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G = C24⋊C6order 96 = 25·3

1st semidirect product of C24 and C6 acting faithfully

metabelian, soluble, monomial

Aliases: C241C6, C231A4, C22≀C2⋊C3, C22⋊A41C2, C22.2(C2×A4), SmallGroup(96,70)

Series: Derived Chief Lower central Upper central

C1C24 — C24⋊C6
C1C22C24C22⋊A4 — C24⋊C6
C24 — C24⋊C6
C1

Generators and relations for C24⋊C6
 G = < a,b,c,d,e | a2=b2=c2=d2=e6=1, ab=ba, ac=ca, ad=da, eae-1=db=bd, bc=cb, ebe-1=abcd, ede-1=cd=dc, ece-1=d >

3C2
4C2
6C2
6C2
16C3
2C22
2C22
3C22
3C22
6C22
6C22
6C22
6C22
6C22
6C4
16C6
3C2×C4
3C23
6C23
6D4
6C23
6D4
4A4
8A4
8A4
3C2×D4
3C22⋊C4
4C2×A4

Character table of C24⋊C6

 class 12A2B2C2D3A3B46A6B
 size 134661616121616
ρ11111111111    trivial
ρ211-11111-1-1-1    linear of order 2
ρ311111ζ3ζ321ζ32ζ3    linear of order 3
ρ411-111ζ32ζ3-1ζ65ζ6    linear of order 6
ρ511-111ζ3ζ32-1ζ6ζ65    linear of order 6
ρ611111ζ32ζ31ζ3ζ32    linear of order 3
ρ7333-1-100-100    orthogonal lifted from A4
ρ833-3-1-100100    orthogonal lifted from C2×A4
ρ96-202-200000    orthogonal faithful
ρ106-20-2200000    orthogonal faithful

Permutation representations of C24⋊C6
On 8 points - transitive group 8T33
Generators in S8
(1 4)(2 5)(3 7)(6 8)
(1 6)(2 7)(3 5)(4 8)
(1 6)(2 3)(4 8)(5 7)
(1 8)(2 5)(3 7)(4 6)
(1 2)(3 4 5 6 7 8)

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

G:=Group( (1,4)(2,5)(3,7)(6,8), (1,6)(2,7)(3,5)(4,8), (1,6)(2,3)(4,8)(5,7), (1,8)(2,5)(3,7)(4,6), (1,2)(3,4,5,6,7,8) );

G=PermutationGroup([(1,4),(2,5),(3,7),(6,8)], [(1,6),(2,7),(3,5),(4,8)], [(1,6),(2,3),(4,8),(5,7)], [(1,8),(2,5),(3,7),(4,6)], [(1,2),(3,4,5,6,7,8)])

G:=TransitiveGroup(8,33);

On 12 points - transitive group 12T58
Generators in S12
(2 11)(6 9)
(2 11)(4 7)
(2 11)(3 12)(5 8)(6 9)
(1 10)(2 11)(4 7)(5 8)
(1 2 3 4 5 6)(7 8 9 10 11 12)

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

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

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

G:=TransitiveGroup(12,58);

On 12 points - transitive group 12T59
Generators in S12
(2 11)(3 9)(4 12)(6 8)
(1 7)(2 11)(5 10)(6 8)
(2 6)(3 4)(8 11)(9 12)
(1 5)(2 6)(7 10)(8 11)
(1 2 3)(4 5 6)(7 8 9 10 11 12)

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

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

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

G:=TransitiveGroup(12,59);

On 16 points - transitive group 16T183
Generators in S16
(1 14)(2 5)(3 11)(4 8)(6 13)(7 15)(9 10)(12 16)
(1 16)(2 13)(3 10)(4 7)(5 6)(8 15)(9 11)(12 14)
(1 3)(2 4)(5 8)(6 15)(7 13)(9 12)(10 16)(11 14)
(1 2)(3 4)(5 14)(6 12)(7 10)(8 11)(9 15)(13 16)
(2 3 4)(5 6 7 8 9 10)(11 12 13 14 15 16)

G:=sub<Sym(16)| (1,14)(2,5)(3,11)(4,8)(6,13)(7,15)(9,10)(12,16), (1,16)(2,13)(3,10)(4,7)(5,6)(8,15)(9,11)(12,14), (1,3)(2,4)(5,8)(6,15)(7,13)(9,12)(10,16)(11,14), (1,2)(3,4)(5,14)(6,12)(7,10)(8,11)(9,15)(13,16), (2,3,4)(5,6,7,8,9,10)(11,12,13,14,15,16)>;

G:=Group( (1,14)(2,5)(3,11)(4,8)(6,13)(7,15)(9,10)(12,16), (1,16)(2,13)(3,10)(4,7)(5,6)(8,15)(9,11)(12,14), (1,3)(2,4)(5,8)(6,15)(7,13)(9,12)(10,16)(11,14), (1,2)(3,4)(5,14)(6,12)(7,10)(8,11)(9,15)(13,16), (2,3,4)(5,6,7,8,9,10)(11,12,13,14,15,16) );

G=PermutationGroup([(1,14),(2,5),(3,11),(4,8),(6,13),(7,15),(9,10),(12,16)], [(1,16),(2,13),(3,10),(4,7),(5,6),(8,15),(9,11),(12,14)], [(1,3),(2,4),(5,8),(6,15),(7,13),(9,12),(10,16),(11,14)], [(1,2),(3,4),(5,14),(6,12),(7,10),(8,11),(9,15),(13,16)], [(2,3,4),(5,6,7,8,9,10),(11,12,13,14,15,16)])

G:=TransitiveGroup(16,183);

On 24 points - transitive group 24T181
Generators in S24
(1 8)(2 13)(3 14)(4 11)(5 24)(6 19)(7 17)(9 21)(10 22)(12 16)(15 23)(18 20)
(1 20)(2 21)(3 10)(4 15)(5 16)(6 7)(8 18)(9 13)(11 23)(12 24)(14 22)(17 19)
(2 9)(3 10)(5 12)(6 7)(13 21)(14 22)(16 24)(17 19)
(1 8)(2 9)(4 11)(5 12)(13 21)(15 23)(16 24)(18 20)
(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)| (1,8)(2,13)(3,14)(4,11)(5,24)(6,19)(7,17)(9,21)(10,22)(12,16)(15,23)(18,20), (1,20)(2,21)(3,10)(4,15)(5,16)(6,7)(8,18)(9,13)(11,23)(12,24)(14,22)(17,19), (2,9)(3,10)(5,12)(6,7)(13,21)(14,22)(16,24)(17,19), (1,8)(2,9)(4,11)(5,12)(13,21)(15,23)(16,24)(18,20), (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( (1,8)(2,13)(3,14)(4,11)(5,24)(6,19)(7,17)(9,21)(10,22)(12,16)(15,23)(18,20), (1,20)(2,21)(3,10)(4,15)(5,16)(6,7)(8,18)(9,13)(11,23)(12,24)(14,22)(17,19), (2,9)(3,10)(5,12)(6,7)(13,21)(14,22)(16,24)(17,19), (1,8)(2,9)(4,11)(5,12)(13,21)(15,23)(16,24)(18,20), (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([(1,8),(2,13),(3,14),(4,11),(5,24),(6,19),(7,17),(9,21),(10,22),(12,16),(15,23),(18,20)], [(1,20),(2,21),(3,10),(4,15),(5,16),(6,7),(8,18),(9,13),(11,23),(12,24),(14,22),(17,19)], [(2,9),(3,10),(5,12),(6,7),(13,21),(14,22),(16,24),(17,19)], [(1,8),(2,9),(4,11),(5,12),(13,21),(15,23),(16,24),(18,20)], [(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(24,181);

On 24 points - transitive group 24T182
Generators in S24
(2 9)(4 21)(6 17)(7 23)(11 15)(13 19)
(2 13)(4 11)(6 23)(7 17)(9 19)(15 21)
(1 24)(2 9)(3 14)(4 21)(5 12)(6 17)(7 23)(8 18)(10 20)(11 15)(13 19)(16 22)
(1 8)(2 13)(3 20)(4 11)(5 16)(6 23)(7 17)(9 19)(10 14)(12 22)(15 21)(18 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)| (2,9)(4,21)(6,17)(7,23)(11,15)(13,19), (2,13)(4,11)(6,23)(7,17)(9,19)(15,21), (1,24)(2,9)(3,14)(4,21)(5,12)(6,17)(7,23)(8,18)(10,20)(11,15)(13,19)(16,22), (1,8)(2,13)(3,20)(4,11)(5,16)(6,23)(7,17)(9,19)(10,14)(12,22)(15,21)(18,24), (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( (2,9)(4,21)(6,17)(7,23)(11,15)(13,19), (2,13)(4,11)(6,23)(7,17)(9,19)(15,21), (1,24)(2,9)(3,14)(4,21)(5,12)(6,17)(7,23)(8,18)(10,20)(11,15)(13,19)(16,22), (1,8)(2,13)(3,20)(4,11)(5,16)(6,23)(7,17)(9,19)(10,14)(12,22)(15,21)(18,24), (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([(2,9),(4,21),(6,17),(7,23),(11,15),(13,19)], [(2,13),(4,11),(6,23),(7,17),(9,19),(15,21)], [(1,24),(2,9),(3,14),(4,21),(5,12),(6,17),(7,23),(8,18),(10,20),(11,15),(13,19),(16,22)], [(1,8),(2,13),(3,20),(4,11),(5,16),(6,23),(7,17),(9,19),(10,14),(12,22),(15,21),(18,24)], [(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(24,182);

On 24 points - transitive group 24T183
Generators in S24
(1 24)(2 9)(3 20)(6 7)(8 18)(10 14)(13 19)(17 23)
(2 9)(3 20)(4 11)(5 22)(10 14)(12 16)(13 19)(15 21)
(1 24)(2 9)(3 14)(4 21)(5 12)(6 17)(7 23)(8 18)(10 20)(11 15)(13 19)(16 22)
(1 8)(2 13)(3 20)(4 11)(5 16)(6 23)(7 17)(9 19)(10 14)(12 22)(15 21)(18 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)| (1,24)(2,9)(3,20)(6,7)(8,18)(10,14)(13,19)(17,23), (2,9)(3,20)(4,11)(5,22)(10,14)(12,16)(13,19)(15,21), (1,24)(2,9)(3,14)(4,21)(5,12)(6,17)(7,23)(8,18)(10,20)(11,15)(13,19)(16,22), (1,8)(2,13)(3,20)(4,11)(5,16)(6,23)(7,17)(9,19)(10,14)(12,22)(15,21)(18,24), (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( (1,24)(2,9)(3,20)(6,7)(8,18)(10,14)(13,19)(17,23), (2,9)(3,20)(4,11)(5,22)(10,14)(12,16)(13,19)(15,21), (1,24)(2,9)(3,14)(4,21)(5,12)(6,17)(7,23)(8,18)(10,20)(11,15)(13,19)(16,22), (1,8)(2,13)(3,20)(4,11)(5,16)(6,23)(7,17)(9,19)(10,14)(12,22)(15,21)(18,24), (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([(1,24),(2,9),(3,20),(6,7),(8,18),(10,14),(13,19),(17,23)], [(2,9),(3,20),(4,11),(5,22),(10,14),(12,16),(13,19),(15,21)], [(1,24),(2,9),(3,14),(4,21),(5,12),(6,17),(7,23),(8,18),(10,20),(11,15),(13,19),(16,22)], [(1,8),(2,13),(3,20),(4,11),(5,16),(6,23),(7,17),(9,19),(10,14),(12,22),(15,21),(18,24)], [(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(24,183);

On 24 points - transitive group 24T184
Generators in S24
(2 13)(3 20)(4 11)(5 22)(6 23)(7 17)(9 19)(10 14)(12 16)(15 21)
(1 24)(2 19)(4 15)(5 22)(6 7)(8 18)(9 13)(11 21)(12 16)(17 23)
(1 8)(2 9)(4 11)(5 12)(13 19)(15 21)(16 22)(18 24)
(1 8)(3 10)(4 11)(6 7)(14 20)(15 21)(17 23)(18 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)| (2,13)(3,20)(4,11)(5,22)(6,23)(7,17)(9,19)(10,14)(12,16)(15,21), (1,24)(2,19)(4,15)(5,22)(6,7)(8,18)(9,13)(11,21)(12,16)(17,23), (1,8)(2,9)(4,11)(5,12)(13,19)(15,21)(16,22)(18,24), (1,8)(3,10)(4,11)(6,7)(14,20)(15,21)(17,23)(18,24), (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( (2,13)(3,20)(4,11)(5,22)(6,23)(7,17)(9,19)(10,14)(12,16)(15,21), (1,24)(2,19)(4,15)(5,22)(6,7)(8,18)(9,13)(11,21)(12,16)(17,23), (1,8)(2,9)(4,11)(5,12)(13,19)(15,21)(16,22)(18,24), (1,8)(3,10)(4,11)(6,7)(14,20)(15,21)(17,23)(18,24), (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([(2,13),(3,20),(4,11),(5,22),(6,23),(7,17),(9,19),(10,14),(12,16),(15,21)], [(1,24),(2,19),(4,15),(5,22),(6,7),(8,18),(9,13),(11,21),(12,16),(17,23)], [(1,8),(2,9),(4,11),(5,12),(13,19),(15,21),(16,22),(18,24)], [(1,8),(3,10),(4,11),(6,7),(14,20),(15,21),(17,23),(18,24)], [(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(24,184);

On 24 points - transitive group 24T185
Generators in S24
(1 6)(2 20)(3 16)(4 18)(5 24)(7 23)(8 13)(9 10)(11 15)(12 21)(14 22)(17 19)
(1 22)(2 18)(3 5)(4 20)(6 14)(7 15)(8 12)(9 19)(10 17)(11 23)(13 21)(16 24)
(2 7)(3 8)(4 11)(5 12)(13 16)(15 18)(20 23)(21 24)
(1 9)(2 7)(4 11)(6 10)(14 17)(15 18)(19 22)(20 23)
(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)| (1,6)(2,20)(3,16)(4,18)(5,24)(7,23)(8,13)(9,10)(11,15)(12,21)(14,22)(17,19), (1,22)(2,18)(3,5)(4,20)(6,14)(7,15)(8,12)(9,19)(10,17)(11,23)(13,21)(16,24), (2,7)(3,8)(4,11)(5,12)(13,16)(15,18)(20,23)(21,24), (1,9)(2,7)(4,11)(6,10)(14,17)(15,18)(19,22)(20,23), (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( (1,6)(2,20)(3,16)(4,18)(5,24)(7,23)(8,13)(9,10)(11,15)(12,21)(14,22)(17,19), (1,22)(2,18)(3,5)(4,20)(6,14)(7,15)(8,12)(9,19)(10,17)(11,23)(13,21)(16,24), (2,7)(3,8)(4,11)(5,12)(13,16)(15,18)(20,23)(21,24), (1,9)(2,7)(4,11)(6,10)(14,17)(15,18)(19,22)(20,23), (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([(1,6),(2,20),(3,16),(4,18),(5,24),(7,23),(8,13),(9,10),(11,15),(12,21),(14,22),(17,19)], [(1,22),(2,18),(3,5),(4,20),(6,14),(7,15),(8,12),(9,19),(10,17),(11,23),(13,21),(16,24)], [(2,7),(3,8),(4,11),(5,12),(13,16),(15,18),(20,23),(21,24)], [(1,9),(2,7),(4,11),(6,10),(14,17),(15,18),(19,22),(20,23)], [(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(24,185);

On 24 points - transitive group 24T186
Generators in S24
(1 4)(2 24)(3 22)(5 18)(6 16)(7 10)(8 15)(9 13)(11 21)(12 19)(14 20)(17 23)
(1 14)(2 18)(3 6)(4 20)(5 24)(7 23)(8 21)(9 12)(10 17)(11 15)(13 19)(16 22)
(2 8)(3 9)(5 11)(6 12)(13 22)(15 24)(16 19)(18 21)
(1 7)(2 8)(4 10)(5 11)(14 23)(15 24)(17 20)(18 21)
(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)| (1,4)(2,24)(3,22)(5,18)(6,16)(7,10)(8,15)(9,13)(11,21)(12,19)(14,20)(17,23), (1,14)(2,18)(3,6)(4,20)(5,24)(7,23)(8,21)(9,12)(10,17)(11,15)(13,19)(16,22), (2,8)(3,9)(5,11)(6,12)(13,22)(15,24)(16,19)(18,21), (1,7)(2,8)(4,10)(5,11)(14,23)(15,24)(17,20)(18,21), (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( (1,4)(2,24)(3,22)(5,18)(6,16)(7,10)(8,15)(9,13)(11,21)(12,19)(14,20)(17,23), (1,14)(2,18)(3,6)(4,20)(5,24)(7,23)(8,21)(9,12)(10,17)(11,15)(13,19)(16,22), (2,8)(3,9)(5,11)(6,12)(13,22)(15,24)(16,19)(18,21), (1,7)(2,8)(4,10)(5,11)(14,23)(15,24)(17,20)(18,21), (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([(1,4),(2,24),(3,22),(5,18),(6,16),(7,10),(8,15),(9,13),(11,21),(12,19),(14,20),(17,23)], [(1,14),(2,18),(3,6),(4,20),(5,24),(7,23),(8,21),(9,12),(10,17),(11,15),(13,19),(16,22)], [(2,8),(3,9),(5,11),(6,12),(13,22),(15,24),(16,19),(18,21)], [(1,7),(2,8),(4,10),(5,11),(14,23),(15,24),(17,20),(18,21)], [(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(24,186);

C24⋊C6 is a maximal subgroup of
C24⋊Dic3  C24⋊D6  C24⋊A4  (C22×S3)⋊A4  A4≀C2  (C22×D5)⋊A4  F16⋊C2
C24⋊C6 is a maximal quotient of
C24⋊C12  C24.A4  (C22×C4).A4  C2≀A4  2+ 1+4.C6  C24⋊C18  (C22×S3)⋊A4  (C22×D5)⋊A4

Polynomial with Galois group C24⋊C6 over ℚ
actionf(x)Disc(f)
8T33x8-x7-15x6+15x5+62x4-72x3-53x2+78x-1922·36·56·74·2512
12T58x12-23x10+158x8-378x6+372x4-160x2+25212·36·510·76·138
12T59x12-4x11-9x10+48x9+5x8-164x7+69x6+188x5-89x4-82x3+23x2+14x+1215·138·474·20292

Matrix representation of C24⋊C6 in GL6(ℤ)

010000
100000
-1-1-1000
000-1-1-1
000001
000010
,
-1-1-1000
001000
010000
000001
000-1-1-1
000100
,
001000
-1-1-1000
100000
000001
000-1-1-1
000100
,
010000
100000
-1-1-1000
000010
000100
000-1-1-1
,
000100
000-1-1-1
000010
100000
-1-1-1000
010000

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

C24⋊C6 in GAP, Magma, Sage, TeX

C_2^4\rtimes C_6
% in TeX

G:=Group("C2^4:C6");
// GroupNames label

G:=SmallGroup(96,70);
// by ID

G=gap.SmallGroup(96,70);
# by ID

G:=PCGroup([6,-2,-3,-2,2,-2,2,542,116,1443,225,730,1307]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^2=c^2=d^2=e^6=1,a*b=b*a,a*c=c*a,a*d=d*a,e*a*e^-1=d*b=b*d,b*c=c*b,e*b*e^-1=a*b*c*d,e*d*e^-1=c*d=d*c,e*c*e^-1=d>;
// generators/relations

Export

Subgroup lattice of C24⋊C6 in TeX
Character table of C24⋊C6 in TeX

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