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G = S3×S3≀C2  order 432 = 24·33

Direct product of S3 and S3≀C2

direct product, non-abelian, soluble, monomial, rational

Aliases: S3×S3≀C2, S32⋊1D6, C33⋊(C2×D4), (S3×C32)⋊D4, C33⋊D4⋊C2, C33⋊C2⋊D4, C32⋊C4⋊1D6, C32⋊2D12⋊C2, C32⋊5(S3×D4), C33⋊C4⋊C22, C32⋊4D6⋊C22, S33⋊C2, (C3×S3≀C2)⋊C2, (C3×S32)⋊C22, (S3×C32⋊C4)⋊C2, C3⋊1(C2×S3≀C2), (C3×C32⋊C4)⋊C22, (S3×C3⋊S3).1C22, C3⋊S3.1(C22×S3), (C3×C3⋊S3).1C23, SmallGroup(432,741)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C32 — C3×C3⋊S3 — S3×S3≀C2
Chief series
C1 — C3 — C33 — C3×C3⋊S3 — S3×C3⋊S3 — S33 — S3×S3≀C2
Lower central
C33 — C3×C3⋊S3 — S3×S3≀C2
Upper central
C1

Generators and relations for S3×S3≀C2
 G = < a,b,c,d,e,f | a3=b2=c3=d3=e4=f2=1, bab=a-1, ac=ca, ad=da, ae=ea, af=fa, bc=cb, bd=db, be=eb, bf=fb, cd=dc, ece-1=d, fcf=ede-1=c-1, df=fd, fef=e-1 >

Subgroups: 1720 in 192 conjugacy classes, 28 normal (18 characteristic)
C1, C2, C3, C3, C4, C22, S3, S3, C6, C2×C4, D4, C23, C32, C32, Dic3, C12, D6, C2×C6, C2×D4, C3×S3, C3⋊S3, C3⋊S3, C3×C6, C4×S3, D12, C3⋊D4, C3×D4, C22×S3, C33, C32⋊C4, C32⋊C4, S32, S32, S3×C6, C2×C3⋊S3, S3×D4, S3×C32, S3×C32, C3×C3⋊S3, C3×C3⋊S3, C33⋊C2, S3≀C2, S3≀C2, C2×C32⋊C4, C2×S32, C3×C32⋊C4, C33⋊C4, C3×S32, C3×S32, S3×C3⋊S3, S3×C3⋊S3, C32⋊4D6, C2×S3≀C2, S3×C32⋊C4, C3×S3≀C2, C33⋊D4, C32⋊2D12, S33, S3×S3≀C2
Quotients: C1, C2, C22, S3, D4, C23, D6, C2×D4, C22×S3, S3×D4, S3≀C2, C2×S3≀C2, S3×S3≀C2

Character table of S3×S3≀C2

 class 12A2B2C2D2E2F2G3A3B3C3D3E4A4B6A6B6C6D6E6F6G6H6I6J6K12
 size 13669181827244881854121212121212182424363636
ρ1111111111111111111111111111    trivial
ρ2111-11-11111111-1-1-11111-111-1-11-1    linear of order 2
ρ31-11-111-1-111111-11-111-1-1-111-11-1-1    linear of order 2
ρ41-1111-1-1-1111111-1111-1-11111-1-11    linear of order 2
ρ51-1-1-1111-1111111-1-1-1-1-1-1-11-1-1111    linear of order 2
ρ61-1-111-11-111111-111-1-1-1-111-11-11-1    linear of order 2
ρ711-1111-1111111-1-11-1-11111-111-1-1    linear of order 2
ρ811-1-11-1-111111111-1-1-111-11-1-1-1-11    linear of order 2
ρ920-2-22000-122-1-120-21-2001-11100-1    orthogonal lifted from D6
ρ102-200-20022222200000-2-20-200000    orthogonal lifted from D4
ρ11202-22000-122-1-1-20-2-12001-1-11001    orthogonal lifted from D6
ρ1220222000-122-1-1202-1200-1-1-1-100-1    orthogonal lifted from S3
ρ132200-200-22222200000220-200000    orthogonal lifted from D4
ρ1420-222000-122-1-1-2021-200-1-11-1001    orthogonal lifted from D6
ρ154-42000-204-21-210002-1-1200-10010    orthogonal lifted from C2×S3≀C2
ρ1644-2000-204-21-21000-211-20010010    orthogonal lifted from S3≀C2
ρ174-4020-20041-21-200-1002-1200-1100    orthogonal lifted from C2×S3≀C2
ρ18440-20-20041-21-200100-21-2001100    orthogonal lifted from S3≀C2
ρ19442000204-21-210002-11-200-100-10    orthogonal lifted from S3≀C2
ρ204000-4000-244-2-200000000200000    orthogonal lifted from S3×D4
ρ214402020041-21-200-100-21200-1-100    orthogonal lifted from S3≀C2
ρ224-40-2020041-21-2001002-1-2001-100    orthogonal lifted from C2×S3≀C2
ρ234-4-2000204-21-21000-21-1200100-10    orthogonal lifted from C2×S3≀C2
ρ2480-400000-4-422-1000220000-10000    orthogonal faithful
ρ25800-40000-42-4-120020000200-1000    orthogonal faithful
ρ2680400000-4-422-1000-2-2000010000    orthogonal faithful
ρ2780040000-42-4-1200-20000-2001000    orthogonal faithful

Permutation representations of S3×S3≀C2
►On 12 points - transitive group 12T156
Generators in S12
(1 9 8)(2 10 5)(3 11 6)(4 12 7)

(1 3)(2 4)(5 12)(6 9)(7 10)(8 11)

(2 10 5)(4 7 12)

(1 9 8)(3 6 11)

(1 2 3 4)(5 6 7 8)(9 10 11 12)

(2 4)(5 7)(10 12)
 
G:=sub<Sym(12)| (1,9,8)(2,10,5)(3,11,6)(4,12,7), (1,3)(2,4)(5,12)(6,9)(7,10)(8,11), (2,10,5)(4,7,12), (1,9,8)(3,6,11), (1,2,3,4)(5,6,7,8)(9,10,11,12), (2,4)(5,7)(10,12)>;
 
G:=Group( (1,9,8)(2,10,5)(3,11,6)(4,12,7), (1,3)(2,4)(5,12)(6,9)(7,10)(8,11), (2,10,5)(4,7,12), (1,9,8)(3,6,11), (1,2,3,4)(5,6,7,8)(9,10,11,12), (2,4)(5,7)(10,12) );
 
G=PermutationGroup([[(1,9,8),(2,10,5),(3,11,6),(4,12,7)], [(1,3),(2,4),(5,12),(6,9),(7,10),(8,11)], [(2,10,5),(4,7,12)], [(1,9,8),(3,6,11)], [(1,2,3,4),(5,6,7,8),(9,10,11,12)], [(2,4),(5,7),(10,12)]])
 
G:=TransitiveGroup(12,156);
 

►On 18 points - transitive group 18T150
Generators in S18
(1 4 5)(2 3 6)(7 14 17)(8 11 18)(9 12 15)(10 13 16)

(1 4)(2 3)(11 18)(12 15)(13 16)(14 17)

(1 11 13)(2 14 12)(3 17 15)(4 18 16)(5 8 10)(6 7 9)

(1 13 11)(2 14 12)(3 17 15)(4 16 18)(5 10 8)(6 7 9)

(1 2)(3 4)(5 6)(7 8 9 10)(11 12 13 14)(15 16 17 18)

(1 2)(3 4)(5 6)(7 10)(8 9)(11 12)(13 14)(15 18)(16 17)
 
G:=sub<Sym(18)| (1,4,5)(2,3,6)(7,14,17)(8,11,18)(9,12,15)(10,13,16), (1,4)(2,3)(11,18)(12,15)(13,16)(14,17), (1,11,13)(2,14,12)(3,17,15)(4,18,16)(5,8,10)(6,7,9), (1,13,11)(2,14,12)(3,17,15)(4,16,18)(5,10,8)(6,7,9), (1,2)(3,4)(5,6)(7,8,9,10)(11,12,13,14)(15,16,17,18), (1,2)(3,4)(5,6)(7,10)(8,9)(11,12)(13,14)(15,18)(16,17)>;
 
G:=Group( (1,4,5)(2,3,6)(7,14,17)(8,11,18)(9,12,15)(10,13,16), (1,4)(2,3)(11,18)(12,15)(13,16)(14,17), (1,11,13)(2,14,12)(3,17,15)(4,18,16)(5,8,10)(6,7,9), (1,13,11)(2,14,12)(3,17,15)(4,16,18)(5,10,8)(6,7,9), (1,2)(3,4)(5,6)(7,8,9,10)(11,12,13,14)(15,16,17,18), (1,2)(3,4)(5,6)(7,10)(8,9)(11,12)(13,14)(15,18)(16,17) );
 
G=PermutationGroup([[(1,4,5),(2,3,6),(7,14,17),(8,11,18),(9,12,15),(10,13,16)], [(1,4),(2,3),(11,18),(12,15),(13,16),(14,17)], [(1,11,13),(2,14,12),(3,17,15),(4,18,16),(5,8,10),(6,7,9)], [(1,13,11),(2,14,12),(3,17,15),(4,16,18),(5,10,8),(6,7,9)], [(1,2),(3,4),(5,6),(7,8,9,10),(11,12,13,14),(15,16,17,18)], [(1,2),(3,4),(5,6),(7,10),(8,9),(11,12),(13,14),(15,18),(16,17)]])
 
G:=TransitiveGroup(18,150);
 

►On 24 points - transitive group 24T1322
Generators in S24
(1 20 21)(2 17 22)(3 18 23)(4 19 24)(5 10 14)(6 11 15)(7 12 16)(8 9 13)

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

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

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

(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)(2 7)(3 6)(4 5)(9 20)(10 19)(11 18)(12 17)(13 21)(14 24)(15 23)(16 22)
 
G:=sub<Sym(24)| (1,20,21)(2,17,22)(3,18,23)(4,19,24)(5,10,14)(6,11,15)(7,12,16)(8,9,13), (1,3)(2,4)(5,7)(6,8)(9,15)(10,16)(11,13)(12,14)(17,24)(18,21)(19,22)(20,23), (1,20,21)(2,22,17)(3,23,18)(4,19,24)(5,14,10)(6,11,15)(7,12,16)(8,13,9), (1,21,20)(2,22,17)(3,18,23)(4,19,24)(5,10,14)(6,11,15)(7,16,12)(8,13,9), (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)(2,7)(3,6)(4,5)(9,20)(10,19)(11,18)(12,17)(13,21)(14,24)(15,23)(16,22)>;
 
G:=Group( (1,20,21)(2,17,22)(3,18,23)(4,19,24)(5,10,14)(6,11,15)(7,12,16)(8,9,13), (1,3)(2,4)(5,7)(6,8)(9,15)(10,16)(11,13)(12,14)(17,24)(18,21)(19,22)(20,23), (1,20,21)(2,22,17)(3,23,18)(4,19,24)(5,14,10)(6,11,15)(7,12,16)(8,13,9), (1,21,20)(2,22,17)(3,18,23)(4,19,24)(5,10,14)(6,11,15)(7,16,12)(8,13,9), (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)(2,7)(3,6)(4,5)(9,20)(10,19)(11,18)(12,17)(13,21)(14,24)(15,23)(16,22) );
 
G=PermutationGroup([[(1,20,21),(2,17,22),(3,18,23),(4,19,24),(5,10,14),(6,11,15),(7,12,16),(8,9,13)], [(1,3),(2,4),(5,7),(6,8),(9,15),(10,16),(11,13),(12,14),(17,24),(18,21),(19,22),(20,23)], [(1,20,21),(2,22,17),(3,23,18),(4,19,24),(5,14,10),(6,11,15),(7,12,16),(8,13,9)], [(1,21,20),(2,22,17),(3,18,23),(4,19,24),(5,10,14),(6,11,15),(7,16,12),(8,13,9)], [(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),(2,7),(3,6),(4,5),(9,20),(10,19),(11,18),(12,17),(13,21),(14,24),(15,23),(16,22)]])
 
G:=TransitiveGroup(24,1322);
 

►On 24 points - transitive group 24T1323
Generators in S24
(1 17 16)(2 18 13)(3 19 14)(4 20 15)(5 10 23)(6 11 24)(7 12 21)(8 9 22)

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

(2 18 13)(4 15 20)(5 23 10)(7 12 21)

(1 17 16)(3 14 19)(6 11 24)(8 22 9)

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

(2 4)(5 7)(10 12)(13 15)(18 20)(21 23)
 
G:=sub<Sym(24)| (1,17,16)(2,18,13)(3,19,14)(4,20,15)(5,10,23)(6,11,24)(7,12,21)(8,9,22), (1,22)(2,23)(3,24)(4,21)(5,13)(6,14)(7,15)(8,16)(9,17)(10,18)(11,19)(12,20), (2,18,13)(4,15,20)(5,23,10)(7,12,21), (1,17,16)(3,14,19)(6,11,24)(8,22,9), (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24), (2,4)(5,7)(10,12)(13,15)(18,20)(21,23)>;
 
G:=Group( (1,17,16)(2,18,13)(3,19,14)(4,20,15)(5,10,23)(6,11,24)(7,12,21)(8,9,22), (1,22)(2,23)(3,24)(4,21)(5,13)(6,14)(7,15)(8,16)(9,17)(10,18)(11,19)(12,20), (2,18,13)(4,15,20)(5,23,10)(7,12,21), (1,17,16)(3,14,19)(6,11,24)(8,22,9), (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24), (2,4)(5,7)(10,12)(13,15)(18,20)(21,23) );
 
G=PermutationGroup([[(1,17,16),(2,18,13),(3,19,14),(4,20,15),(5,10,23),(6,11,24),(7,12,21),(8,9,22)], [(1,22),(2,23),(3,24),(4,21),(5,13),(6,14),(7,15),(8,16),(9,17),(10,18),(11,19),(12,20)], [(2,18,13),(4,15,20),(5,23,10),(7,12,21)], [(1,17,16),(3,14,19),(6,11,24),(8,22,9)], [(1,2,3,4),(5,6,7,8),(9,10,11,12),(13,14,15,16),(17,18,19,20),(21,22,23,24)], [(2,4),(5,7),(10,12),(13,15),(18,20),(21,23)]])
 
G:=TransitiveGroup(24,1323);
 

►On 24 points - transitive group 24T1324
Generators in S24
(1 20 21)(2 17 22)(3 18 23)(4 19 24)(5 10 14)(6 11 15)(7 12 16)(8 9 13)

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

(1 20 21)(3 23 18)(6 11 15)(8 13 9)

(2 22 17)(4 19 24)(5 10 14)(7 16 12)

(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)(2 7)(3 6)(4 5)(9 20)(10 19)(11 18)(12 17)(13 21)(14 24)(15 23)(16 22)
 
G:=sub<Sym(24)| (1,20,21)(2,17,22)(3,18,23)(4,19,24)(5,10,14)(6,11,15)(7,12,16)(8,9,13), (1,8)(2,5)(3,6)(4,7)(9,21)(10,22)(11,23)(12,24)(13,20)(14,17)(15,18)(16,19), (1,20,21)(3,23,18)(6,11,15)(8,13,9), (2,22,17)(4,19,24)(5,10,14)(7,16,12), (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)(2,7)(3,6)(4,5)(9,20)(10,19)(11,18)(12,17)(13,21)(14,24)(15,23)(16,22)>;
 
G:=Group( (1,20,21)(2,17,22)(3,18,23)(4,19,24)(5,10,14)(6,11,15)(7,12,16)(8,9,13), (1,8)(2,5)(3,6)(4,7)(9,21)(10,22)(11,23)(12,24)(13,20)(14,17)(15,18)(16,19), (1,20,21)(3,23,18)(6,11,15)(8,13,9), (2,22,17)(4,19,24)(5,10,14)(7,16,12), (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)(2,7)(3,6)(4,5)(9,20)(10,19)(11,18)(12,17)(13,21)(14,24)(15,23)(16,22) );
 
G=PermutationGroup([[(1,20,21),(2,17,22),(3,18,23),(4,19,24),(5,10,14),(6,11,15),(7,12,16),(8,9,13)], [(1,8),(2,5),(3,6),(4,7),(9,21),(10,22),(11,23),(12,24),(13,20),(14,17),(15,18),(16,19)], [(1,20,21),(3,23,18),(6,11,15),(8,13,9)], [(2,22,17),(4,19,24),(5,10,14),(7,16,12)], [(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),(2,7),(3,6),(4,5),(9,20),(10,19),(11,18),(12,17),(13,21),(14,24),(15,23),(16,22)]])
 
G:=TransitiveGroup(24,1324);
 

►On 27 points - transitive group 27T137
Generators in S27
(1 2 3)(4 18 23)(5 19 20)(6 16 21)(7 17 22)(8 26 12)(9 27 13)(10 24 14)(11 25 15)

(2 3)(8 12)(9 13)(10 14)(11 15)(16 21)(17 22)(18 23)(19 20)

(1 26 24)(2 12 14)(3 8 10)(4 5 27)(6 25 7)(9 23 20)(11 22 21)(13 18 19)(15 17 16)

(1 25 27)(2 15 13)(3 11 9)(4 26 7)(5 24 6)(8 22 23)(10 21 20)(12 17 18)(14 16 19)

(4 5 6 7)(8 9 10 11)(12 13 14 15)(16 17 18 19)(20 21 22 23)(24 25 26 27)

(4 5)(6 7)(8 10)(12 14)(16 17)(18 19)(20 23)(21 22)(24 26)
 
G:=sub<Sym(27)| (1,2,3)(4,18,23)(5,19,20)(6,16,21)(7,17,22)(8,26,12)(9,27,13)(10,24,14)(11,25,15), (2,3)(8,12)(9,13)(10,14)(11,15)(16,21)(17,22)(18,23)(19,20), (1,26,24)(2,12,14)(3,8,10)(4,5,27)(6,25,7)(9,23,20)(11,22,21)(13,18,19)(15,17,16), (1,25,27)(2,15,13)(3,11,9)(4,26,7)(5,24,6)(8,22,23)(10,21,20)(12,17,18)(14,16,19), (4,5,6,7)(8,9,10,11)(12,13,14,15)(16,17,18,19)(20,21,22,23)(24,25,26,27), (4,5)(6,7)(8,10)(12,14)(16,17)(18,19)(20,23)(21,22)(24,26)>;
 
G:=Group( (1,2,3)(4,18,23)(5,19,20)(6,16,21)(7,17,22)(8,26,12)(9,27,13)(10,24,14)(11,25,15), (2,3)(8,12)(9,13)(10,14)(11,15)(16,21)(17,22)(18,23)(19,20), (1,26,24)(2,12,14)(3,8,10)(4,5,27)(6,25,7)(9,23,20)(11,22,21)(13,18,19)(15,17,16), (1,25,27)(2,15,13)(3,11,9)(4,26,7)(5,24,6)(8,22,23)(10,21,20)(12,17,18)(14,16,19), (4,5,6,7)(8,9,10,11)(12,13,14,15)(16,17,18,19)(20,21,22,23)(24,25,26,27), (4,5)(6,7)(8,10)(12,14)(16,17)(18,19)(20,23)(21,22)(24,26) );
 
G=PermutationGroup([[(1,2,3),(4,18,23),(5,19,20),(6,16,21),(7,17,22),(8,26,12),(9,27,13),(10,24,14),(11,25,15)], [(2,3),(8,12),(9,13),(10,14),(11,15),(16,21),(17,22),(18,23),(19,20)], [(1,26,24),(2,12,14),(3,8,10),(4,5,27),(6,25,7),(9,23,20),(11,22,21),(13,18,19),(15,17,16)], [(1,25,27),(2,15,13),(3,11,9),(4,26,7),(5,24,6),(8,22,23),(10,21,20),(12,17,18),(14,16,19)], [(4,5,6,7),(8,9,10,11),(12,13,14,15),(16,17,18,19),(20,21,22,23),(24,25,26,27)], [(4,5),(6,7),(8,10),(12,14),(16,17),(18,19),(20,23),(21,22),(24,26)]])
 
G:=TransitiveGroup(27,137);
 

Polynomial with Galois group S3×S3≀C2 over ℚ
actionf(x)Disc(f)
12T156x12-3x10-2x9-45x8-60x7-101x6-162x5+621x4+1920x3+1944x2+864x+144-244·334·56·113

Matrix representation of S3×S3≀C2 ►in GL8(ℤ)

-1-1000000
10000000
00-1-10000
00100000
0000-1-100
00001000
000000-1-1
00000010
,
00100000
00-1-10000
10000000
-1-1000000
00000010
000000-1-1
00001000
0000-1-100
,
-1-1000000
10000000
00010000
00-1-10000
00000100
0000-1-100
000000-1-1
00000010
,
01000000
-1-1000000
00-1-10000
00100000
00000100
0000-1-100
000000-1-1
00000010
,
000000-10
0000000-1
0000-1000
00000-100
-10000000
0-1000000
00-100000
000-10000
,
00001000
00000100
00000010
00000001
10000000
01000000
00100000
00010000

G:=sub<GL(8,Integers())| [-1,1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,-1,0],[0,0,1,-1,0,0,0,0,0,0,0,-1,0,0,0,0,1,-1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,-1,0,0,0,0,1,-1,0,0,0,0,0,0,0,-1,0,0],[-1,1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,-1,0],[0,-1,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,-1,0],[0,0,0,0,-1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,-1,0,0,-1,0,0,0,0,0,0,0,0,-1,0,0,0,0,-1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0] >;
 

S3×S3≀C2 in GAP, Magma, Sage, TeX 

S_3\times S_3\wr C_2
 
% in TeX
 
G:=Group("S3xS3wrC2");
 
// GroupNames label
 
G:=SmallGroup(432,741);
 
// by ID
 
G=gap.SmallGroup(432,741);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-3,3,-3,135,851,298,165,348,530,14118]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e,f|a^3=b^2=c^3=d^3=e^4=f^2=1,b*a*b=a^-1,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,b*c=c*b,b*d=d*b,b*e=e*b,b*f=f*b,c*d=d*c,e*c*e^-1=d,f*c*f=e*d*e^-1=c^-1,d*f=f*d,f*e*f=e^-1>;
 
// generators/relations
 

Export

Character table of S3×S3≀C2 in TeX

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