metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C24⋊3Q8, C8⋊2Dic6, C3⋊C8⋊1Q8, C3⋊2(C8⋊Q8), C4⋊C4.33D6, (C2×C8).59D6, C12⋊Q8.6C2, C4.21(S3×Q8), C4.Q8.3S3, C6.14(C4⋊Q8), C2.9(C12⋊Q8), C12.57(C2×Q8), C24⋊C4.2C2, C24⋊1C4.17C2, C4.21(C2×Dic6), C6.Q16.4C2, C2.20(Q8⋊3D6), C6.67(C8⋊C22), (C2×Dic3).38D4, C22.211(S3×D4), C4.Dic6.4C2, C12.Q8.6C2, (C2×C24).108C22, (C2×C12).272C23, C2.21(D4.D6), C6.39(C8.C22), C4⋊Dic3.104C22, (C4×Dic3).29C22, (C3×C4.Q8).3C2, (C2×C6).277(C2×D4), (C2×C3⋊C8).53C22, (C3×C4⋊C4).65C22, (C2×C4).375(C22×S3), SmallGroup(192,415)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C24⋊3Q8
G = < a,b,c | a24=b4=1, c2=b2, bab-1=a19, cac-1=a5, cbc-1=b-1 >
Subgroups: 240 in 90 conjugacy classes, 43 normal (37 characteristic)
C1, C2, C3, C4, C4, C22, C6, C8, C8, C2×C4, C2×C4, Q8, Dic3, C12, C12, C2×C6, C42, C4⋊C4, C4⋊C4, C2×C8, C2×C8, C2×Q8, C3⋊C8, C24, Dic6, C2×Dic3, C2×Dic3, C2×C12, C2×C12, C8⋊C4, C4.Q8, C4.Q8, C2.D8, C42.C2, C4⋊Q8, C2×C3⋊C8, C4×Dic3, Dic3⋊C4, C4⋊Dic3, C4⋊Dic3, C3×C4⋊C4, C2×C24, C2×Dic6, C8⋊Q8, C6.Q16, C12.Q8, C24⋊C4, C24⋊1C4, C3×C4.Q8, C12⋊Q8, C4.Dic6, C24⋊3Q8
Quotients: C1, C2, C22, S3, D4, Q8, C23, D6, C2×D4, C2×Q8, Dic6, C22×S3, C4⋊Q8, C8⋊C22, C8.C22, C2×Dic6, S3×D4, S3×Q8, C8⋊Q8, C12⋊Q8, Q8⋊3D6, D4.D6, C24⋊3Q8
Character table of C24⋊3Q8
| class | 1 | 2A | 2B | 2C | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 6A | 6B | 6C | 8A | 8B | 8C | 8D | 12A | 12B | 12C | 12D | 12E | 12F | 24A | 24B | 24C | 24D | |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 8 | 8 | 12 | 12 | 24 | 24 | 2 | 2 | 2 | 4 | 4 | 12 | 12 | 4 | 4 | 8 | 8 | 8 | 8 | 4 | 4 | 4 | 4 | |
| 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 | 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 |
| ρ4 | 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 |
| ρ5 | 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 |
| ρ6 | 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 |
| ρ7 | 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 |
| ρ8 | 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 |
| ρ9 | 2 | 2 | 2 | 2 | 2 | -2 | -2 | 0 | 0 | -2 | 2 | 0 | 0 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ10 | 2 | 2 | 2 | 2 | 2 | -2 | -2 | 0 | 0 | 2 | -2 | 0 | 0 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ11 | 2 | 2 | 2 | 2 | -1 | 2 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | -1 | -1 | -1 | 2 | 2 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | orthogonal lifted from S3 |
| ρ12 | 2 | 2 | 2 | 2 | -1 | 2 | 2 | -2 | -2 | 0 | 0 | 0 | 0 | -1 | -1 | -1 | 2 | 2 | 0 | 0 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | orthogonal lifted from D6 |
| ρ13 | 2 | 2 | 2 | 2 | -1 | 2 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | -1 | -1 | -1 | -2 | -2 | 0 | 0 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | orthogonal lifted from D6 |
| ρ14 | 2 | 2 | 2 | 2 | -1 | 2 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | -1 | -1 | -1 | -2 | -2 | 0 | 0 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | orthogonal lifted from D6 |
| ρ15 | 2 | -2 | -2 | 2 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | -2 | 2 | 0 | 0 | -2 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from Q8, Schur index 2 |
| ρ16 | 2 | -2 | -2 | 2 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | -2 | 2 | 2 | -2 | 0 | 0 | 2 | -2 | 0 | 0 | 0 | 0 | 2 | -2 | -2 | 2 | symplectic lifted from Q8, Schur index 2 |
| ρ17 | 2 | -2 | -2 | 2 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | -2 | 2 | 0 | 0 | 2 | -2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from Q8, Schur index 2 |
| ρ18 | 2 | -2 | -2 | 2 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | -2 | 2 | -2 | 2 | 0 | 0 | 2 | -2 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | -2 | symplectic lifted from Q8, Schur index 2 |
| ρ19 | 2 | -2 | -2 | 2 | -1 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | -1 | 2 | -2 | 0 | 0 | -1 | 1 | √3 | -√3 | -√3 | √3 | -1 | 1 | 1 | -1 | symplectic lifted from Dic6, Schur index 2 |
| ρ20 | 2 | -2 | -2 | 2 | -1 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | -1 | 2 | -2 | 0 | 0 | -1 | 1 | -√3 | √3 | √3 | -√3 | -1 | 1 | 1 | -1 | symplectic lifted from Dic6, Schur index 2 |
| ρ21 | 2 | -2 | -2 | 2 | -1 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | -1 | -2 | 2 | 0 | 0 | -1 | 1 | -√3 | √3 | -√3 | √3 | 1 | -1 | -1 | 1 | symplectic lifted from Dic6, Schur index 2 |
| ρ22 | 2 | -2 | -2 | 2 | -1 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | -1 | -2 | 2 | 0 | 0 | -1 | 1 | √3 | -√3 | √3 | -√3 | 1 | -1 | -1 | 1 | symplectic lifted from Dic6, Schur index 2 |
| ρ23 | 4 | -4 | 4 | -4 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -√6 | -√6 | √6 | √6 | orthogonal lifted from Q8⋊3D6 |
| ρ24 | 4 | 4 | 4 | 4 | -2 | -4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | -2 | -2 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from S3×D4 |
| ρ25 | 4 | -4 | 4 | -4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4 | -4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from C8⋊C22 |
| ρ26 | 4 | -4 | 4 | -4 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | √6 | √6 | -√6 | -√6 | orthogonal lifted from Q8⋊3D6 |
| ρ27 | 4 | -4 | -4 | 4 | -2 | -4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from S3×Q8, Schur index 2 |
| ρ28 | 4 | 4 | -4 | -4 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | √6 | -√6 | √6 | -√6 | symplectic lifted from D4.D6, Schur index 2 |
| ρ29 | 4 | 4 | -4 | -4 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -√6 | √6 | -√6 | √6 | symplectic lifted from D4.D6, Schur index 2 |
| ρ30 | 4 | 4 | -4 | -4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -4 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from C8.C22, Schur index 2 |
►Regular action on 192 points
Generators in S192
(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)(121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144)(145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168)(169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192)
(1 143 62 94)(2 138 63 89)(3 133 64 84)(4 128 65 79)(5 123 66 74)(6 142 67 93)(7 137 68 88)(8 132 69 83)(9 127 70 78)(10 122 71 73)(11 141 72 92)(12 136 49 87)(13 131 50 82)(14 126 51 77)(15 121 52 96)(16 140 53 91)(17 135 54 86)(18 130 55 81)(19 125 56 76)(20 144 57 95)(21 139 58 90)(22 134 59 85)(23 129 60 80)(24 124 61 75)(25 182 166 108)(26 177 167 103)(27 172 168 98)(28 191 145 117)(29 186 146 112)(30 181 147 107)(31 176 148 102)(32 171 149 97)(33 190 150 116)(34 185 151 111)(35 180 152 106)(36 175 153 101)(37 170 154 120)(38 189 155 115)(39 184 156 110)(40 179 157 105)(41 174 158 100)(42 169 159 119)(43 188 160 114)(44 183 161 109)(45 178 162 104)(46 173 163 99)(47 192 164 118)(48 187 165 113)
(1 27 62 168)(2 32 63 149)(3 37 64 154)(4 42 65 159)(5 47 66 164)(6 28 67 145)(7 33 68 150)(8 38 69 155)(9 43 70 160)(10 48 71 165)(11 29 72 146)(12 34 49 151)(13 39 50 156)(14 44 51 161)(15 25 52 166)(16 30 53 147)(17 35 54 152)(18 40 55 157)(19 45 56 162)(20 26 57 167)(21 31 58 148)(22 36 59 153)(23 41 60 158)(24 46 61 163)(73 187 122 113)(74 192 123 118)(75 173 124 99)(76 178 125 104)(77 183 126 109)(78 188 127 114)(79 169 128 119)(80 174 129 100)(81 179 130 105)(82 184 131 110)(83 189 132 115)(84 170 133 120)(85 175 134 101)(86 180 135 106)(87 185 136 111)(88 190 137 116)(89 171 138 97)(90 176 139 102)(91 181 140 107)(92 186 141 112)(93 191 142 117)(94 172 143 98)(95 177 144 103)(96 182 121 108)
G:=sub<Sym(192)| (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)(121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144)(145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192), (1,143,62,94)(2,138,63,89)(3,133,64,84)(4,128,65,79)(5,123,66,74)(6,142,67,93)(7,137,68,88)(8,132,69,83)(9,127,70,78)(10,122,71,73)(11,141,72,92)(12,136,49,87)(13,131,50,82)(14,126,51,77)(15,121,52,96)(16,140,53,91)(17,135,54,86)(18,130,55,81)(19,125,56,76)(20,144,57,95)(21,139,58,90)(22,134,59,85)(23,129,60,80)(24,124,61,75)(25,182,166,108)(26,177,167,103)(27,172,168,98)(28,191,145,117)(29,186,146,112)(30,181,147,107)(31,176,148,102)(32,171,149,97)(33,190,150,116)(34,185,151,111)(35,180,152,106)(36,175,153,101)(37,170,154,120)(38,189,155,115)(39,184,156,110)(40,179,157,105)(41,174,158,100)(42,169,159,119)(43,188,160,114)(44,183,161,109)(45,178,162,104)(46,173,163,99)(47,192,164,118)(48,187,165,113), (1,27,62,168)(2,32,63,149)(3,37,64,154)(4,42,65,159)(5,47,66,164)(6,28,67,145)(7,33,68,150)(8,38,69,155)(9,43,70,160)(10,48,71,165)(11,29,72,146)(12,34,49,151)(13,39,50,156)(14,44,51,161)(15,25,52,166)(16,30,53,147)(17,35,54,152)(18,40,55,157)(19,45,56,162)(20,26,57,167)(21,31,58,148)(22,36,59,153)(23,41,60,158)(24,46,61,163)(73,187,122,113)(74,192,123,118)(75,173,124,99)(76,178,125,104)(77,183,126,109)(78,188,127,114)(79,169,128,119)(80,174,129,100)(81,179,130,105)(82,184,131,110)(83,189,132,115)(84,170,133,120)(85,175,134,101)(86,180,135,106)(87,185,136,111)(88,190,137,116)(89,171,138,97)(90,176,139,102)(91,181,140,107)(92,186,141,112)(93,191,142,117)(94,172,143,98)(95,177,144,103)(96,182,121,108)>;
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)(97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144)(145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192), (1,143,62,94)(2,138,63,89)(3,133,64,84)(4,128,65,79)(5,123,66,74)(6,142,67,93)(7,137,68,88)(8,132,69,83)(9,127,70,78)(10,122,71,73)(11,141,72,92)(12,136,49,87)(13,131,50,82)(14,126,51,77)(15,121,52,96)(16,140,53,91)(17,135,54,86)(18,130,55,81)(19,125,56,76)(20,144,57,95)(21,139,58,90)(22,134,59,85)(23,129,60,80)(24,124,61,75)(25,182,166,108)(26,177,167,103)(27,172,168,98)(28,191,145,117)(29,186,146,112)(30,181,147,107)(31,176,148,102)(32,171,149,97)(33,190,150,116)(34,185,151,111)(35,180,152,106)(36,175,153,101)(37,170,154,120)(38,189,155,115)(39,184,156,110)(40,179,157,105)(41,174,158,100)(42,169,159,119)(43,188,160,114)(44,183,161,109)(45,178,162,104)(46,173,163,99)(47,192,164,118)(48,187,165,113), (1,27,62,168)(2,32,63,149)(3,37,64,154)(4,42,65,159)(5,47,66,164)(6,28,67,145)(7,33,68,150)(8,38,69,155)(9,43,70,160)(10,48,71,165)(11,29,72,146)(12,34,49,151)(13,39,50,156)(14,44,51,161)(15,25,52,166)(16,30,53,147)(17,35,54,152)(18,40,55,157)(19,45,56,162)(20,26,57,167)(21,31,58,148)(22,36,59,153)(23,41,60,158)(24,46,61,163)(73,187,122,113)(74,192,123,118)(75,173,124,99)(76,178,125,104)(77,183,126,109)(78,188,127,114)(79,169,128,119)(80,174,129,100)(81,179,130,105)(82,184,131,110)(83,189,132,115)(84,170,133,120)(85,175,134,101)(86,180,135,106)(87,185,136,111)(88,190,137,116)(89,171,138,97)(90,176,139,102)(91,181,140,107)(92,186,141,112)(93,191,142,117)(94,172,143,98)(95,177,144,103)(96,182,121,108) );
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),(97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120),(121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144),(145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168),(169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192)], [(1,143,62,94),(2,138,63,89),(3,133,64,84),(4,128,65,79),(5,123,66,74),(6,142,67,93),(7,137,68,88),(8,132,69,83),(9,127,70,78),(10,122,71,73),(11,141,72,92),(12,136,49,87),(13,131,50,82),(14,126,51,77),(15,121,52,96),(16,140,53,91),(17,135,54,86),(18,130,55,81),(19,125,56,76),(20,144,57,95),(21,139,58,90),(22,134,59,85),(23,129,60,80),(24,124,61,75),(25,182,166,108),(26,177,167,103),(27,172,168,98),(28,191,145,117),(29,186,146,112),(30,181,147,107),(31,176,148,102),(32,171,149,97),(33,190,150,116),(34,185,151,111),(35,180,152,106),(36,175,153,101),(37,170,154,120),(38,189,155,115),(39,184,156,110),(40,179,157,105),(41,174,158,100),(42,169,159,119),(43,188,160,114),(44,183,161,109),(45,178,162,104),(46,173,163,99),(47,192,164,118),(48,187,165,113)], [(1,27,62,168),(2,32,63,149),(3,37,64,154),(4,42,65,159),(5,47,66,164),(6,28,67,145),(7,33,68,150),(8,38,69,155),(9,43,70,160),(10,48,71,165),(11,29,72,146),(12,34,49,151),(13,39,50,156),(14,44,51,161),(15,25,52,166),(16,30,53,147),(17,35,54,152),(18,40,55,157),(19,45,56,162),(20,26,57,167),(21,31,58,148),(22,36,59,153),(23,41,60,158),(24,46,61,163),(73,187,122,113),(74,192,123,118),(75,173,124,99),(76,178,125,104),(77,183,126,109),(78,188,127,114),(79,169,128,119),(80,174,129,100),(81,179,130,105),(82,184,131,110),(83,189,132,115),(84,170,133,120),(85,175,134,101),(86,180,135,106),(87,185,136,111),(88,190,137,116),(89,171,138,97),(90,176,139,102),(91,181,140,107),(92,186,141,112),(93,191,142,117),(94,172,143,98),(95,177,144,103),(96,182,121,108)]])
Matrix representation of C24⋊3Q8 ►in GL6(𝔽73)
| 51 | 17 | 0 | 0 | 0 | 0 |
| 23 | 22 | 0 | 0 | 0 | 0 |
| 0 | 0 | 34 | 39 | 39 | 34 |
| 0 | 0 | 34 | 68 | 39 | 5 |
| 0 | 0 | 34 | 39 | 34 | 39 |
| 0 | 0 | 34 | 68 | 34 | 68 |
| 72 | 2 | 0 | 0 | 0 | 0 |
| 72 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 61 | 60 | 33 | 25 |
| 0 | 0 | 13 | 1 | 48 | 8 |
| 0 | 0 | 33 | 25 | 12 | 13 |
| 0 | 0 | 48 | 8 | 60 | 72 |
| 51 | 17 | 0 | 0 | 0 | 0 |
| 23 | 22 | 0 | 0 | 0 | 0 |
| 0 | 0 | 49 | 24 | 11 | 11 |
| 0 | 0 | 48 | 24 | 0 | 62 |
| 0 | 0 | 62 | 62 | 49 | 24 |
| 0 | 0 | 0 | 11 | 48 | 24 |
G:=sub<GL(6,GF(73))| [51,23,0,0,0,0,17,22,0,0,0,0,0,0,34,34,34,34,0,0,39,68,39,68,0,0,39,39,34,34,0,0,34,5,39,68],[72,72,0,0,0,0,2,1,0,0,0,0,0,0,61,13,33,48,0,0,60,1,25,8,0,0,33,48,12,60,0,0,25,8,13,72],[51,23,0,0,0,0,17,22,0,0,0,0,0,0,49,48,62,0,0,0,24,24,62,11,0,0,11,0,49,48,0,0,11,62,24,24] >;
C24⋊3Q8 in GAP, Magma, Sage, TeX
C_{24}\rtimes_3Q_8 % in TeX
G:=Group("C24:3Q8"); // GroupNames label
G:=SmallGroup(192,415);
// by ID
G=gap.SmallGroup(192,415);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,56,477,120,254,555,58,438,102,6278]);
// Polycyclic
G:=Group<a,b,c|a^24=b^4=1,c^2=b^2,b*a*b^-1=a^19,c*a*c^-1=a^5,c*b*c^-1=b^-1>;
// generators/relations
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