 -2 2 -1 -1 0 0 0 0 1 1 -1 1 -1 1 symplectic lifted from SL2(𝔽3), Schur index 2 ρ9 2 -2 2 -2 -2 2 ζ6 ζ65 0 0 0 0 ζ3 ζ3 ζ6 ζ32 ζ65 ζ32 complex lifted from SL2(𝔽3) ρ10 2 -2 2 -2 -2 2 ζ65 ζ6 0 0 0 0 ζ32 ζ32 ζ65 ζ3 ζ6 ζ3 complex lifted from SL2(𝔽3) ρ11 2 -2 2 -2 2 -2 ζ6 ζ65 0 0 0 0 ζ65 ζ3 ζ32 ζ6 ζ3 ζ32 complex lifted from SL2(𝔽3) ρ12 2 -2 2 -2 2 -2 ζ65 ζ6 0 0 0 0 ζ6 ζ32 ζ3 ζ65 ζ32 ζ3 complex lifted from SL2(𝔽3) ρ13 3 3 3 3 -3 -3 0 0 -1 -1 1 1 0 0 0 0 0 0 orthogonal lifted from C2×A4 ρ14 3 3 3 3 3 3 0 0 -1 -1 -1 -1 0 0 0 0 0 0 orthogonal lifted from A4 ρ15 6 -6 -2 2 0 0 0 0 0 0 2 -2 0 0 0 0 0 0 orthogonal faithful ρ16 6 -6 -2 2 0 0 0 0 0 0 -2 2 0 0 0 0 0 0 orthogonal faithful ρ17 6 6 -2 -2 0 0 0 0 2i -2i 0 0 0 0 0 0 0 0 complex lifted from C42⋊C6 ρ18 6 6 -2 -2 0 0 0 0 -2i 2i 0 0 0 0 0 0 0 0 complex lifted from C42⋊C6

Permutation representations of C24.2A4
On 12 points - transitive group 12T91
Generators in S12
```(1 4)(2 3)(5 6)(7 8)(9 10)(11 12)
(5 7)(6 8)
(1 2)(3 4)
(1 2)(3 4)(5 7)(6 8)(9 11)(10 12)
(3 4)(5 6)(7 8)(9 10 11 12)
(1 3)(2 4)(5 6 7 8)(9 11)
(1 10 7)(2 12 5)(3 11 6)(4 9 8)```

`G:=sub<Sym(12)| (1,4)(2,3)(5,6)(7,8)(9,10)(11,12), (5,7)(6,8), (1,2)(3,4), (1,2)(3,4)(5,7)(6,8)(9,11)(10,12), (3,4)(5,6)(7,8)(9,10,11,12), (1,3)(2,4)(5,6,7,8)(9,11), (1,10,7)(2,12,5)(3,11,6)(4,9,8)>;`

`G:=Group( (1,4)(2,3)(5,6)(7,8)(9,10)(11,12), (5,7)(6,8), (1,2)(3,4), (1,2)(3,4)(5,7)(6,8)(9,11)(10,12), (3,4)(5,6)(7,8)(9,10,11,12), (1,3)(2,4)(5,6,7,8)(9,11), (1,10,7)(2,12,5)(3,11,6)(4,9,8) );`

`G=PermutationGroup([[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)], [(5,7),(6,8)], [(1,2),(3,4)], [(1,2),(3,4),(5,7),(6,8),(9,11),(10,12)], [(3,4),(5,6),(7,8),(9,10,11,12)], [(1,3),(2,4),(5,6,7,8),(9,11)], [(1,10,7),(2,12,5),(3,11,6),(4,9,8)]])`

`G:=TransitiveGroup(12,91);`

On 12 points - transitive group 12T93
Generators in S12
```(3 8)(5 6)(10 12)
(1 2)(5 6)
(3 8)(4 7)
(1 2)(3 8)(4 7)(5 6)(9 11)(10 12)
(3 4)(5 6)(7 8)(9 10 11 12)
(1 5 2 6)(4 7)(9 10)(11 12)
(1 7 9)(2 4 11)(3 12 5)(6 8 10)```

`G:=sub<Sym(12)| (3,8)(5,6)(10,12), (1,2)(5,6), (3,8)(4,7), (1,2)(3,8)(4,7)(5,6)(9,11)(10,12), (3,4)(5,6)(7,8)(9,10,11,12), (1,5,2,6)(4,7)(9,10)(11,12), (1,7,9)(2,4,11)(3,12,5)(6,8,10)>;`

`G:=Group( (3,8)(5,6)(10,12), (1,2)(5,6), (3,8)(4,7), (1,2)(3,8)(4,7)(5,6)(9,11)(10,12), (3,4)(5,6)(7,8)(9,10,11,12), (1,5,2,6)(4,7)(9,10)(11,12), (1,7,9)(2,4,11)(3,12,5)(6,8,10) );`

`G=PermutationGroup([[(3,8),(5,6),(10,12)], [(1,2),(5,6)], [(3,8),(4,7)], [(1,2),(3,8),(4,7),(5,6),(9,11),(10,12)], [(3,4),(5,6),(7,8),(9,10,11,12)], [(1,5,2,6),(4,7),(9,10),(11,12)], [(1,7,9),(2,4,11),(3,12,5),(6,8,10)]])`

`G:=TransitiveGroup(12,93);`

On 24 points - transitive group 24T460
Generators in S24
```(1 7)(2 14)(3 8)(4 13)(5 15)(6 16)(9 12)(10 11)(17 22)(18 21)(19 24)(20 23)
(5 10)(6 9)(11 15)(12 16)
(1 3)(2 4)(7 8)(13 14)
(1 3)(2 4)(5 10)(6 9)(7 8)(11 15)(12 16)(13 14)(17 19)(18 20)(21 23)(22 24)
(5 6)(7 8)(9 10)(11 12)(13 14)(15 16)(17 18 19 20)(21 22 23 24)
(1 13)(2 8)(3 14)(4 7)(5 9 10 6)(11 12 15 16)(17 19)(21 23)
(1 18 6)(2 22 15)(3 20 9)(4 24 11)(5 14 17)(7 21 16)(8 23 12)(10 13 19)```

`G:=sub<Sym(24)| (1,7)(2,14)(3,8)(4,13)(5,15)(6,16)(9,12)(10,11)(17,22)(18,21)(19,24)(20,23), (5,10)(6,9)(11,15)(12,16), (1,3)(2,4)(7,8)(13,14), (1,3)(2,4)(5,10)(6,9)(7,8)(11,15)(12,16)(13,14)(17,19)(18,20)(21,23)(22,24), (5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18,19,20)(21,22,23,24), (1,13)(2,8)(3,14)(4,7)(5,9,10,6)(11,12,15,16)(17,19)(21,23), (1,18,6)(2,22,15)(3,20,9)(4,24,11)(5,14,17)(7,21,16)(8,23,12)(10,13,19)>;`

`G:=Group( (1,7)(2,14)(3,8)(4,13)(5,15)(6,16)(9,12)(10,11)(17,22)(18,21)(19,24)(20,23), (5,10)(6,9)(11,15)(12,16), (1,3)(2,4)(7,8)(13,14), (1,3)(2,4)(5,10)(6,9)(7,8)(11,15)(12,16)(13,14)(17,19)(18,20)(21,23)(22,24), (5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18,19,20)(21,22,23,24), (1,13)(2,8)(3,14)(4,7)(5,9,10,6)(11,12,15,16)(17,19)(21,23), (1,18,6)(2,22,15)(3,20,9)(4,24,11)(5,14,17)(7,21,16)(8,23,12)(10,13,19) );`

`G=PermutationGroup([[(1,7),(2,14),(3,8),(4,13),(5,15),(6,16),(9,12),(10,11),(17,22),(18,21),(19,24),(20,23)], [(5,10),(6,9),(11,15),(12,16)], [(1,3),(2,4),(7,8),(13,14)], [(1,3),(2,4),(5,10),(6,9),(7,8),(11,15),(12,16),(13,14),(17,19),(18,20),(21,23),(22,24)], [(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18,19,20),(21,22,23,24)], [(1,13),(2,8),(3,14),(4,7),(5,9,10,6),(11,12,15,16),(17,19),(21,23)], [(1,18,6),(2,22,15),(3,20,9),(4,24,11),(5,14,17),(7,21,16),(8,23,12),(10,13,19)]])`

`G:=TransitiveGroup(24,460);`

On 24 points - transitive group 24T461
Generators in S24
```(1 2)(3 16)(4 14)(5 6)(7 8)(9 10)(11 15)(12 13)(17 22)(18 21)(19 24)(20 23)
(1 6)(2 5)(7 9)(8 10)
(3 12)(4 11)(13 16)(14 15)
(1 6)(2 5)(3 12)(4 11)(7 9)(8 10)(13 16)(14 15)(17 19)(18 20)(21 23)(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)
(1 8 6 10)(2 9 5 7)(3 13)(4 15)(11 14)(12 16)(17 23)(18 22)(19 21)(20 24)
(1 13 17)(2 12 22)(3 24 5)(4 20 8)(6 16 19)(7 14 23)(9 15 21)(10 11 18)```

`G:=sub<Sym(24)| (1,2)(3,16)(4,14)(5,6)(7,8)(9,10)(11,15)(12,13)(17,22)(18,21)(19,24)(20,23), (1,6)(2,5)(7,9)(8,10), (3,12)(4,11)(13,16)(14,15), (1,6)(2,5)(3,12)(4,11)(7,9)(8,10)(13,16)(14,15)(17,19)(18,20)(21,23)(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), (1,8,6,10)(2,9,5,7)(3,13)(4,15)(11,14)(12,16)(17,23)(18,22)(19,21)(20,24), (1,13,17)(2,12,22)(3,24,5)(4,20,8)(6,16,19)(7,14,23)(9,15,21)(10,11,18)>;`

`G:=Group( (1,2)(3,16)(4,14)(5,6)(7,8)(9,10)(11,15)(12,13)(17,22)(18,21)(19,24)(20,23), (1,6)(2,5)(7,9)(8,10), (3,12)(4,11)(13,16)(14,15), (1,6)(2,5)(3,12)(4,11)(7,9)(8,10)(13,16)(14,15)(17,19)(18,20)(21,23)(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), (1,8,6,10)(2,9,5,7)(3,13)(4,15)(11,14)(12,16)(17,23)(18,22)(19,21)(20,24), (1,13,17)(2,12,22)(3,24,5)(4,20,8)(6,16,19)(7,14,23)(9,15,21)(10,11,18) );`

`G=PermutationGroup([[(1,2),(3,16),(4,14),(5,6),(7,8),(9,10),(11,15),(12,13),(17,22),(18,21),(19,24),(20,23)], [(1,6),(2,5),(7,9),(8,10)], [(3,12),(4,11),(13,16),(14,15)], [(1,6),(2,5),(3,12),(4,11),(7,9),(8,10),(13,16),(14,15),(17,19),(18,20),(21,23),(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)], [(1,8,6,10),(2,9,5,7),(3,13),(4,15),(11,14),(12,16),(17,23),(18,22),(19,21),(20,24)], [(1,13,17),(2,12,22),(3,24,5),(4,20,8),(6,16,19),(7,14,23),(9,15,21),(10,11,18)]])`

`G:=TransitiveGroup(24,461);`

On 24 points - transitive group 24T462
Generators in S24
```(1 4)(2 3)(5 14)(6 13)(7 11)(8 9)(10 16)(12 15)(17 18)(19 20)(21 22)(23 24)
(1 14)(2 13)(3 6)(4 5)
(7 16)(8 15)(9 12)(10 11)
(1 14)(2 13)(3 6)(4 5)(7 16)(8 15)(9 12)(10 11)(17 19)(18 20)(21 23)(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)
(1 4 14 5)(2 6 13 3)(7 12)(8 10)(9 16)(11 15)(17 21)(18 24)(19 23)(20 22)
(1 16 24)(2 12 17)(3 15 18)(4 10 23)(5 11 21)(6 8 20)(7 22 14)(9 19 13)```

`G:=sub<Sym(24)| (1,4)(2,3)(5,14)(6,13)(7,11)(8,9)(10,16)(12,15)(17,18)(19,20)(21,22)(23,24), (1,14)(2,13)(3,6)(4,5), (7,16)(8,15)(9,12)(10,11), (1,14)(2,13)(3,6)(4,5)(7,16)(8,15)(9,12)(10,11)(17,19)(18,20)(21,23)(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), (1,4,14,5)(2,6,13,3)(7,12)(8,10)(9,16)(11,15)(17,21)(18,24)(19,23)(20,22), (1,16,24)(2,12,17)(3,15,18)(4,10,23)(5,11,21)(6,8,20)(7,22,14)(9,19,13)>;`

`G:=Group( (1,4)(2,3)(5,14)(6,13)(7,11)(8,9)(10,16)(12,15)(17,18)(19,20)(21,22)(23,24), (1,14)(2,13)(3,6)(4,5), (7,16)(8,15)(9,12)(10,11), (1,14)(2,13)(3,6)(4,5)(7,16)(8,15)(9,12)(10,11)(17,19)(18,20)(21,23)(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), (1,4,14,5)(2,6,13,3)(7,12)(8,10)(9,16)(11,15)(17,21)(18,24)(19,23)(20,22), (1,16,24)(2,12,17)(3,15,18)(4,10,23)(5,11,21)(6,8,20)(7,22,14)(9,19,13) );`

`G=PermutationGroup([[(1,4),(2,3),(5,14),(6,13),(7,11),(8,9),(10,16),(12,15),(17,18),(19,20),(21,22),(23,24)], [(1,14),(2,13),(3,6),(4,5)], [(7,16),(8,15),(9,12),(10,11)], [(1,14),(2,13),(3,6),(4,5),(7,16),(8,15),(9,12),(10,11),(17,19),(18,20),(21,23),(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)], [(1,4,14,5),(2,6,13,3),(7,12),(8,10),(9,16),(11,15),(17,21),(18,24),(19,23),(20,22)], [(1,16,24),(2,12,17),(3,15,18),(4,10,23),(5,11,21),(6,8,20),(7,22,14),(9,19,13)]])`

`G:=TransitiveGroup(24,462);`

On 24 points - transitive group 24T467
Generators in S24
```(1 14)(3 8)(4 7)(10 15)(18 20)(22 24)
(3 8)(4 7)(5 12)(6 11)
(1 14)(2 13)(9 16)(10 15)
(1 14)(2 13)(3 8)(4 7)(5 12)(6 11)(9 16)(10 15)(17 19)(18 20)(21 23)(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)
(1 15)(2 9)(3 11 8 6)(4 5 7 12)(10 14)(13 16)(17 24)(18 23)(19 22)(20 21)
(1 18 7)(2 23 11)(3 15 24)(4 14 20)(5 9 19)(6 13 21)(8 10 22)(12 16 17)```

`G:=sub<Sym(24)| (1,14)(3,8)(4,7)(10,15)(18,20)(22,24), (3,8)(4,7)(5,12)(6,11), (1,14)(2,13)(9,16)(10,15), (1,14)(2,13)(3,8)(4,7)(5,12)(6,11)(9,16)(10,15)(17,19)(18,20)(21,23)(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), (1,15)(2,9)(3,11,8,6)(4,5,7,12)(10,14)(13,16)(17,24)(18,23)(19,22)(20,21), (1,18,7)(2,23,11)(3,15,24)(4,14,20)(5,9,19)(6,13,21)(8,10,22)(12,16,17)>;`

`G:=Group( (1,14)(3,8)(4,7)(10,15)(18,20)(22,24), (3,8)(4,7)(5,12)(6,11), (1,14)(2,13)(9,16)(10,15), (1,14)(2,13)(3,8)(4,7)(5,12)(6,11)(9,16)(10,15)(17,19)(18,20)(21,23)(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), (1,15)(2,9)(3,11,8,6)(4,5,7,12)(10,14)(13,16)(17,24)(18,23)(19,22)(20,21), (1,18,7)(2,23,11)(3,15,24)(4,14,20)(5,9,19)(6,13,21)(8,10,22)(12,16,17) );`

`G=PermutationGroup([[(1,14),(3,8),(4,7),(10,15),(18,20),(22,24)], [(3,8),(4,7),(5,12),(6,11)], [(1,14),(2,13),(9,16),(10,15)], [(1,14),(2,13),(3,8),(4,7),(5,12),(6,11),(9,16),(10,15),(17,19),(18,20),(21,23),(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)], [(1,15),(2,9),(3,11,8,6),(4,5,7,12),(10,14),(13,16),(17,24),(18,23),(19,22),(20,21)], [(1,18,7),(2,23,11),(3,15,24),(4,14,20),(5,9,19),(6,13,21),(8,10,22),(12,16,17)]])`

`G:=TransitiveGroup(24,467);`

On 24 points - transitive group 24T468
Generators in S24
```(1 3)(2 4)(5 14)(6 8)(7 10)(9 13)(11 15)(12 16)(17 23)(18 22)(19 21)(20 24)
(1 2)(3 4)(11 12)(15 16)
(5 10)(6 9)(7 14)(8 13)
(1 2)(3 4)(5 10)(6 9)(7 14)(8 13)(11 12)(15 16)(17 19)(18 20)(21 23)(22 24)
(5 6)(7 8)(9 10)(11 12)(13 14)(15 16)(17 18 19 20)(21 22 23 24)
(1 12 2 11)(3 15 4 16)(5 10)(7 14)(17 20)(18 19)(21 24)(22 23)
(1 14 20)(2 7 18)(3 5 24)(4 10 22)(6 21 16)(8 19 12)(9 23 15)(11 13 17)```

`G:=sub<Sym(24)| (1,3)(2,4)(5,14)(6,8)(7,10)(9,13)(11,15)(12,16)(17,23)(18,22)(19,21)(20,24), (1,2)(3,4)(11,12)(15,16), (5,10)(6,9)(7,14)(8,13), (1,2)(3,4)(5,10)(6,9)(7,14)(8,13)(11,12)(15,16)(17,19)(18,20)(21,23)(22,24), (5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18,19,20)(21,22,23,24), (1,12,2,11)(3,15,4,16)(5,10)(7,14)(17,20)(18,19)(21,24)(22,23), (1,14,20)(2,7,18)(3,5,24)(4,10,22)(6,21,16)(8,19,12)(9,23,15)(11,13,17)>;`

`G:=Group( (1,3)(2,4)(5,14)(6,8)(7,10)(9,13)(11,15)(12,16)(17,23)(18,22)(19,21)(20,24), (1,2)(3,4)(11,12)(15,16), (5,10)(6,9)(7,14)(8,13), (1,2)(3,4)(5,10)(6,9)(7,14)(8,13)(11,12)(15,16)(17,19)(18,20)(21,23)(22,24), (5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18,19,20)(21,22,23,24), (1,12,2,11)(3,15,4,16)(5,10)(7,14)(17,20)(18,19)(21,24)(22,23), (1,14,20)(2,7,18)(3,5,24)(4,10,22)(6,21,16)(8,19,12)(9,23,15)(11,13,17) );`

`G=PermutationGroup([[(1,3),(2,4),(5,14),(6,8),(7,10),(9,13),(11,15),(12,16),(17,23),(18,22),(19,21),(20,24)], [(1,2),(3,4),(11,12),(15,16)], [(5,10),(6,9),(7,14),(8,13)], [(1,2),(3,4),(5,10),(6,9),(7,14),(8,13),(11,12),(15,16),(17,19),(18,20),(21,23),(22,24)], [(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18,19,20),(21,22,23,24)], [(1,12,2,11),(3,15,4,16),(5,10),(7,14),(17,20),(18,19),(21,24),(22,23)], [(1,14,20),(2,7,18),(3,5,24),(4,10,22),(6,21,16),(8,19,12),(9,23,15),(11,13,17)]])`

`G:=TransitiveGroup(24,468);`

Polynomial with Galois group C24.2A4 over ℚ
actionf(x)Disc(f)
12T91x12-534x10+78489x8-4839186x6+143348046x4-2021896020x2+10884540241236·316·1730·1930·4235574
12T93x12-30x10+327x8-1566x6+3096x4-1938x2+323224·320·712·175·195

Matrix representation of C24.2A4 in GL6(ℤ)

 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0
,
 1 0 0 0 0 0 0 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
 -1 0 0 0 0 0 0 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
 -1 0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 0 0 0 0 0 0 -1
,
 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 1 0
,
 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 -1
,
 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0

`G:=sub<GL(6,Integers())| [0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,-1,0,0,0,0,0,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[-1,0,0,0,0,0,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[-1,0,0,0,0,0,0,-1,0,0,0,0,0,0,-1,0,0,0,0,0,0,-1,0,0,0,0,0,0,-1,0,0,0,0,0,0,-1],[1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,-1,0,0,0,0,-1,0,0,0,0,0,0,0,0,1,0,0,0,0,-1,0],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,-1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,-1],[0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0] >;`

C24.2A4 in GAP, Magma, Sage, TeX

`C_2^4._2A_4`
`% in TeX`

`G:=Group("C2^4.2A4");`
`// GroupNames label`

`G:=SmallGroup(192,197);`
`// by ID`

`G=gap.SmallGroup(192,197);`
`# by ID`

`G:=PCGroup([7,-2,-3,-2,2,-2,2,-2,632,135,268,4371,934,521,304,2531,1524]);`
`// Polycyclic`

`G:=Group<a,b,c,d,e,f,g|a^2=b^2=c^2=d^2=g^3=1,e^2=g*b*g^-1=b*c*d,f^2=g*c*g^-1=b,a*b=b*a,a*c=c*a,a*d=d*a,e*a*e^-1=a*b*d,f*a*f^-1=a*c*d,a*g=g*a,b*c=c*b,b*d=d*b,b*e=e*b,b*f=f*b,c*d=d*c,c*e=e*c,c*f=f*c,f*e*f^-1=d*e=e*d,d*f=f*d,d*g=g*d,g*e*g^-1=b*e*f,g*f*g^-1=c*d*e>;`
`// generators/relations`

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