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## G = C33⋊(C3×S3)  order 486 = 2·35

### 4th semidirect product of C33 and C3×S3 acting faithfully

Aliases: C3≀C31C6, C33⋊S3⋊C3, C334(C3×S3), (C3×He3)⋊12S3, He3.7(C3×S3), C33.15(C3⋊S3), C33⋊C321C2, 3- 1+23(C3×S3), (C3×3- 1+2)⋊7S3, C32.8(He3⋊C2), C32.8(C3×C3⋊S3), C3.9(C3×He3⋊C2), SmallGroup(486,176)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C32 — C3≀C3 — C33⋊(C3×S3)
 Chief series C1 — C3 — C32 — C33 — C3≀C3 — C33⋊C32 — C33⋊(C3×S3)
 Lower central C3≀C3 — C33⋊(C3×S3)
 Upper central C1

Generators and relations for C33⋊(C3×S3)
G = < a,b,c,d,e,f | a3=b3=c3=d3=e3=f2=1, ab=ba, dad-1=ac=ca, eae-1=ab-1c, faf=a-1, bc=cb, bd=db, ebe-1=fbf=bc-1, cd=dc, ce=ec, fcf=c-1, de=ed, df=fd, fef=e-1 >

Subgroups: 632 in 100 conjugacy classes, 19 normal (13 characteristic)
C1, C2, C3, C3, S3, C6, C9, C32, C32, C32, D9, C3×S3, C3⋊S3, C3×C6, C3×C9, He3, He3, 3- 1+2, 3- 1+2, C33, C33, C3×D9, C32⋊C6, C9⋊C6, S3×C32, C3×C3⋊S3, C3≀C3, C3≀C3, C3×He3, C3×3- 1+2, C33⋊S3, C3×C32⋊C6, C3×C9⋊C6, C33⋊C32, C33⋊(C3×S3)
Quotients: C1, C2, C3, S3, C6, C3×S3, C3⋊S3, He3⋊C2, C3×C3⋊S3, C3×He3⋊C2, C33⋊(C3×S3)

Permutation representations of C33⋊(C3×S3)
On 27 points - transitive group 27T160
Generators in S27
(1 2 3)(4 5 6)(7 8 9)(10 11 12)(13 14 15)(16 17 18)(19 20 21)(22 23 24)(25 26 27)
(1 6 14)(2 4 15)(3 5 13)(7 24 16)(8 22 17)(9 23 18)(10 27 19)(11 25 20)(12 26 21)
(1 26 8)(2 27 9)(3 25 7)(4 19 23)(5 20 24)(6 21 22)(10 18 15)(11 16 13)(12 17 14)
(2 9 27)(3 25 7)(4 23 19)(5 20 24)(10 15 18)(11 16 13)
(2 4 10)(3 13 24)(5 25 11)(6 21 22)(7 16 20)(9 23 15)(12 14 17)(18 27 19)
(2 3)(4 24)(5 23)(6 22)(7 27)(8 26)(9 25)(10 13)(11 15)(12 14)(16 18)(19 20)

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

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

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

G:=TransitiveGroup(27,160);

On 27 points - transitive group 27T166
Generators in S27
(10 11 12)(13 14 15)(16 17 18)(19 20 21)(22 23 24)(25 26 27)
(1 9 3)(6 7 8)(10 12 11)(16 18 17)(19 20 21)(25 26 27)
(1 3 9)(2 4 5)(6 7 8)(10 11 12)(13 15 14)(16 18 17)(19 21 20)(22 23 24)(25 26 27)
(1 10 19)(2 22 13)(3 11 21)(4 23 15)(5 24 14)(6 26 16)(7 27 18)(8 25 17)(9 12 20)
(1 16 13)(2 10 6)(3 18 15)(4 11 7)(5 12 8)(9 17 14)(19 26 22)(20 25 24)(21 27 23)
(2 6)(3 9)(4 8)(5 7)(11 12)(13 16)(14 18)(15 17)(20 21)(22 26)(23 25)(24 27)

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

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

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

G:=TransitiveGroup(27,166);

On 27 points - transitive group 27T187
Generators in S27
(1 2 3)(4 5 6)(7 8 9)(10 11 12)(13 14 15)(16 17 18)(19 20 21)(22 23 24)(25 26 27)
(1 12 15)(2 10 13)(3 11 14)(4 26 8)(5 27 9)(6 25 7)
(1 15 12)(2 13 10)(3 14 11)(4 26 8)(5 27 9)(6 25 7)(16 22 19)(17 23 20)(18 24 21)
(2 10 13)(3 14 11)(4 26 8)(6 7 25)(16 19 22)(17 23 20)
(1 5 21)(2 25 16)(3 8 23)(4 20 14)(6 19 10)(7 22 13)(9 24 12)(11 26 17)(15 27 18)
(2 3)(4 19)(5 21)(6 20)(7 17)(8 16)(9 18)(10 14)(11 13)(12 15)(22 26)(23 25)(24 27)

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

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

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

G:=TransitiveGroup(27,187);

31 conjugacy classes

 class 1 2 3A 3B ··· 3I 3J ··· 3O 6A ··· 6H 9A ··· 9F order 1 2 3 3 ··· 3 3 ··· 3 6 ··· 6 9 ··· 9 size 1 27 2 3 ··· 3 18 ··· 18 27 ··· 27 18 ··· 18

31 irreducible representations

 dim 1 1 1 1 18 2 2 2 2 2 3 type + + + + + image C1 C2 C3 C6 C33⋊(C3×S3) S3 S3 C3×S3 C3×S3 C3×S3 He3⋊C2 kernel C33⋊(C3×S3) C33⋊C32 C33⋊S3 C3≀C3 C1 C3×He3 C3×3- 1+2 He3 3- 1+2 C33 C32 # reps 1 1 2 2 1 2 2 2 4 2 12

Matrix representation of C33⋊(C3×S3) in GL18(ℤ)

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

G:=sub<GL(18,Integers())| [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0],[0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1],[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0],[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0],[1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0] >;

C33⋊(C3×S3) in GAP, Magma, Sage, TeX

C_3^3\rtimes (C_3\times S_3)
% in TeX

G:=Group("C3^3:(C3xS3)");
// GroupNames label

G:=SmallGroup(486,176);
// by ID

G=gap.SmallGroup(486,176);
# by ID

G:=PCGroup([6,-2,-3,-3,-3,-3,-3,218,867,2169,303,11344,1096,11669]);
// Polycyclic

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

׿
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