non-abelian, supersoluble, monomial
Aliases: (C3×C9)⋊6D9, C32⋊C9.12S3, C32.9(C9⋊S3), (C32×C9).12S3, C33.22(C3⋊S3), C3.4(He3⋊S3), C3.5(C32⋊2D9), C32.20He3⋊3C2, C32.22(He3⋊C2), C3.4(3- 1+2.S3), SmallGroup(486,54)
Series: Derived ►Chief ►Lower central ►Upper central
| C32.20He3 — (C3×C9)⋊6D9 |
Generators and relations for (C3×C9)⋊6D9
G = < a,b,c,d | a3=b9=c9=d2=1, ab=ba, cac-1=ab6, dad=ab3, cbc-1=ab4, dbd=ab5, dcd=c-1 >
Subgroups: 646 in 63 conjugacy classes, 17 normal (9 characteristic)
C1, C2, C3, C3, C3, S3, C6, C9, C32, C32, D9, C3×S3, C3⋊S3, C3×C9, C3×C9, C33, C3×D9, C9⋊S3, C3×C3⋊S3, C32⋊C9, C32×C9, C32⋊D9, C3×C9⋊S3, C32.20He3, (C3×C9)⋊6D9
Quotients: C1, C2, S3, D9, C3⋊S3, C9⋊S3, He3⋊C2, C32⋊2D9, He3⋊S3, 3- 1+2.S3, (C3×C9)⋊6D9
Character table of (C3×C9)⋊6D9
| class | 1 | 2 | 3A | 3B | 3C | 3D | 3E | 3F | 3G | 3H | 6A | 6B | 9A | 9B | 9C | 9D | 9E | 9F | 9G | 9H | 9I | 9J | 9K | 9L | 9M | 9N | 9O | 9P | 9Q | 9R | |
| size | 1 | 81 | 2 | 2 | 2 | 2 | 3 | 3 | 6 | 6 | 81 | 81 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 18 | 18 | 18 | 18 | 18 | 18 | 18 | 18 | 18 | |
| ρ1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | trivial |
| ρ2 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 2 |
| ρ3 | 2 | 0 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 2 | 2 | 2 | orthogonal lifted from S3 |
| ρ4 | 2 | 0 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 2 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | orthogonal lifted from S3 |
| ρ5 | 2 | 0 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 0 | 0 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | orthogonal lifted from S3 |
| ρ6 | 2 | 0 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 2 | 2 | 2 | -1 | -1 | -1 | orthogonal lifted from S3 |
| ρ7 | 2 | 0 | 2 | -1 | -1 | -1 | 2 | 2 | -1 | -1 | 0 | 0 | -1 | -1 | -1 | 2 | 2 | 2 | -1 | -1 | -1 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | orthogonal lifted from D9 |
| ρ8 | 2 | 0 | 2 | -1 | -1 | -1 | 2 | 2 | -1 | -1 | 0 | 0 | 2 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | orthogonal lifted from D9 |
| ρ9 | 2 | 0 | 2 | -1 | -1 | -1 | 2 | 2 | -1 | -1 | 0 | 0 | 2 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | orthogonal lifted from D9 |
| ρ10 | 2 | 0 | 2 | -1 | -1 | -1 | 2 | 2 | -1 | -1 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | 2 | 2 | 2 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | orthogonal lifted from D9 |
| ρ11 | 2 | 0 | 2 | -1 | -1 | -1 | 2 | 2 | -1 | -1 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | 2 | 2 | 2 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | orthogonal lifted from D9 |
| ρ12 | 2 | 0 | 2 | -1 | -1 | -1 | 2 | 2 | -1 | -1 | 0 | 0 | 2 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | orthogonal lifted from D9 |
| ρ13 | 2 | 0 | 2 | -1 | -1 | -1 | 2 | 2 | -1 | -1 | 0 | 0 | -1 | -1 | -1 | 2 | 2 | 2 | -1 | -1 | -1 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | orthogonal lifted from D9 |
| ρ14 | 2 | 0 | 2 | -1 | -1 | -1 | 2 | 2 | -1 | -1 | 0 | 0 | -1 | -1 | -1 | 2 | 2 | 2 | -1 | -1 | -1 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | orthogonal lifted from D9 |
| ρ15 | 2 | 0 | 2 | -1 | -1 | -1 | 2 | 2 | -1 | -1 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | 2 | 2 | 2 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | orthogonal lifted from D9 |
| ρ16 | 3 | 1 | 3 | 3 | 3 | 3 | -3+3√-3/2 | -3-3√-3/2 | -3+3√-3/2 | -3-3√-3/2 | ζ3 | ζ32 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from He3⋊C2 |
| ρ17 | 3 | -1 | 3 | 3 | 3 | 3 | -3+3√-3/2 | -3-3√-3/2 | -3+3√-3/2 | -3-3√-3/2 | ζ65 | ζ6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from He3⋊C2 |
| ρ18 | 3 | -1 | 3 | 3 | 3 | 3 | -3-3√-3/2 | -3+3√-3/2 | -3-3√-3/2 | -3+3√-3/2 | ζ6 | ζ65 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from He3⋊C2 |
| ρ19 | 3 | 1 | 3 | 3 | 3 | 3 | -3-3√-3/2 | -3+3√-3/2 | -3-3√-3/2 | -3+3√-3/2 | ζ32 | ζ3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from He3⋊C2 |
| ρ20 | 6 | 0 | -3 | 6 | -3 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | -ζ98+2ζ97+ζ94+ζ92 | ζ95+2ζ94-ζ92+ζ9 | 2ζ98-ζ94+ζ92+ζ9 | -ζ98+2ζ97+ζ94+ζ92 | ζ95+2ζ94-ζ92+ζ9 | 2ζ98-ζ94+ζ92+ζ9 | -ζ98+2ζ97+ζ94+ζ92 | ζ95+2ζ94-ζ92+ζ9 | 2ζ98-ζ94+ζ92+ζ9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from He3⋊S3 |
| ρ21 | 6 | 0 | -3 | -3 | -3 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | -ζ98+2ζ97+ζ94+ζ92 | ζ95+2ζ94-ζ92+ζ9 | 2ζ98-ζ94+ζ92+ζ9 | ζ95+2ζ94-ζ92+ζ9 | 2ζ98-ζ94+ζ92+ζ9 | -ζ98+2ζ97+ζ94+ζ92 | 2ζ98-ζ94+ζ92+ζ9 | -ζ98+2ζ97+ζ94+ζ92 | ζ95+2ζ94-ζ92+ζ9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from 3- 1+2.S3 |
| ρ22 | 6 | 0 | -3 | 6 | -3 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | ζ95+2ζ94-ζ92+ζ9 | 2ζ98-ζ94+ζ92+ζ9 | -ζ98+2ζ97+ζ94+ζ92 | ζ95+2ζ94-ζ92+ζ9 | 2ζ98-ζ94+ζ92+ζ9 | -ζ98+2ζ97+ζ94+ζ92 | ζ95+2ζ94-ζ92+ζ9 | 2ζ98-ζ94+ζ92+ζ9 | -ζ98+2ζ97+ζ94+ζ92 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from He3⋊S3 |
| ρ23 | 6 | 0 | -3 | -3 | 6 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | -ζ98+2ζ97+ζ94+ζ92 | ζ95+2ζ94-ζ92+ζ9 | 2ζ98-ζ94+ζ92+ζ9 | 2ζ98-ζ94+ζ92+ζ9 | -ζ98+2ζ97+ζ94+ζ92 | ζ95+2ζ94-ζ92+ζ9 | ζ95+2ζ94-ζ92+ζ9 | 2ζ98-ζ94+ζ92+ζ9 | -ζ98+2ζ97+ζ94+ζ92 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from 3- 1+2.S3 |
| ρ24 | 6 | 0 | -3 | -3 | 6 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | ζ95+2ζ94-ζ92+ζ9 | 2ζ98-ζ94+ζ92+ζ9 | -ζ98+2ζ97+ζ94+ζ92 | -ζ98+2ζ97+ζ94+ζ92 | ζ95+2ζ94-ζ92+ζ9 | 2ζ98-ζ94+ζ92+ζ9 | 2ζ98-ζ94+ζ92+ζ9 | -ζ98+2ζ97+ζ94+ζ92 | ζ95+2ζ94-ζ92+ζ9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from 3- 1+2.S3 |
| ρ25 | 6 | 0 | -3 | -3 | -3 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | ζ95+2ζ94-ζ92+ζ9 | 2ζ98-ζ94+ζ92+ζ9 | -ζ98+2ζ97+ζ94+ζ92 | 2ζ98-ζ94+ζ92+ζ9 | -ζ98+2ζ97+ζ94+ζ92 | ζ95+2ζ94-ζ92+ζ9 | -ζ98+2ζ97+ζ94+ζ92 | ζ95+2ζ94-ζ92+ζ9 | 2ζ98-ζ94+ζ92+ζ9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from 3- 1+2.S3 |
| ρ26 | 6 | 0 | -3 | 6 | -3 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | 2ζ98-ζ94+ζ92+ζ9 | -ζ98+2ζ97+ζ94+ζ92 | ζ95+2ζ94-ζ92+ζ9 | 2ζ98-ζ94+ζ92+ζ9 | -ζ98+2ζ97+ζ94+ζ92 | ζ95+2ζ94-ζ92+ζ9 | 2ζ98-ζ94+ζ92+ζ9 | -ζ98+2ζ97+ζ94+ζ92 | ζ95+2ζ94-ζ92+ζ9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from He3⋊S3 |
| ρ27 | 6 | 0 | -3 | -3 | -3 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | 2ζ98-ζ94+ζ92+ζ9 | -ζ98+2ζ97+ζ94+ζ92 | ζ95+2ζ94-ζ92+ζ9 | -ζ98+2ζ97+ζ94+ζ92 | ζ95+2ζ94-ζ92+ζ9 | 2ζ98-ζ94+ζ92+ζ9 | ζ95+2ζ94-ζ92+ζ9 | 2ζ98-ζ94+ζ92+ζ9 | -ζ98+2ζ97+ζ94+ζ92 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from 3- 1+2.S3 |
| ρ28 | 6 | 0 | -3 | -3 | 6 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | 2ζ98-ζ94+ζ92+ζ9 | -ζ98+2ζ97+ζ94+ζ92 | ζ95+2ζ94-ζ92+ζ9 | ζ95+2ζ94-ζ92+ζ9 | 2ζ98-ζ94+ζ92+ζ9 | -ζ98+2ζ97+ζ94+ζ92 | -ζ98+2ζ97+ζ94+ζ92 | ζ95+2ζ94-ζ92+ζ9 | 2ζ98-ζ94+ζ92+ζ9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from 3- 1+2.S3 |
| ρ29 | 6 | 0 | 6 | -3 | -3 | -3 | -3-3√-3 | -3+3√-3 | 3+3√-3/2 | 3-3√-3/2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from C32⋊2D9 |
| ρ30 | 6 | 0 | 6 | -3 | -3 | -3 | -3+3√-3 | -3-3√-3 | 3-3√-3/2 | 3+3√-3/2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from C32⋊2D9 |
►On 81 points
Generators in S81
(1 7 4)(2 8 5)(3 9 6)(10 13 16)(11 14 17)(12 15 18)(19 22 25)(20 23 26)(21 24 27)(28 34 31)(29 35 32)(30 36 33)(37 43 40)(38 44 41)(39 45 42)(73 76 79)(74 77 80)(75 78 81)
(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)(28 29 30 31 32 33 34 35 36)(37 38 39 40 41 42 43 44 45)(46 47 48 49 50 51 52 53 54)(55 56 57 58 59 60 61 62 63)(64 65 66 67 68 69 70 71 72)(73 74 75 76 77 78 79 80 81)
(1 23 69 38 75 48 35 17 63)(2 24 64 39 76 52 36 18 58)(3 25 68 40 77 47 28 10 62)(4 26 72 41 78 51 29 11 57)(5 27 67 42 79 46 30 12 61)(6 19 71 43 80 50 31 13 56)(7 20 66 44 81 54 32 14 60)(8 21 70 45 73 49 33 15 55)(9 22 65 37 74 53 34 16 59)
(1 63)(2 59)(3 55)(4 60)(5 56)(6 61)(7 57)(8 62)(9 58)(10 21)(11 20)(12 19)(13 27)(14 26)(15 25)(16 24)(17 23)(18 22)(28 70)(29 66)(30 71)(31 67)(32 72)(33 68)(34 64)(35 69)(36 65)(37 52)(38 48)(39 53)(40 49)(41 54)(42 50)(43 46)(44 51)(45 47)(73 77)(74 76)(78 81)(79 80)
G:=sub<Sym(81)| (1,7,4)(2,8,5)(3,9,6)(10,13,16)(11,14,17)(12,15,18)(19,22,25)(20,23,26)(21,24,27)(28,34,31)(29,35,32)(30,36,33)(37,43,40)(38,44,41)(39,45,42)(73,76,79)(74,77,80)(75,78,81), (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)(28,29,30,31,32,33,34,35,36)(37,38,39,40,41,42,43,44,45)(46,47,48,49,50,51,52,53,54)(55,56,57,58,59,60,61,62,63)(64,65,66,67,68,69,70,71,72)(73,74,75,76,77,78,79,80,81), (1,23,69,38,75,48,35,17,63)(2,24,64,39,76,52,36,18,58)(3,25,68,40,77,47,28,10,62)(4,26,72,41,78,51,29,11,57)(5,27,67,42,79,46,30,12,61)(6,19,71,43,80,50,31,13,56)(7,20,66,44,81,54,32,14,60)(8,21,70,45,73,49,33,15,55)(9,22,65,37,74,53,34,16,59), (1,63)(2,59)(3,55)(4,60)(5,56)(6,61)(7,57)(8,62)(9,58)(10,21)(11,20)(12,19)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(28,70)(29,66)(30,71)(31,67)(32,72)(33,68)(34,64)(35,69)(36,65)(37,52)(38,48)(39,53)(40,49)(41,54)(42,50)(43,46)(44,51)(45,47)(73,77)(74,76)(78,81)(79,80)>;
G:=Group( (1,7,4)(2,8,5)(3,9,6)(10,13,16)(11,14,17)(12,15,18)(19,22,25)(20,23,26)(21,24,27)(28,34,31)(29,35,32)(30,36,33)(37,43,40)(38,44,41)(39,45,42)(73,76,79)(74,77,80)(75,78,81), (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)(28,29,30,31,32,33,34,35,36)(37,38,39,40,41,42,43,44,45)(46,47,48,49,50,51,52,53,54)(55,56,57,58,59,60,61,62,63)(64,65,66,67,68,69,70,71,72)(73,74,75,76,77,78,79,80,81), (1,23,69,38,75,48,35,17,63)(2,24,64,39,76,52,36,18,58)(3,25,68,40,77,47,28,10,62)(4,26,72,41,78,51,29,11,57)(5,27,67,42,79,46,30,12,61)(6,19,71,43,80,50,31,13,56)(7,20,66,44,81,54,32,14,60)(8,21,70,45,73,49,33,15,55)(9,22,65,37,74,53,34,16,59), (1,63)(2,59)(3,55)(4,60)(5,56)(6,61)(7,57)(8,62)(9,58)(10,21)(11,20)(12,19)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(28,70)(29,66)(30,71)(31,67)(32,72)(33,68)(34,64)(35,69)(36,65)(37,52)(38,48)(39,53)(40,49)(41,54)(42,50)(43,46)(44,51)(45,47)(73,77)(74,76)(78,81)(79,80) );
G=PermutationGroup([[(1,7,4),(2,8,5),(3,9,6),(10,13,16),(11,14,17),(12,15,18),(19,22,25),(20,23,26),(21,24,27),(28,34,31),(29,35,32),(30,36,33),(37,43,40),(38,44,41),(39,45,42),(73,76,79),(74,77,80),(75,78,81)], [(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),(28,29,30,31,32,33,34,35,36),(37,38,39,40,41,42,43,44,45),(46,47,48,49,50,51,52,53,54),(55,56,57,58,59,60,61,62,63),(64,65,66,67,68,69,70,71,72),(73,74,75,76,77,78,79,80,81)], [(1,23,69,38,75,48,35,17,63),(2,24,64,39,76,52,36,18,58),(3,25,68,40,77,47,28,10,62),(4,26,72,41,78,51,29,11,57),(5,27,67,42,79,46,30,12,61),(6,19,71,43,80,50,31,13,56),(7,20,66,44,81,54,32,14,60),(8,21,70,45,73,49,33,15,55),(9,22,65,37,74,53,34,16,59)], [(1,63),(2,59),(3,55),(4,60),(5,56),(6,61),(7,57),(8,62),(9,58),(10,21),(11,20),(12,19),(13,27),(14,26),(15,25),(16,24),(17,23),(18,22),(28,70),(29,66),(30,71),(31,67),(32,72),(33,68),(34,64),(35,69),(36,65),(37,52),(38,48),(39,53),(40,49),(41,54),(42,50),(43,46),(44,51),(45,47),(73,77),(74,76),(78,81),(79,80)]])
Matrix representation of (C3×C9)⋊6D9 ►in GL8(𝔽19)
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 18 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 18 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 18 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 18 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 18 | 18 |
| 0 | 0 | 18 | 0 | 0 | 0 | 1 | 0 |
| 0 | 18 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 18 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 14 | 0 | 0 | 0 | 0 |
| 0 | 0 | 5 | 2 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 14 | 5 | 7 | 0 | 0 |
| 0 | 0 | 7 | 2 | 12 | 17 | 0 | 0 |
| 0 | 0 | 5 | 0 | 0 | 0 | 2 | 14 |
| 0 | 0 | 0 | 14 | 0 | 0 | 5 | 7 |
| 17 | 7 | 0 | 0 | 0 | 0 | 0 | 0 |
| 12 | 5 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 18 | 1 | 0 | 0 |
| 0 | 0 | 1 | 1 | 17 | 18 | 0 | 0 |
| 0 | 0 | 0 | 0 | 18 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 18 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 18 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 18 | 0 | 0 | 0 |
| 12 | 5 | 0 | 0 | 0 | 0 | 0 | 0 |
| 17 | 7 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 17 | 18 | 0 | 0 |
| 0 | 0 | 0 | 0 | 18 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 18 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 18 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 18 | 0 | 1 | 0 |
| 0 | 0 | 1 | 1 | 18 | 0 | 18 | 18 |
G:=sub<GL(8,GF(19))| [1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,18,18,18,18,0,18,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,18,1,0,0,0,0,0,0,18,0],[0,1,0,0,0,0,0,0,18,18,0,0,0,0,0,0,0,0,7,5,0,7,5,0,0,0,14,2,14,2,0,14,0,0,0,0,5,12,0,0,0,0,0,0,7,17,0,0,0,0,0,0,0,0,2,5,0,0,0,0,0,0,14,7],[17,12,0,0,0,0,0,0,7,5,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,0,0,0,18,17,18,18,18,18,0,0,1,18,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0],[12,17,0,0,0,0,0,0,5,7,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,0,0,1,0,1,0,0,17,18,18,18,18,18,0,0,18,1,0,0,0,0,0,0,0,0,0,0,1,18,0,0,0,0,0,0,0,18] >;
(C3×C9)⋊6D9 in GAP, Magma, Sage, TeX
(C_3\times C_9)\rtimes_6D_9
% in TeX
G:=Group("(C3xC9):6D9"); // GroupNames label
G:=SmallGroup(486,54);
// by ID
G=gap.SmallGroup(486,54);
# by ID
G:=PCGroup([6,-2,-3,-3,-3,-3,-3,265,223,3134,548,986,867,11344,3250,11669]);
// Polycyclic
G:=Group<a,b,c,d|a^3=b^9=c^9=d^2=1,a*b=b*a,c*a*c^-1=a*b^6,d*a*d=a*b^3,c*b*c^-1=a*b^4,d*b*d=a*b^5,d*c*d=c^-1>;
// generators/relations
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