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G = C24⋊Dic3order 192 = 26·3

The semidirect product of C24 and Dic3 acting faithfully

non-abelian, soluble, monomial

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

C1C24C22⋊A4 — C24⋊Dic3
C1C22C24C22⋊A4C24⋊C6 — C24⋊Dic3
C22⋊A4 — C24⋊Dic3
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
3C2×C4
12D4
12C8
12C2×C4
12C23
4A4
16Dic3
16A4
3C2×D4
3C22⋊C4
6M4(2)
6C22⋊C4
4C2×A4
3C4.D4
3C23⋊C4
4A4⋊C4
3C2≀C4

Character table of C24⋊Dic3

 class 12A2B2C34A4B4C68A8B
 size 1341232122424322424
ρ111111111111    trivial
ρ2111111-1-11-1-1    linear of order 2
ρ311-111-1i-i-1i-i    linear of order 4
ρ411-111-1-ii-1-ii    linear of order 4
ρ52222-1200-100    orthogonal lifted from S3
ρ622-22-1-200100    symplectic lifted from Dic3, Schur index 2
ρ7333-10-1110-1-1    orthogonal lifted from S4
ρ8333-10-1-1-1011    orthogonal lifted from S4
ρ933-3-101-ii0i-i    complex lifted from A4⋊C4
ρ1033-3-101i-i0-ii    complex lifted from A4⋊C4
ρ1112-4000000000    orthogonal faithful

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

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

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

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

G:=TransitiveGroup(16,432);

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

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

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

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

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

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

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

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

G:=TransitiveGroup(24,375);

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

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

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

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

G:=TransitiveGroup(24,379);

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

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

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

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

G:=TransitiveGroup(24,383);

Matrix representation of C24⋊Dic3 in GL12(ℤ)

000000-1-1-1000
000000001000
000000010000
000000000-1-1-1
000000000001
000000000010
-1-1-1000000000
001000000000
010000000000
000-1-1-1000000
000001000000
000010000000
,
000100000000
000010000000
000001000000
100000000000
010000000000
001000000000
000000000100
000000000010
000000000001
000000100000
000000010000
000000001000
,
001000000000
-1-1-1000000000
100000000000
000001000000
000-1-1-1000000
000100000000
000000001000
000000-1-1-1000
000000100000
000000000001
000000000-1-1-1
000000000100
,
010000000000
100000000000
-1-1-1000000000
000010000000
000100000000
000-1-1-1000000
000000010000
000000100000
000000-1-1-1000
000000000010
000000000100
000000000-1-1-1
,
100000000000
001000000000
-1-1-1000000000
000000010000
000000-1-1-1000
000000001000
000000000100
000000000001
000000000-1-1-1
000010000000
000-1-1-1000000
000001000000
,
100000000000
010000000000
-1-1-1000000000
000000100000
000000010000
000000-1-1-1000
000001000000
000-1-1-1000000
000010000000
000000000001
000000000-1-1-1
000000000010

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

Export

Subgroup lattice of C24⋊Dic3 in TeX
Character table of C24⋊Dic3 in TeX

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