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G = (C3×He3)⋊C6order 486 = 2·35

8th semidirect product of C3×He3 and C6 acting faithfully

Aliases: C3≀C33C6, C33⋊C6⋊C3, (C3×He3)⋊8C6, (C3×He3)⋊6S3, C332(C3×C6), He3.3(C3×S3), He34S32C3, C33.14(C3×S3), C33⋊C22C32, C33⋊C323C2, C32.7(C32⋊C6), C32.16(S3×C32), C3.7(C3×C32⋊C6), SmallGroup(486,127)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C33 — (C3×He3)⋊C6
 Chief series C1 — C3 — C32 — C33 — C3×He3 — C33⋊C32 — (C3×He3)⋊C6
 Lower central C33 — (C3×He3)⋊C6
 Upper central C1

Generators and relations for (C3×He3)⋊C6
G = < a,b,c,d,e | a3=b3=c3=d3=e6=1, ab=ba, ac=ca, ede-1=ad=da, eae-1=a-1c-1, bc=cb, dbd-1=bc-1, ebe-1=a-1b-1, cd=dc, ece-1=c-1 >

Subgroups: 654 in 82 conjugacy classes, 21 normal (12 characteristic)
C1, C2, C3, C3, S3, C6, C9, C32, C32, C3×S3, C3⋊S3, C3×C6, C3×C9, He3, He3, 3- 1+2, C33, C33, C32⋊C6, S3×C32, C3×C3⋊S3, C33⋊C2, C3≀C3, C3≀C3, C3×He3, C3×3- 1+2, C33⋊C6, C3×C32⋊C6, He34S3, C33⋊C32, (C3×He3)⋊C6
Quotients: C1, C2, C3, S3, C6, C32, C3×S3, C3×C6, C32⋊C6, S3×C32, C3×C32⋊C6, (C3×He3)⋊C6

Permutation representations of (C3×He3)⋊C6
On 27 points - transitive group 27T155
Generators in S27
(1 13 10)(3 12 15)(4 23 26)(5 24 27)(8 21 18)(9 16 19)
(2 11 14)(3 15 12)(5 27 24)(7 17 20)(8 21 18)(9 16 19)
(1 10 13)(2 14 11)(3 12 15)(4 23 26)(5 27 24)(6 25 22)(7 17 20)(8 21 18)(9 19 16)
(1 9 5)(2 17 22)(3 18 23)(4 15 21)(6 14 20)(7 25 11)(8 26 12)(10 19 27)(13 16 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 25 26 27)

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

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

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

G:=TransitiveGroup(27,155);

On 27 points - transitive group 27T171
Generators in S27
(1 23 26)(2 24 27)(4 17 10)(5 18 11)(7 13 20)(8 14 21)
(1 10 13)(2 8 5)(3 12 15)(4 20 23)(6 16 25)(7 26 17)(9 22 19)(11 27 21)(14 18 24)
(1 23 26)(2 27 24)(3 25 22)(4 17 10)(5 11 18)(6 19 12)(7 13 20)(8 21 14)(9 15 16)
(1 26 23)(3 25 22)(5 18 11)(6 12 19)(7 13 20)(8 21 14)
(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)

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

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

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

G:=TransitiveGroup(27,171);

On 27 points - transitive group 27T182
Generators in S27
(1 5 8)(2 9 4)(3 7 6)(10 25 12)(11 19 21)(13 15 22)(14 18 16)(17 24 26)(20 23 27)
(1 13 10)(2 24 16)(3 19 27)(4 17 18)(5 15 25)(6 11 23)(7 21 20)(8 22 12)(9 26 14)
(1 3 2)(4 8 6)(5 7 9)(10 27 16)(11 17 22)(12 23 18)(13 19 24)(14 25 20)(15 21 26)
(1 7 4)(2 5 6)(3 9 8)(10 25 12)(11 13 26)(14 18 16)(15 17 19)(20 23 27)(21 22 24)
(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)

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

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

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

G:=TransitiveGroup(27,182);

31 conjugacy classes

 class 1 2 3A 3B 3C 3D 3E 3F 3G ··· 3L 3M 3N 3O 6A ··· 6H 9A ··· 9F order 1 2 3 3 3 3 3 3 3 ··· 3 3 3 3 6 ··· 6 9 ··· 9 size 1 27 2 3 3 6 6 6 9 ··· 9 18 18 18 27 ··· 27 18 ··· 18

31 irreducible representations

 dim 1 1 1 1 1 1 18 2 2 2 6 6 type + + + + + image C1 C2 C3 C3 C6 C6 (C3×He3)⋊C6 S3 C3×S3 C3×S3 C32⋊C6 C3×C32⋊C6 kernel (C3×He3)⋊C6 C33⋊C32 C33⋊C6 He3⋊4S3 C3≀C3 C3×He3 C1 C3×He3 He3 C33 C32 C3 # reps 1 1 6 2 6 2 1 1 6 2 1 2

Matrix representation of (C3×He3)⋊C6 in GL18(ℤ)

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

(C3×He3)⋊C6 in GAP, Magma, Sage, TeX

(C_3\times {\rm He}_3)\rtimes C_6
% in TeX

G:=Group("(C3xHe3):C6");
// GroupNames label

G:=SmallGroup(486,127);
// by ID

G=gap.SmallGroup(486,127);
# by ID

G:=PCGroup([6,-2,-3,-3,-3,-3,-3,867,873,735,3244,3250,11669]);
// Polycyclic

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

׿
×
𝔽