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## G = C24⋊Dic3order 192 = 26·3

### The semidirect product of C24 and Dic3 acting faithfully

Aliases: C24⋊Dic3, C23.1S4, C22⋊A4⋊C4, C22≀C2.S3, C24⋊C6.C2, C22.2(A4⋊C4), SmallGroup(192,184)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C24 — C22⋊A4 — C24⋊Dic3
 Chief series C1 — C22 — C24 — C22⋊A4 — C24⋊C6 — C24⋊Dic3
 Lower central C22⋊A4 — C24⋊Dic3
 Upper central C1

Generators and relations for C24⋊Dic3
G = < a,b,c,d,e,f | a2=b2=c2=d2=e6=1, f2=e3, ab=ba, ebe-1=ac=ca, ad=da, eae-1=abc, faf-1=b, bc=cb, bd=db, fbf-1=acd, ece-1=fcf-1=cd=dc, ede-1=c, df=fd, fef-1=e-1 >

3C2
4C2
12C2
16C3
4C22
6C22
6C22
6C4
12C22
12C22
24C4
16C6
3C23
12D4
12C8
12C2×C4
12C23
4A4
16Dic3
16A4

Character table of C24⋊Dic3

 class 1 2A 2B 2C 3 4A 4B 4C 6 8A 8B size 1 3 4 12 32 12 24 24 32 24 24 ρ1 1 1 1 1 1 1 1 1 1 1 1 trivial ρ2 1 1 1 1 1 1 -1 -1 1 -1 -1 linear of order 2 ρ3 1 1 -1 1 1 -1 i -i -1 i -i linear of order 4 ρ4 1 1 -1 1 1 -1 -i i -1 -i i linear of order 4 ρ5 2 2 2 2 -1 2 0 0 -1 0 0 orthogonal lifted from S3 ρ6 2 2 -2 2 -1 -2 0 0 1 0 0 symplectic lifted from Dic3, Schur index 2 ρ7 3 3 3 -1 0 -1 1 1 0 -1 -1 orthogonal lifted from S4 ρ8 3 3 3 -1 0 -1 -1 -1 0 1 1 orthogonal lifted from S4 ρ9 3 3 -3 -1 0 1 -i i 0 i -i complex lifted from A4⋊C4 ρ10 3 3 -3 -1 0 1 i -i 0 -i i complex lifted from A4⋊C4 ρ11 12 -4 0 0 0 0 0 0 0 0 0 orthogonal faithful

Permutation representations of C24⋊Dic3
On 16 points - transitive group 16T432
Generators in S16
(2 12)(3 10)(4 5)(6 8)(7 9)(14 16)
(1 15)(2 14)(3 10)(6 8)(11 13)(12 16)
(1 13)(2 16)(3 10)(4 7)(5 9)(6 8)(11 15)(12 14)
(1 11)(2 14)(3 8)(4 5)(6 10)(7 9)(12 16)(13 15)
(1 2)(3 4)(5 6 7 8 9 10)(11 12 13 14 15 16)
(1 3 2 4)(5 11 8 14)(6 16 9 13)(7 15 10 12)

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

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

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

G:=TransitiveGroup(16,432);

On 16 points - transitive group 16T433
Generators in S16
(1 11)(2 7)(3 14)(4 10)(5 6)(8 16)(9 12)(13 15)
(1 5)(2 12)(3 15)(4 8)(6 11)(7 9)(10 16)(13 14)
(1 4)(2 3)(5 8)(6 16)(7 14)(9 13)(10 11)(12 15)
(1 2)(3 4)(5 12)(6 9)(7 11)(8 15)(10 14)(13 16)
(2 3 4)(5 6 7 8 9 10)(11 12 13 14 15 16)
(3 4)(5 11 8 14)(6 16 9 13)(7 15 10 12)

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

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

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

G:=TransitiveGroup(16,433);

On 24 points - transitive group 24T370
Generators in S24
(3 15)(4 16)(5 17)(6 18)(7 19)(11 23)
(3 15)(5 17)(7 19)(8 20)(9 21)(10 22)
(2 14)(3 15)(5 17)(6 18)(8 20)(9 21)(11 23)(12 24)
(1 13)(3 15)(4 16)(6 18)(7 19)(9 21)(10 22)(12 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 21 4 24)(2 20 5 23)(3 19 6 22)(7 18 10 15)(8 17 11 14)(9 16 12 13)

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

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

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

G:=TransitiveGroup(24,370);

On 24 points - transitive group 24T375
Generators in S24
(1 16)(2 24)(3 6)(4 20)(5 14)(7 17)(8 10)(9 23)(11 13)(12 21)(15 19)(18 22)
(1 9)(2 17)(3 22)(4 11)(5 21)(6 18)(7 24)(8 15)(10 19)(12 14)(13 20)(16 23)
(2 12)(3 10)(5 7)(6 8)(14 17)(15 18)(19 22)(21 24)
(1 11)(3 10)(4 9)(6 8)(13 16)(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)
(1 10)(2 12)(3 11)(4 6)(8 9)(13 19 16 22)(14 24 17 21)(15 23 18 20)

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

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

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

G:=TransitiveGroup(24,375);

On 24 points - transitive group 24T379
Generators in S24
(1 23)(2 21)(4 20)(5 24)(7 16)(8 17)(9 12)(10 13)(11 14)(15 18)
(1 4)(2 24)(3 19)(5 21)(6 22)(8 17)(9 15)(11 14)(12 18)(20 23)
(2 5)(3 6)(8 11)(9 12)(14 17)(15 18)(19 22)(21 24)
(1 4)(3 6)(7 10)(9 12)(13 16)(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)
(1 12)(2 11)(3 10)(4 9)(5 8)(6 7)(13 22 16 19)(14 21 17 24)(15 20 18 23)

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

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

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

G:=TransitiveGroup(24,379);

On 24 points - transitive group 24T383
Generators in S24
(1 10)(2 21)(3 9)(4 17)(5 24)(6 16)(7 20)(8 11)(12 22)(13 19)(14 23)(15 18)
(1 17)(2 15)(3 6)(4 10)(5 8)(7 23)(9 16)(11 24)(12 13)(14 20)(18 21)(19 22)
(1 23)(2 24)(4 20)(5 21)(7 17)(8 18)(10 14)(11 15)
(2 24)(3 19)(5 21)(6 22)(8 18)(9 13)(11 15)(12 16)
(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 17 4 14)(2 16 5 13)(3 15 6 18)(7 20 10 23)(8 19 11 22)(9 24 12 21)

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

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

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

G:=TransitiveGroup(24,383);

Matrix representation of C24⋊Dic3 in GL12(ℤ)

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

G:=sub<GL(12,Integers())| [0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,0,0,0,0,-1,1,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0],[0,-1,1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,-1,0],[0,1,-1,0,0,0,0,0,0,0,0,0,1,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,1,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,1,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,1,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1],[1,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0],[1,0,-1,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,1,0,-1,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,1,-1,0] >;

C24⋊Dic3 in GAP, Magma, Sage, TeX

C_2^4\rtimes {\rm Dic}_3
% in TeX

G:=Group("C2^4:Dic3");
// GroupNames label

G:=SmallGroup(192,184);
// by ID

G=gap.SmallGroup(192,184);
# by ID

G:=PCGroup([7,-2,-2,-3,-2,2,-2,2,14,170,675,2194,857,5464,1271,753,6053,1027,1784]);
// Polycyclic

G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=e^6=1,f^2=e^3,a*b=b*a,e*b*e^-1=a*c=c*a,a*d=d*a,e*a*e^-1=a*b*c,f*a*f^-1=b,b*c=c*b,b*d=d*b,f*b*f^-1=a*c*d,e*c*e^-1=f*c*f^-1=c*d=d*c,e*d*e^-1=c,d*f=f*d,f*e*f^-1=e^-1>;
// generators/relations

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