direct product, metacyclic, supersoluble, monomial, Z-group, 3-hyperelementary
Aliases: C2×C7⋊C9, C14⋊C9, C7⋊2C18, C42.C3, C21.2C6, C6.(C7⋊C3), C3.(C2×C7⋊C3), SmallGroup(126,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C7 — C2×C7⋊C9 |
Generators and relations for C2×C7⋊C9
G = < a,b,c | a2=b7=c9=1, ab=ba, ac=ca, cbc-1=b4 >
Character table of C2×C7⋊C9
| class | 1 | 2 | 3A | 3B | 6A | 6B | 7A | 7B | 9A | 9B | 9C | 9D | 9E | 9F | 14A | 14B | 18A | 18B | 18C | 18D | 18E | 18F | 21A | 21B | 21C | 21D | 42A | 42B | 42C | 42D | |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 3 | 7 | 7 | 7 | 7 | 7 | 7 | 3 | 3 | 7 | 7 | 7 | 7 | 7 | 7 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | |
| 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 | 1 | 1 | ζ32 | ζ3 | ζ3 | ζ32 | ζ3 | ζ32 | -1 | -1 | ζ65 | ζ6 | ζ6 | ζ6 | ζ65 | ζ65 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | linear of order 6 |
| ρ4 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ζ32 | ζ3 | ζ3 | ζ32 | ζ3 | ζ32 | 1 | 1 | ζ3 | ζ32 | ζ32 | ζ32 | ζ3 | ζ3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 3 |
| ρ5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ζ3 | ζ32 | ζ32 | ζ3 | ζ32 | ζ3 | 1 | 1 | ζ32 | ζ3 | ζ3 | ζ3 | ζ32 | ζ32 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 3 |
| ρ6 | 1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | ζ3 | ζ32 | ζ32 | ζ3 | ζ32 | ζ3 | -1 | -1 | ζ6 | ζ65 | ζ65 | ζ65 | ζ6 | ζ6 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | linear of order 6 |
| ρ7 | 1 | -1 | ζ32 | ζ3 | ζ6 | ζ65 | 1 | 1 | ζ97 | ζ92 | ζ95 | ζ9 | ζ98 | ζ94 | -1 | -1 | -ζ95 | -ζ94 | -ζ97 | -ζ9 | -ζ98 | -ζ92 | ζ32 | ζ3 | ζ3 | ζ32 | ζ6 | ζ6 | ζ65 | ζ65 | linear of order 18 |
| ρ8 | 1 | -1 | ζ3 | ζ32 | ζ65 | ζ6 | 1 | 1 | ζ92 | ζ97 | ζ94 | ζ98 | ζ9 | ζ95 | -1 | -1 | -ζ94 | -ζ95 | -ζ92 | -ζ98 | -ζ9 | -ζ97 | ζ3 | ζ32 | ζ32 | ζ3 | ζ65 | ζ65 | ζ6 | ζ6 | linear of order 18 |
| ρ9 | 1 | -1 | ζ32 | ζ3 | ζ6 | ζ65 | 1 | 1 | ζ94 | ζ95 | ζ98 | ζ97 | ζ92 | ζ9 | -1 | -1 | -ζ98 | -ζ9 | -ζ94 | -ζ97 | -ζ92 | -ζ95 | ζ32 | ζ3 | ζ3 | ζ32 | ζ6 | ζ6 | ζ65 | ζ65 | linear of order 18 |
| ρ10 | 1 | 1 | ζ32 | ζ3 | ζ32 | ζ3 | 1 | 1 | ζ94 | ζ95 | ζ98 | ζ97 | ζ92 | ζ9 | 1 | 1 | ζ98 | ζ9 | ζ94 | ζ97 | ζ92 | ζ95 | ζ32 | ζ3 | ζ3 | ζ32 | ζ32 | ζ32 | ζ3 | ζ3 | linear of order 9 |
| ρ11 | 1 | -1 | ζ3 | ζ32 | ζ65 | ζ6 | 1 | 1 | ζ95 | ζ94 | ζ9 | ζ92 | ζ97 | ζ98 | -1 | -1 | -ζ9 | -ζ98 | -ζ95 | -ζ92 | -ζ97 | -ζ94 | ζ3 | ζ32 | ζ32 | ζ3 | ζ65 | ζ65 | ζ6 | ζ6 | linear of order 18 |
| ρ12 | 1 | 1 | ζ3 | ζ32 | ζ3 | ζ32 | 1 | 1 | ζ98 | ζ9 | ζ97 | ζ95 | ζ94 | ζ92 | 1 | 1 | ζ97 | ζ92 | ζ98 | ζ95 | ζ94 | ζ9 | ζ3 | ζ32 | ζ32 | ζ3 | ζ3 | ζ3 | ζ32 | ζ32 | linear of order 9 |
| ρ13 | 1 | -1 | ζ3 | ζ32 | ζ65 | ζ6 | 1 | 1 | ζ98 | ζ9 | ζ97 | ζ95 | ζ94 | ζ92 | -1 | -1 | -ζ97 | -ζ92 | -ζ98 | -ζ95 | -ζ94 | -ζ9 | ζ3 | ζ32 | ζ32 | ζ3 | ζ65 | ζ65 | ζ6 | ζ6 | linear of order 18 |
| ρ14 | 1 | 1 | ζ32 | ζ3 | ζ32 | ζ3 | 1 | 1 | ζ97 | ζ92 | ζ95 | ζ9 | ζ98 | ζ94 | 1 | 1 | ζ95 | ζ94 | ζ97 | ζ9 | ζ98 | ζ92 | ζ32 | ζ3 | ζ3 | ζ32 | ζ32 | ζ32 | ζ3 | ζ3 | linear of order 9 |
| ρ15 | 1 | -1 | ζ32 | ζ3 | ζ6 | ζ65 | 1 | 1 | ζ9 | ζ98 | ζ92 | ζ94 | ζ95 | ζ97 | -1 | -1 | -ζ92 | -ζ97 | -ζ9 | -ζ94 | -ζ95 | -ζ98 | ζ32 | ζ3 | ζ3 | ζ32 | ζ6 | ζ6 | ζ65 | ζ65 | linear of order 18 |
| ρ16 | 1 | 1 | ζ3 | ζ32 | ζ3 | ζ32 | 1 | 1 | ζ95 | ζ94 | ζ9 | ζ92 | ζ97 | ζ98 | 1 | 1 | ζ9 | ζ98 | ζ95 | ζ92 | ζ97 | ζ94 | ζ3 | ζ32 | ζ32 | ζ3 | ζ3 | ζ3 | ζ32 | ζ32 | linear of order 9 |
| ρ17 | 1 | 1 | ζ3 | ζ32 | ζ3 | ζ32 | 1 | 1 | ζ92 | ζ97 | ζ94 | ζ98 | ζ9 | ζ95 | 1 | 1 | ζ94 | ζ95 | ζ92 | ζ98 | ζ9 | ζ97 | ζ3 | ζ32 | ζ32 | ζ3 | ζ3 | ζ3 | ζ32 | ζ32 | linear of order 9 |
| ρ18 | 1 | 1 | ζ32 | ζ3 | ζ32 | ζ3 | 1 | 1 | ζ9 | ζ98 | ζ92 | ζ94 | ζ95 | ζ97 | 1 | 1 | ζ92 | ζ97 | ζ9 | ζ94 | ζ95 | ζ98 | ζ32 | ζ3 | ζ3 | ζ32 | ζ32 | ζ32 | ζ3 | ζ3 | linear of order 9 |
| ρ19 | 3 | -3 | 3 | 3 | -3 | -3 | -1+√-7/2 | -1-√-7/2 | 0 | 0 | 0 | 0 | 0 | 0 | 1+√-7/2 | 1-√-7/2 | 0 | 0 | 0 | 0 | 0 | 0 | -1+√-7/2 | -1+√-7/2 | -1-√-7/2 | -1-√-7/2 | 1+√-7/2 | 1-√-7/2 | 1-√-7/2 | 1+√-7/2 | complex lifted from C2×C7⋊C3 |
| ρ20 | 3 | -3 | 3 | 3 | -3 | -3 | -1-√-7/2 | -1+√-7/2 | 0 | 0 | 0 | 0 | 0 | 0 | 1-√-7/2 | 1+√-7/2 | 0 | 0 | 0 | 0 | 0 | 0 | -1-√-7/2 | -1-√-7/2 | -1+√-7/2 | -1+√-7/2 | 1-√-7/2 | 1+√-7/2 | 1+√-7/2 | 1-√-7/2 | complex lifted from C2×C7⋊C3 |
| ρ21 | 3 | 3 | 3 | 3 | 3 | 3 | -1-√-7/2 | -1+√-7/2 | 0 | 0 | 0 | 0 | 0 | 0 | -1+√-7/2 | -1-√-7/2 | 0 | 0 | 0 | 0 | 0 | 0 | -1-√-7/2 | -1-√-7/2 | -1+√-7/2 | -1+√-7/2 | -1+√-7/2 | -1-√-7/2 | -1-√-7/2 | -1+√-7/2 | complex lifted from C7⋊C3 |
| ρ22 | 3 | 3 | 3 | 3 | 3 | 3 | -1+√-7/2 | -1-√-7/2 | 0 | 0 | 0 | 0 | 0 | 0 | -1-√-7/2 | -1+√-7/2 | 0 | 0 | 0 | 0 | 0 | 0 | -1+√-7/2 | -1+√-7/2 | -1-√-7/2 | -1-√-7/2 | -1-√-7/2 | -1+√-7/2 | -1+√-7/2 | -1-√-7/2 | complex lifted from C7⋊C3 |
| ρ23 | 3 | -3 | -3+3√-3/2 | -3-3√-3/2 | 3-3√-3/2 | 3+3√-3/2 | -1-√-7/2 | -1+√-7/2 | 0 | 0 | 0 | 0 | 0 | 0 | 1-√-7/2 | 1+√-7/2 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3ζ76+ζ3ζ75+ζ3ζ73 | ζ32ζ76+ζ32ζ75+ζ32ζ73 | ζ32ζ74+ζ32ζ72+ζ32ζ7 | ζ3ζ74+ζ3ζ72+ζ3ζ7 | -ζ3ζ74-ζ3ζ72-ζ3ζ7 | -ζ3ζ76-ζ3ζ75-ζ3ζ73 | -ζ32ζ76-ζ32ζ75-ζ32ζ73 | -ζ32ζ74-ζ32ζ72-ζ32ζ7 | complex faithful, Schur index 3 |
| ρ24 | 3 | 3 | -3+3√-3/2 | -3-3√-3/2 | -3+3√-3/2 | -3-3√-3/2 | -1-√-7/2 | -1+√-7/2 | 0 | 0 | 0 | 0 | 0 | 0 | -1+√-7/2 | -1-√-7/2 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3ζ76+ζ3ζ75+ζ3ζ73 | ζ32ζ76+ζ32ζ75+ζ32ζ73 | ζ32ζ74+ζ32ζ72+ζ32ζ7 | ζ3ζ74+ζ3ζ72+ζ3ζ7 | ζ3ζ74+ζ3ζ72+ζ3ζ7 | ζ3ζ76+ζ3ζ75+ζ3ζ73 | ζ32ζ76+ζ32ζ75+ζ32ζ73 | ζ32ζ74+ζ32ζ72+ζ32ζ7 | complex lifted from C7⋊C9, Schur index 3 |
| ρ25 | 3 | -3 | -3-3√-3/2 | -3+3√-3/2 | 3+3√-3/2 | 3-3√-3/2 | -1-√-7/2 | -1+√-7/2 | 0 | 0 | 0 | 0 | 0 | 0 | 1-√-7/2 | 1+√-7/2 | 0 | 0 | 0 | 0 | 0 | 0 | ζ32ζ76+ζ32ζ75+ζ32ζ73 | ζ3ζ76+ζ3ζ75+ζ3ζ73 | ζ3ζ74+ζ3ζ72+ζ3ζ7 | ζ32ζ74+ζ32ζ72+ζ32ζ7 | -ζ32ζ74-ζ32ζ72-ζ32ζ7 | -ζ32ζ76-ζ32ζ75-ζ32ζ73 | -ζ3ζ76-ζ3ζ75-ζ3ζ73 | -ζ3ζ74-ζ3ζ72-ζ3ζ7 | complex faithful, Schur index 3 |
| ρ26 | 3 | 3 | -3+3√-3/2 | -3-3√-3/2 | -3+3√-3/2 | -3-3√-3/2 | -1+√-7/2 | -1-√-7/2 | 0 | 0 | 0 | 0 | 0 | 0 | -1-√-7/2 | -1+√-7/2 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3ζ74+ζ3ζ72+ζ3ζ7 | ζ32ζ74+ζ32ζ72+ζ32ζ7 | ζ32ζ76+ζ32ζ75+ζ32ζ73 | ζ3ζ76+ζ3ζ75+ζ3ζ73 | ζ3ζ76+ζ3ζ75+ζ3ζ73 | ζ3ζ74+ζ3ζ72+ζ3ζ7 | ζ32ζ74+ζ32ζ72+ζ32ζ7 | ζ32ζ76+ζ32ζ75+ζ32ζ73 | complex lifted from C7⋊C9, Schur index 3 |
| ρ27 | 3 | -3 | -3-3√-3/2 | -3+3√-3/2 | 3+3√-3/2 | 3-3√-3/2 | -1+√-7/2 | -1-√-7/2 | 0 | 0 | 0 | 0 | 0 | 0 | 1+√-7/2 | 1-√-7/2 | 0 | 0 | 0 | 0 | 0 | 0 | ζ32ζ74+ζ32ζ72+ζ32ζ7 | ζ3ζ74+ζ3ζ72+ζ3ζ7 | ζ3ζ76+ζ3ζ75+ζ3ζ73 | ζ32ζ76+ζ32ζ75+ζ32ζ73 | -ζ32ζ76-ζ32ζ75-ζ32ζ73 | -ζ32ζ74-ζ32ζ72-ζ32ζ7 | -ζ3ζ74-ζ3ζ72-ζ3ζ7 | -ζ3ζ76-ζ3ζ75-ζ3ζ73 | complex faithful, Schur index 3 |
| ρ28 | 3 | 3 | -3-3√-3/2 | -3+3√-3/2 | -3-3√-3/2 | -3+3√-3/2 | -1-√-7/2 | -1+√-7/2 | 0 | 0 | 0 | 0 | 0 | 0 | -1+√-7/2 | -1-√-7/2 | 0 | 0 | 0 | 0 | 0 | 0 | ζ32ζ76+ζ32ζ75+ζ32ζ73 | ζ3ζ76+ζ3ζ75+ζ3ζ73 | ζ3ζ74+ζ3ζ72+ζ3ζ7 | ζ32ζ74+ζ32ζ72+ζ32ζ7 | ζ32ζ74+ζ32ζ72+ζ32ζ7 | ζ32ζ76+ζ32ζ75+ζ32ζ73 | ζ3ζ76+ζ3ζ75+ζ3ζ73 | ζ3ζ74+ζ3ζ72+ζ3ζ7 | complex lifted from C7⋊C9, Schur index 3 |
| ρ29 | 3 | -3 | -3+3√-3/2 | -3-3√-3/2 | 3-3√-3/2 | 3+3√-3/2 | -1+√-7/2 | -1-√-7/2 | 0 | 0 | 0 | 0 | 0 | 0 | 1+√-7/2 | 1-√-7/2 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3ζ74+ζ3ζ72+ζ3ζ7 | ζ32ζ74+ζ32ζ72+ζ32ζ7 | ζ32ζ76+ζ32ζ75+ζ32ζ73 | ζ3ζ76+ζ3ζ75+ζ3ζ73 | -ζ3ζ76-ζ3ζ75-ζ3ζ73 | -ζ3ζ74-ζ3ζ72-ζ3ζ7 | -ζ32ζ74-ζ32ζ72-ζ32ζ7 | -ζ32ζ76-ζ32ζ75-ζ32ζ73 | complex faithful, Schur index 3 |
| ρ30 | 3 | 3 | -3-3√-3/2 | -3+3√-3/2 | -3-3√-3/2 | -3+3√-3/2 | -1+√-7/2 | -1-√-7/2 | 0 | 0 | 0 | 0 | 0 | 0 | -1-√-7/2 | -1+√-7/2 | 0 | 0 | 0 | 0 | 0 | 0 | ζ32ζ74+ζ32ζ72+ζ32ζ7 | ζ3ζ74+ζ3ζ72+ζ3ζ7 | ζ3ζ76+ζ3ζ75+ζ3ζ73 | ζ32ζ76+ζ32ζ75+ζ32ζ73 | ζ32ζ76+ζ32ζ75+ζ32ζ73 | ζ32ζ74+ζ32ζ72+ζ32ζ7 | ζ3ζ74+ζ3ζ72+ζ3ζ7 | ζ3ζ76+ζ3ζ75+ζ3ζ73 | complex lifted from C7⋊C9, Schur index 3 |
►Regular action on 126 points
Generators in S126
(1 48)(2 49)(3 50)(4 51)(5 52)(6 53)(7 54)(8 46)(9 47)(10 88)(11 89)(12 90)(13 82)(14 83)(15 84)(16 85)(17 86)(18 87)(19 116)(20 117)(21 109)(22 110)(23 111)(24 112)(25 113)(26 114)(27 115)(28 99)(29 91)(30 92)(31 93)(32 94)(33 95)(34 96)(35 97)(36 98)(37 80)(38 81)(39 73)(40 74)(41 75)(42 76)(43 77)(44 78)(45 79)(55 103)(56 104)(57 105)(58 106)(59 107)(60 108)(61 100)(62 101)(63 102)(64 125)(65 126)(66 118)(67 119)(68 120)(69 121)(70 122)(71 123)(72 124)
(1 68 91 116 89 78 104)(2 90 69 79 92 105 117)(3 93 82 106 70 109 80)(4 71 94 110 83 81 107)(5 84 72 73 95 108 111)(6 96 85 100 64 112 74)(7 65 97 113 86 75 101)(8 87 66 76 98 102 114)(9 99 88 103 67 115 77)(10 55 119 27 43 47 28)(11 44 56 48 120 29 19)(12 121 45 30 57 20 49)(13 58 122 21 37 50 31)(14 38 59 51 123 32 22)(15 124 39 33 60 23 52)(16 61 125 24 40 53 34)(17 41 62 54 126 35 25)(18 118 42 36 63 26 46)
(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)(109 110 111 112 113 114 115 116 117)(118 119 120 121 122 123 124 125 126)
G:=sub<Sym(126)| (1,48)(2,49)(3,50)(4,51)(5,52)(6,53)(7,54)(8,46)(9,47)(10,88)(11,89)(12,90)(13,82)(14,83)(15,84)(16,85)(17,86)(18,87)(19,116)(20,117)(21,109)(22,110)(23,111)(24,112)(25,113)(26,114)(27,115)(28,99)(29,91)(30,92)(31,93)(32,94)(33,95)(34,96)(35,97)(36,98)(37,80)(38,81)(39,73)(40,74)(41,75)(42,76)(43,77)(44,78)(45,79)(55,103)(56,104)(57,105)(58,106)(59,107)(60,108)(61,100)(62,101)(63,102)(64,125)(65,126)(66,118)(67,119)(68,120)(69,121)(70,122)(71,123)(72,124), (1,68,91,116,89,78,104)(2,90,69,79,92,105,117)(3,93,82,106,70,109,80)(4,71,94,110,83,81,107)(5,84,72,73,95,108,111)(6,96,85,100,64,112,74)(7,65,97,113,86,75,101)(8,87,66,76,98,102,114)(9,99,88,103,67,115,77)(10,55,119,27,43,47,28)(11,44,56,48,120,29,19)(12,121,45,30,57,20,49)(13,58,122,21,37,50,31)(14,38,59,51,123,32,22)(15,124,39,33,60,23,52)(16,61,125,24,40,53,34)(17,41,62,54,126,35,25)(18,118,42,36,63,26,46), (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)(109,110,111,112,113,114,115,116,117)(118,119,120,121,122,123,124,125,126)>;
G:=Group( (1,48)(2,49)(3,50)(4,51)(5,52)(6,53)(7,54)(8,46)(9,47)(10,88)(11,89)(12,90)(13,82)(14,83)(15,84)(16,85)(17,86)(18,87)(19,116)(20,117)(21,109)(22,110)(23,111)(24,112)(25,113)(26,114)(27,115)(28,99)(29,91)(30,92)(31,93)(32,94)(33,95)(34,96)(35,97)(36,98)(37,80)(38,81)(39,73)(40,74)(41,75)(42,76)(43,77)(44,78)(45,79)(55,103)(56,104)(57,105)(58,106)(59,107)(60,108)(61,100)(62,101)(63,102)(64,125)(65,126)(66,118)(67,119)(68,120)(69,121)(70,122)(71,123)(72,124), (1,68,91,116,89,78,104)(2,90,69,79,92,105,117)(3,93,82,106,70,109,80)(4,71,94,110,83,81,107)(5,84,72,73,95,108,111)(6,96,85,100,64,112,74)(7,65,97,113,86,75,101)(8,87,66,76,98,102,114)(9,99,88,103,67,115,77)(10,55,119,27,43,47,28)(11,44,56,48,120,29,19)(12,121,45,30,57,20,49)(13,58,122,21,37,50,31)(14,38,59,51,123,32,22)(15,124,39,33,60,23,52)(16,61,125,24,40,53,34)(17,41,62,54,126,35,25)(18,118,42,36,63,26,46), (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)(109,110,111,112,113,114,115,116,117)(118,119,120,121,122,123,124,125,126) );
G=PermutationGroup([[(1,48),(2,49),(3,50),(4,51),(5,52),(6,53),(7,54),(8,46),(9,47),(10,88),(11,89),(12,90),(13,82),(14,83),(15,84),(16,85),(17,86),(18,87),(19,116),(20,117),(21,109),(22,110),(23,111),(24,112),(25,113),(26,114),(27,115),(28,99),(29,91),(30,92),(31,93),(32,94),(33,95),(34,96),(35,97),(36,98),(37,80),(38,81),(39,73),(40,74),(41,75),(42,76),(43,77),(44,78),(45,79),(55,103),(56,104),(57,105),(58,106),(59,107),(60,108),(61,100),(62,101),(63,102),(64,125),(65,126),(66,118),(67,119),(68,120),(69,121),(70,122),(71,123),(72,124)], [(1,68,91,116,89,78,104),(2,90,69,79,92,105,117),(3,93,82,106,70,109,80),(4,71,94,110,83,81,107),(5,84,72,73,95,108,111),(6,96,85,100,64,112,74),(7,65,97,113,86,75,101),(8,87,66,76,98,102,114),(9,99,88,103,67,115,77),(10,55,119,27,43,47,28),(11,44,56,48,120,29,19),(12,121,45,30,57,20,49),(13,58,122,21,37,50,31),(14,38,59,51,123,32,22),(15,124,39,33,60,23,52),(16,61,125,24,40,53,34),(17,41,62,54,126,35,25),(18,118,42,36,63,26,46)], [(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),(109,110,111,112,113,114,115,116,117),(118,119,120,121,122,123,124,125,126)]])
C2×C7⋊C9 is a maximal subgroup of
C7⋊C36 C18×C7⋊C3
Matrix representation of C2×C7⋊C9 ►in GL3(𝔽127) generated by
| 126 | 0 | 0 |
| 0 | 126 | 0 |
| 0 | 0 | 126 |
| 126 | 22 | 1 |
| 0 | 22 | 1 |
| 126 | 23 | 1 |
| 81 | 31 | 5 |
| 42 | 75 | 50 |
| 40 | 34 | 98 |
G:=sub<GL(3,GF(127))| [126,0,0,0,126,0,0,0,126],[126,0,126,22,22,23,1,1,1],[81,42,40,31,75,34,5,50,98] >;
C2×C7⋊C9 in GAP, Magma, Sage, TeX
C_2\times C_7\rtimes C_9
% in TeX
G:=Group("C2xC7:C9"); // GroupNames label
G:=SmallGroup(126,2);
// by ID
G=gap.SmallGroup(126,2);
# by ID
G:=PCGroup([4,-2,-3,-3,-7,29,295]);
// Polycyclic
G:=Group<a,b,c|a^2=b^7=c^9=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^4>;
// generators/relations
Export
Subgroup lattice of C2×C7⋊C9 in TeX
Character table of C2×C7⋊C9 in TeX