metabelian, supersoluble, monomial, A-group
Aliases: C9⋊Dic3, C3⋊Dic9, C6.3D9, C18.3S3, C32.3Dic3, (C3×C9)⋊3C4, C2.(C9⋊S3), (C3×C6).6S3, C6.1(C3⋊S3), (C3×C18).3C2, C3.(C3⋊Dic3), SmallGroup(108,10)
Series: Derived ►Chief ►Lower central ►Upper central
| C3×C9 — C9⋊Dic3 |
Generators and relations for C9⋊Dic3
G = < a,b,c | a9=b6=1, c2=b3, ab=ba, cac-1=a-1, cbc-1=b-1 >
Character table of C9⋊Dic3
| class | 1 | 2 | 3A | 3B | 3C | 3D | 4A | 4B | 6A | 6B | 6C | 6D | 9A | 9B | 9C | 9D | 9E | 9F | 9G | 9H | 9I | 18A | 18B | 18C | 18D | 18E | 18F | 18G | 18H | 18I | |
| size | 1 | 1 | 2 | 2 | 2 | 2 | 27 | 27 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | |
| 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 | 1 | -1 | 1 | 1 | 1 | 1 | -i | i | -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 4 |
| ρ4 | 1 | -1 | 1 | 1 | 1 | 1 | i | -i | -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 4 |
| ρ5 | 2 | 2 | -1 | -1 | -1 | 2 | 0 | 0 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | 2 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | orthogonal lifted from S3 |
| ρ6 | 2 | 2 | 2 | 2 | 2 | 2 | 0 | 0 | 2 | 2 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | orthogonal lifted from S3 |
| ρ7 | 2 | 2 | -1 | -1 | -1 | 2 | 0 | 0 | -1 | 2 | -1 | -1 | -1 | 2 | -1 | -1 | -1 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | 2 | 2 | 2 | -1 | -1 | orthogonal lifted from S3 |
| ρ8 | 2 | 2 | 2 | -1 | -1 | -1 | 0 | 0 | -1 | -1 | 2 | -1 | ζ95+ζ94 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ98+ζ9 | ζ97+ζ92 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | orthogonal lifted from D9 |
| ρ9 | 2 | 2 | -1 | -1 | -1 | 2 | 0 | 0 | -1 | 2 | -1 | -1 | -1 | -1 | 2 | -1 | -1 | -1 | -1 | 2 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | 2 | 2 | orthogonal lifted from S3 |
| ρ10 | 2 | 2 | -1 | -1 | 2 | -1 | 0 | 0 | 2 | -1 | -1 | -1 | ζ97+ζ92 | ζ97+ζ92 | ζ98+ζ9 | ζ95+ζ94 | ζ98+ζ9 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ95+ζ94 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ98+ζ9 | ζ97+ζ92 | orthogonal lifted from D9 |
| ρ11 | 2 | 2 | 2 | -1 | -1 | -1 | 0 | 0 | -1 | -1 | 2 | -1 | ζ98+ζ9 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ97+ζ92 | ζ95+ζ94 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | orthogonal lifted from D9 |
| ρ12 | 2 | 2 | 2 | -1 | -1 | -1 | 0 | 0 | -1 | -1 | 2 | -1 | ζ97+ζ92 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ95+ζ94 | ζ98+ζ9 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | orthogonal lifted from D9 |
| ρ13 | 2 | 2 | -1 | -1 | 2 | -1 | 0 | 0 | 2 | -1 | -1 | -1 | ζ98+ζ9 | ζ98+ζ9 | ζ95+ζ94 | ζ97+ζ92 | ζ95+ζ94 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ97+ζ92 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ95+ζ94 | ζ98+ζ9 | orthogonal lifted from D9 |
| ρ14 | 2 | 2 | -1 | 2 | -1 | -1 | 0 | 0 | -1 | -1 | -1 | 2 | ζ97+ζ92 | ζ95+ζ94 | ζ95+ζ94 | ζ95+ζ94 | ζ98+ζ9 | ζ98+ζ9 | ζ97+ζ92 | ζ98+ζ9 | ζ97+ζ92 | ζ97+ζ92 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ95+ζ94 | ζ98+ζ9 | orthogonal lifted from D9 |
| ρ15 | 2 | 2 | -1 | 2 | -1 | -1 | 0 | 0 | -1 | -1 | -1 | 2 | ζ98+ζ9 | ζ97+ζ92 | ζ97+ζ92 | ζ97+ζ92 | ζ95+ζ94 | ζ95+ζ94 | ζ98+ζ9 | ζ95+ζ94 | ζ98+ζ9 | ζ98+ζ9 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ97+ζ92 | ζ95+ζ94 | orthogonal lifted from D9 |
| ρ16 | 2 | 2 | -1 | -1 | 2 | -1 | 0 | 0 | 2 | -1 | -1 | -1 | ζ95+ζ94 | ζ95+ζ94 | ζ97+ζ92 | ζ98+ζ9 | ζ97+ζ92 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ98+ζ9 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ97+ζ92 | ζ95+ζ94 | orthogonal lifted from D9 |
| ρ17 | 2 | 2 | -1 | 2 | -1 | -1 | 0 | 0 | -1 | -1 | -1 | 2 | ζ95+ζ94 | ζ98+ζ9 | ζ98+ζ9 | ζ98+ζ9 | ζ97+ζ92 | ζ97+ζ92 | ζ95+ζ94 | ζ97+ζ92 | ζ95+ζ94 | ζ95+ζ94 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ98+ζ9 | ζ97+ζ92 | orthogonal lifted from D9 |
| ρ18 | 2 | -2 | -1 | -1 | -1 | 2 | 0 | 0 | 1 | -2 | 1 | 1 | 2 | -1 | -1 | 2 | 2 | -1 | -1 | -1 | -1 | 1 | -2 | -2 | -2 | 1 | 1 | 1 | 1 | 1 | symplectic lifted from Dic3, Schur index 2 |
| ρ19 | 2 | -2 | -1 | -1 | -1 | 2 | 0 | 0 | 1 | -2 | 1 | 1 | -1 | 2 | -1 | -1 | -1 | 2 | 2 | -1 | -1 | 1 | 1 | 1 | 1 | -2 | -2 | -2 | 1 | 1 | symplectic lifted from Dic3, Schur index 2 |
| ρ20 | 2 | -2 | 2 | -1 | -1 | -1 | 0 | 0 | 1 | 1 | -2 | 1 | ζ95+ζ94 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ98+ζ9 | ζ97+ζ92 | -ζ97-ζ92 | -ζ95-ζ94 | -ζ98-ζ9 | -ζ97-ζ92 | -ζ95-ζ94 | -ζ98-ζ9 | -ζ97-ζ92 | -ζ95-ζ94 | -ζ98-ζ9 | symplectic lifted from Dic9, Schur index 2 |
| ρ21 | 2 | -2 | -1 | -1 | -1 | 2 | 0 | 0 | 1 | -2 | 1 | 1 | -1 | -1 | 2 | -1 | -1 | -1 | -1 | 2 | 2 | -2 | 1 | 1 | 1 | 1 | 1 | 1 | -2 | -2 | symplectic lifted from Dic3, Schur index 2 |
| ρ22 | 2 | -2 | -1 | 2 | -1 | -1 | 0 | 0 | 1 | 1 | 1 | -2 | ζ95+ζ94 | ζ98+ζ9 | ζ98+ζ9 | ζ98+ζ9 | ζ97+ζ92 | ζ97+ζ92 | ζ95+ζ94 | ζ97+ζ92 | ζ95+ζ94 | -ζ95-ζ94 | -ζ95-ζ94 | -ζ98-ζ9 | -ζ97-ζ92 | -ζ97-ζ92 | -ζ95-ζ94 | -ζ98-ζ9 | -ζ98-ζ9 | -ζ97-ζ92 | symplectic lifted from Dic9, Schur index 2 |
| ρ23 | 2 | -2 | -1 | 2 | -1 | -1 | 0 | 0 | 1 | 1 | 1 | -2 | ζ97+ζ92 | ζ95+ζ94 | ζ95+ζ94 | ζ95+ζ94 | ζ98+ζ9 | ζ98+ζ9 | ζ97+ζ92 | ζ98+ζ9 | ζ97+ζ92 | -ζ97-ζ92 | -ζ97-ζ92 | -ζ95-ζ94 | -ζ98-ζ9 | -ζ98-ζ9 | -ζ97-ζ92 | -ζ95-ζ94 | -ζ95-ζ94 | -ζ98-ζ9 | symplectic lifted from Dic9, Schur index 2 |
| ρ24 | 2 | -2 | -1 | -1 | 2 | -1 | 0 | 0 | -2 | 1 | 1 | 1 | ζ98+ζ9 | ζ98+ζ9 | ζ95+ζ94 | ζ97+ζ92 | ζ95+ζ94 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | -ζ97-ζ92 | -ζ98-ζ9 | -ζ97-ζ92 | -ζ95-ζ94 | -ζ97-ζ92 | -ζ95-ζ94 | -ζ98-ζ9 | -ζ95-ζ94 | -ζ98-ζ9 | symplectic lifted from Dic9, Schur index 2 |
| ρ25 | 2 | -2 | -1 | -1 | 2 | -1 | 0 | 0 | -2 | 1 | 1 | 1 | ζ95+ζ94 | ζ95+ζ94 | ζ97+ζ92 | ζ98+ζ9 | ζ97+ζ92 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | -ζ98-ζ9 | -ζ95-ζ94 | -ζ98-ζ9 | -ζ97-ζ92 | -ζ98-ζ9 | -ζ97-ζ92 | -ζ95-ζ94 | -ζ97-ζ92 | -ζ95-ζ94 | symplectic lifted from Dic9, Schur index 2 |
| ρ26 | 2 | -2 | 2 | -1 | -1 | -1 | 0 | 0 | 1 | 1 | -2 | 1 | ζ97+ζ92 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ95+ζ94 | ζ98+ζ9 | -ζ98-ζ9 | -ζ97-ζ92 | -ζ95-ζ94 | -ζ98-ζ9 | -ζ97-ζ92 | -ζ95-ζ94 | -ζ98-ζ9 | -ζ97-ζ92 | -ζ95-ζ94 | symplectic lifted from Dic9, Schur index 2 |
| ρ27 | 2 | -2 | 2 | 2 | 2 | 2 | 0 | 0 | -2 | -2 | -2 | -2 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | symplectic lifted from Dic3, Schur index 2 |
| ρ28 | 2 | -2 | -1 | 2 | -1 | -1 | 0 | 0 | 1 | 1 | 1 | -2 | ζ98+ζ9 | ζ97+ζ92 | ζ97+ζ92 | ζ97+ζ92 | ζ95+ζ94 | ζ95+ζ94 | ζ98+ζ9 | ζ95+ζ94 | ζ98+ζ9 | -ζ98-ζ9 | -ζ98-ζ9 | -ζ97-ζ92 | -ζ95-ζ94 | -ζ95-ζ94 | -ζ98-ζ9 | -ζ97-ζ92 | -ζ97-ζ92 | -ζ95-ζ94 | symplectic lifted from Dic9, Schur index 2 |
| ρ29 | 2 | -2 | -1 | -1 | 2 | -1 | 0 | 0 | -2 | 1 | 1 | 1 | ζ97+ζ92 | ζ97+ζ92 | ζ98+ζ9 | ζ95+ζ94 | ζ98+ζ9 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | -ζ95-ζ94 | -ζ97-ζ92 | -ζ95-ζ94 | -ζ98-ζ9 | -ζ95-ζ94 | -ζ98-ζ9 | -ζ97-ζ92 | -ζ98-ζ9 | -ζ97-ζ92 | symplectic lifted from Dic9, Schur index 2 |
| ρ30 | 2 | -2 | 2 | -1 | -1 | -1 | 0 | 0 | 1 | 1 | -2 | 1 | ζ98+ζ9 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ95+ζ94 | ζ98+ζ9 | ζ97+ζ92 | ζ97+ζ92 | ζ95+ζ94 | -ζ95-ζ94 | -ζ98-ζ9 | -ζ97-ζ92 | -ζ95-ζ94 | -ζ98-ζ9 | -ζ97-ζ92 | -ζ95-ζ94 | -ζ98-ζ9 | -ζ97-ζ92 | symplectic lifted from Dic9, Schur index 2 |
►Regular action on 108 points
Generators in S108
(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)(82 83 84 85 86 87 88 89 90)(91 92 93 94 95 96 97 98 99)(100 101 102 103 104 105 106 107 108)
(1 48 35 59 37 65)(2 49 36 60 38 66)(3 50 28 61 39 67)(4 51 29 62 40 68)(5 52 30 63 41 69)(6 53 31 55 42 70)(7 54 32 56 43 71)(8 46 33 57 44 72)(9 47 34 58 45 64)(10 80 25 98 107 84)(11 81 26 99 108 85)(12 73 27 91 100 86)(13 74 19 92 101 87)(14 75 20 93 102 88)(15 76 21 94 103 89)(16 77 22 95 104 90)(17 78 23 96 105 82)(18 79 24 97 106 83)
(1 23 59 82)(2 22 60 90)(3 21 61 89)(4 20 62 88)(5 19 63 87)(6 27 55 86)(7 26 56 85)(8 25 57 84)(9 24 58 83)(10 72 98 33)(11 71 99 32)(12 70 91 31)(13 69 92 30)(14 68 93 29)(15 67 94 28)(16 66 95 36)(17 65 96 35)(18 64 97 34)(37 105 48 78)(38 104 49 77)(39 103 50 76)(40 102 51 75)(41 101 52 74)(42 100 53 73)(43 108 54 81)(44 107 46 80)(45 106 47 79)
G:=sub<Sym(108)| (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)(82,83,84,85,86,87,88,89,90)(91,92,93,94,95,96,97,98,99)(100,101,102,103,104,105,106,107,108), (1,48,35,59,37,65)(2,49,36,60,38,66)(3,50,28,61,39,67)(4,51,29,62,40,68)(5,52,30,63,41,69)(6,53,31,55,42,70)(7,54,32,56,43,71)(8,46,33,57,44,72)(9,47,34,58,45,64)(10,80,25,98,107,84)(11,81,26,99,108,85)(12,73,27,91,100,86)(13,74,19,92,101,87)(14,75,20,93,102,88)(15,76,21,94,103,89)(16,77,22,95,104,90)(17,78,23,96,105,82)(18,79,24,97,106,83), (1,23,59,82)(2,22,60,90)(3,21,61,89)(4,20,62,88)(5,19,63,87)(6,27,55,86)(7,26,56,85)(8,25,57,84)(9,24,58,83)(10,72,98,33)(11,71,99,32)(12,70,91,31)(13,69,92,30)(14,68,93,29)(15,67,94,28)(16,66,95,36)(17,65,96,35)(18,64,97,34)(37,105,48,78)(38,104,49,77)(39,103,50,76)(40,102,51,75)(41,101,52,74)(42,100,53,73)(43,108,54,81)(44,107,46,80)(45,106,47,79)>;
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)(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)(82,83,84,85,86,87,88,89,90)(91,92,93,94,95,96,97,98,99)(100,101,102,103,104,105,106,107,108), (1,48,35,59,37,65)(2,49,36,60,38,66)(3,50,28,61,39,67)(4,51,29,62,40,68)(5,52,30,63,41,69)(6,53,31,55,42,70)(7,54,32,56,43,71)(8,46,33,57,44,72)(9,47,34,58,45,64)(10,80,25,98,107,84)(11,81,26,99,108,85)(12,73,27,91,100,86)(13,74,19,92,101,87)(14,75,20,93,102,88)(15,76,21,94,103,89)(16,77,22,95,104,90)(17,78,23,96,105,82)(18,79,24,97,106,83), (1,23,59,82)(2,22,60,90)(3,21,61,89)(4,20,62,88)(5,19,63,87)(6,27,55,86)(7,26,56,85)(8,25,57,84)(9,24,58,83)(10,72,98,33)(11,71,99,32)(12,70,91,31)(13,69,92,30)(14,68,93,29)(15,67,94,28)(16,66,95,36)(17,65,96,35)(18,64,97,34)(37,105,48,78)(38,104,49,77)(39,103,50,76)(40,102,51,75)(41,101,52,74)(42,100,53,73)(43,108,54,81)(44,107,46,80)(45,106,47,79) );
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),(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),(82,83,84,85,86,87,88,89,90),(91,92,93,94,95,96,97,98,99),(100,101,102,103,104,105,106,107,108)], [(1,48,35,59,37,65),(2,49,36,60,38,66),(3,50,28,61,39,67),(4,51,29,62,40,68),(5,52,30,63,41,69),(6,53,31,55,42,70),(7,54,32,56,43,71),(8,46,33,57,44,72),(9,47,34,58,45,64),(10,80,25,98,107,84),(11,81,26,99,108,85),(12,73,27,91,100,86),(13,74,19,92,101,87),(14,75,20,93,102,88),(15,76,21,94,103,89),(16,77,22,95,104,90),(17,78,23,96,105,82),(18,79,24,97,106,83)], [(1,23,59,82),(2,22,60,90),(3,21,61,89),(4,20,62,88),(5,19,63,87),(6,27,55,86),(7,26,56,85),(8,25,57,84),(9,24,58,83),(10,72,98,33),(11,71,99,32),(12,70,91,31),(13,69,92,30),(14,68,93,29),(15,67,94,28),(16,66,95,36),(17,65,96,35),(18,64,97,34),(37,105,48,78),(38,104,49,77),(39,103,50,76),(40,102,51,75),(41,101,52,74),(42,100,53,73),(43,108,54,81),(44,107,46,80),(45,106,47,79)]])
C9⋊Dic3 is a maximal subgroup of
C9⋊Dic6 Dic3×D9 S3×Dic9 D6⋊D9 C12.D9 C4×C9⋊S3 C6.D18 C32⋊Dic9 He3.Dic3 He3.2Dic3 C9⋊Dic9 C27⋊Dic3 C33.Dic3 He3.4Dic3 C32⋊5Dic9 C18.5S4 A4⋊Dic9 C32.3CSU2(𝔽3) C62.10Dic3
C9⋊Dic3 is a maximal quotient of
C36.S3 C9⋊Dic9 C32⋊2Dic9 C27⋊Dic3 C32⋊5Dic9 A4⋊Dic9 C62.10Dic3
Matrix representation of C9⋊Dic3 ►in GL4(𝔽37) generated by
| 17 | 11 | 0 | 0 |
| 26 | 6 | 0 | 0 |
| 0 | 0 | 26 | 6 |
| 0 | 0 | 31 | 20 |
| 1 | 1 | 0 | 0 |
| 36 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 36 | 36 |
| 7 | 14 | 0 | 0 |
| 7 | 30 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 |
G:=sub<GL(4,GF(37))| [17,26,0,0,11,6,0,0,0,0,26,31,0,0,6,20],[1,36,0,0,1,0,0,0,0,0,0,36,0,0,1,36],[7,7,0,0,14,30,0,0,0,0,0,1,0,0,1,0] >;
C9⋊Dic3 in GAP, Magma, Sage, TeX
C_9\rtimes {\rm Dic}_3 % in TeX
G:=Group("C9:Dic3"); // GroupNames label
G:=SmallGroup(108,10);
// by ID
G=gap.SmallGroup(108,10);
# by ID
G:=PCGroup([5,-2,-2,-3,-3,-3,10,662,282,483,1804]);
// Polycyclic
G:=Group<a,b,c|a^9=b^6=1,c^2=b^3,a*b=b*a,c*a*c^-1=a^-1,c*b*c^-1=b^-1>;
// generators/relations
Export
Subgroup lattice of C9⋊Dic3 in TeX
Character table of C9⋊Dic3 in TeX