metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C30.9D8, C40.9D6, C15⋊6SD32, C10.8D24, C60.51D4, C20.3D12, Dic12⋊1D5, D120.4C2, C24.42D10, C120.19C22, C5⋊2C16⋊3S3, C8.18(S3×D5), C5⋊3(C48⋊C2), C6.3(D4⋊D5), C3⋊1(C5⋊SD32), (C5×Dic12)⋊1C2, C2.6(C5⋊D24), C4.3(C5⋊D12), C12.53(C5⋊D4), (C3×C5⋊2C16)⋊3C2, SmallGroup(480,21)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic12⋊D5
G = < a,b,c,d | a24=c5=d2=1, b2=a12, bab-1=dad=a-1, ac=ca, bc=cb, dbd=a21b, dcd=c-1 >
120C2
12C4
60C22
40S3
24D5
6Q8
30D4
4Dic3
20D6
12D10
12C20
8D15
3Q16
5C16
15D8
2Dic6
10D12
6D20
4D30
15SD32
5C48
5D24
3D40
2D60
Smallest permutation representation of Dic12⋊D5
►On 240 points
Generators in S240
(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)(193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216)(217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240)
(1 81 13 93)(2 80 14 92)(3 79 15 91)(4 78 16 90)(5 77 17 89)(6 76 18 88)(7 75 19 87)(8 74 20 86)(9 73 21 85)(10 96 22 84)(11 95 23 83)(12 94 24 82)(25 112 37 100)(26 111 38 99)(27 110 39 98)(28 109 40 97)(29 108 41 120)(30 107 42 119)(31 106 43 118)(32 105 44 117)(33 104 45 116)(34 103 46 115)(35 102 47 114)(36 101 48 113)(49 136 61 124)(50 135 62 123)(51 134 63 122)(52 133 64 121)(53 132 65 144)(54 131 66 143)(55 130 67 142)(56 129 68 141)(57 128 69 140)(58 127 70 139)(59 126 71 138)(60 125 72 137)(145 197 157 209)(146 196 158 208)(147 195 159 207)(148 194 160 206)(149 193 161 205)(150 216 162 204)(151 215 163 203)(152 214 164 202)(153 213 165 201)(154 212 166 200)(155 211 167 199)(156 210 168 198)(169 238 181 226)(170 237 182 225)(171 236 183 224)(172 235 184 223)(173 234 185 222)(174 233 186 221)(175 232 187 220)(176 231 188 219)(177 230 189 218)(178 229 190 217)(179 228 191 240)(180 227 192 239)
(1 166 46 69 222)(2 167 47 70 223)(3 168 48 71 224)(4 145 25 72 225)(5 146 26 49 226)(6 147 27 50 227)(7 148 28 51 228)(8 149 29 52 229)(9 150 30 53 230)(10 151 31 54 231)(11 152 32 55 232)(12 153 33 56 233)(13 154 34 57 234)(14 155 35 58 235)(15 156 36 59 236)(16 157 37 60 237)(17 158 38 61 238)(18 159 39 62 239)(19 160 40 63 240)(20 161 41 64 217)(21 162 42 65 218)(22 163 43 66 219)(23 164 44 67 220)(24 165 45 68 221)(73 216 107 132 189)(74 193 108 133 190)(75 194 109 134 191)(76 195 110 135 192)(77 196 111 136 169)(78 197 112 137 170)(79 198 113 138 171)(80 199 114 139 172)(81 200 115 140 173)(82 201 116 141 174)(83 202 117 142 175)(84 203 118 143 176)(85 204 119 144 177)(86 205 120 121 178)(87 206 97 122 179)(88 207 98 123 180)(89 208 99 124 181)(90 209 100 125 182)(91 210 101 126 183)(92 211 102 127 184)(93 212 103 128 185)(94 213 104 129 186)(95 214 105 130 187)(96 215 106 131 188)
(1 222)(2 221)(3 220)(4 219)(5 218)(6 217)(7 240)(8 239)(9 238)(10 237)(11 236)(12 235)(13 234)(14 233)(15 232)(16 231)(17 230)(18 229)(19 228)(20 227)(21 226)(22 225)(23 224)(24 223)(25 43)(26 42)(27 41)(28 40)(29 39)(30 38)(31 37)(32 36)(33 35)(44 48)(45 47)(49 162)(50 161)(51 160)(52 159)(53 158)(54 157)(55 156)(56 155)(57 154)(58 153)(59 152)(60 151)(61 150)(62 149)(63 148)(64 147)(65 146)(66 145)(67 168)(68 167)(69 166)(70 165)(71 164)(72 163)(73 184)(74 183)(75 182)(76 181)(77 180)(78 179)(79 178)(80 177)(81 176)(82 175)(83 174)(84 173)(85 172)(86 171)(87 170)(88 169)(89 192)(90 191)(91 190)(92 189)(93 188)(94 187)(95 186)(96 185)(97 112)(98 111)(99 110)(100 109)(101 108)(102 107)(103 106)(104 105)(113 120)(114 119)(115 118)(116 117)(121 198)(122 197)(123 196)(124 195)(125 194)(126 193)(127 216)(128 215)(129 214)(130 213)(131 212)(132 211)(133 210)(134 209)(135 208)(136 207)(137 206)(138 205)(139 204)(140 203)(141 202)(142 201)(143 200)(144 199)
G:=sub<Sym(240)| (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)(193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216)(217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240), (1,81,13,93)(2,80,14,92)(3,79,15,91)(4,78,16,90)(5,77,17,89)(6,76,18,88)(7,75,19,87)(8,74,20,86)(9,73,21,85)(10,96,22,84)(11,95,23,83)(12,94,24,82)(25,112,37,100)(26,111,38,99)(27,110,39,98)(28,109,40,97)(29,108,41,120)(30,107,42,119)(31,106,43,118)(32,105,44,117)(33,104,45,116)(34,103,46,115)(35,102,47,114)(36,101,48,113)(49,136,61,124)(50,135,62,123)(51,134,63,122)(52,133,64,121)(53,132,65,144)(54,131,66,143)(55,130,67,142)(56,129,68,141)(57,128,69,140)(58,127,70,139)(59,126,71,138)(60,125,72,137)(145,197,157,209)(146,196,158,208)(147,195,159,207)(148,194,160,206)(149,193,161,205)(150,216,162,204)(151,215,163,203)(152,214,164,202)(153,213,165,201)(154,212,166,200)(155,211,167,199)(156,210,168,198)(169,238,181,226)(170,237,182,225)(171,236,183,224)(172,235,184,223)(173,234,185,222)(174,233,186,221)(175,232,187,220)(176,231,188,219)(177,230,189,218)(178,229,190,217)(179,228,191,240)(180,227,192,239), (1,166,46,69,222)(2,167,47,70,223)(3,168,48,71,224)(4,145,25,72,225)(5,146,26,49,226)(6,147,27,50,227)(7,148,28,51,228)(8,149,29,52,229)(9,150,30,53,230)(10,151,31,54,231)(11,152,32,55,232)(12,153,33,56,233)(13,154,34,57,234)(14,155,35,58,235)(15,156,36,59,236)(16,157,37,60,237)(17,158,38,61,238)(18,159,39,62,239)(19,160,40,63,240)(20,161,41,64,217)(21,162,42,65,218)(22,163,43,66,219)(23,164,44,67,220)(24,165,45,68,221)(73,216,107,132,189)(74,193,108,133,190)(75,194,109,134,191)(76,195,110,135,192)(77,196,111,136,169)(78,197,112,137,170)(79,198,113,138,171)(80,199,114,139,172)(81,200,115,140,173)(82,201,116,141,174)(83,202,117,142,175)(84,203,118,143,176)(85,204,119,144,177)(86,205,120,121,178)(87,206,97,122,179)(88,207,98,123,180)(89,208,99,124,181)(90,209,100,125,182)(91,210,101,126,183)(92,211,102,127,184)(93,212,103,128,185)(94,213,104,129,186)(95,214,105,130,187)(96,215,106,131,188), (1,222)(2,221)(3,220)(4,219)(5,218)(6,217)(7,240)(8,239)(9,238)(10,237)(11,236)(12,235)(13,234)(14,233)(15,232)(16,231)(17,230)(18,229)(19,228)(20,227)(21,226)(22,225)(23,224)(24,223)(25,43)(26,42)(27,41)(28,40)(29,39)(30,38)(31,37)(32,36)(33,35)(44,48)(45,47)(49,162)(50,161)(51,160)(52,159)(53,158)(54,157)(55,156)(56,155)(57,154)(58,153)(59,152)(60,151)(61,150)(62,149)(63,148)(64,147)(65,146)(66,145)(67,168)(68,167)(69,166)(70,165)(71,164)(72,163)(73,184)(74,183)(75,182)(76,181)(77,180)(78,179)(79,178)(80,177)(81,176)(82,175)(83,174)(84,173)(85,172)(86,171)(87,170)(88,169)(89,192)(90,191)(91,190)(92,189)(93,188)(94,187)(95,186)(96,185)(97,112)(98,111)(99,110)(100,109)(101,108)(102,107)(103,106)(104,105)(113,120)(114,119)(115,118)(116,117)(121,198)(122,197)(123,196)(124,195)(125,194)(126,193)(127,216)(128,215)(129,214)(130,213)(131,212)(132,211)(133,210)(134,209)(135,208)(136,207)(137,206)(138,205)(139,204)(140,203)(141,202)(142,201)(143,200)(144,199)>;
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)(193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216)(217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240), (1,81,13,93)(2,80,14,92)(3,79,15,91)(4,78,16,90)(5,77,17,89)(6,76,18,88)(7,75,19,87)(8,74,20,86)(9,73,21,85)(10,96,22,84)(11,95,23,83)(12,94,24,82)(25,112,37,100)(26,111,38,99)(27,110,39,98)(28,109,40,97)(29,108,41,120)(30,107,42,119)(31,106,43,118)(32,105,44,117)(33,104,45,116)(34,103,46,115)(35,102,47,114)(36,101,48,113)(49,136,61,124)(50,135,62,123)(51,134,63,122)(52,133,64,121)(53,132,65,144)(54,131,66,143)(55,130,67,142)(56,129,68,141)(57,128,69,140)(58,127,70,139)(59,126,71,138)(60,125,72,137)(145,197,157,209)(146,196,158,208)(147,195,159,207)(148,194,160,206)(149,193,161,205)(150,216,162,204)(151,215,163,203)(152,214,164,202)(153,213,165,201)(154,212,166,200)(155,211,167,199)(156,210,168,198)(169,238,181,226)(170,237,182,225)(171,236,183,224)(172,235,184,223)(173,234,185,222)(174,233,186,221)(175,232,187,220)(176,231,188,219)(177,230,189,218)(178,229,190,217)(179,228,191,240)(180,227,192,239), (1,166,46,69,222)(2,167,47,70,223)(3,168,48,71,224)(4,145,25,72,225)(5,146,26,49,226)(6,147,27,50,227)(7,148,28,51,228)(8,149,29,52,229)(9,150,30,53,230)(10,151,31,54,231)(11,152,32,55,232)(12,153,33,56,233)(13,154,34,57,234)(14,155,35,58,235)(15,156,36,59,236)(16,157,37,60,237)(17,158,38,61,238)(18,159,39,62,239)(19,160,40,63,240)(20,161,41,64,217)(21,162,42,65,218)(22,163,43,66,219)(23,164,44,67,220)(24,165,45,68,221)(73,216,107,132,189)(74,193,108,133,190)(75,194,109,134,191)(76,195,110,135,192)(77,196,111,136,169)(78,197,112,137,170)(79,198,113,138,171)(80,199,114,139,172)(81,200,115,140,173)(82,201,116,141,174)(83,202,117,142,175)(84,203,118,143,176)(85,204,119,144,177)(86,205,120,121,178)(87,206,97,122,179)(88,207,98,123,180)(89,208,99,124,181)(90,209,100,125,182)(91,210,101,126,183)(92,211,102,127,184)(93,212,103,128,185)(94,213,104,129,186)(95,214,105,130,187)(96,215,106,131,188), (1,222)(2,221)(3,220)(4,219)(5,218)(6,217)(7,240)(8,239)(9,238)(10,237)(11,236)(12,235)(13,234)(14,233)(15,232)(16,231)(17,230)(18,229)(19,228)(20,227)(21,226)(22,225)(23,224)(24,223)(25,43)(26,42)(27,41)(28,40)(29,39)(30,38)(31,37)(32,36)(33,35)(44,48)(45,47)(49,162)(50,161)(51,160)(52,159)(53,158)(54,157)(55,156)(56,155)(57,154)(58,153)(59,152)(60,151)(61,150)(62,149)(63,148)(64,147)(65,146)(66,145)(67,168)(68,167)(69,166)(70,165)(71,164)(72,163)(73,184)(74,183)(75,182)(76,181)(77,180)(78,179)(79,178)(80,177)(81,176)(82,175)(83,174)(84,173)(85,172)(86,171)(87,170)(88,169)(89,192)(90,191)(91,190)(92,189)(93,188)(94,187)(95,186)(96,185)(97,112)(98,111)(99,110)(100,109)(101,108)(102,107)(103,106)(104,105)(113,120)(114,119)(115,118)(116,117)(121,198)(122,197)(123,196)(124,195)(125,194)(126,193)(127,216)(128,215)(129,214)(130,213)(131,212)(132,211)(133,210)(134,209)(135,208)(136,207)(137,206)(138,205)(139,204)(140,203)(141,202)(142,201)(143,200)(144,199) );
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),(193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216),(217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240)], [(1,81,13,93),(2,80,14,92),(3,79,15,91),(4,78,16,90),(5,77,17,89),(6,76,18,88),(7,75,19,87),(8,74,20,86),(9,73,21,85),(10,96,22,84),(11,95,23,83),(12,94,24,82),(25,112,37,100),(26,111,38,99),(27,110,39,98),(28,109,40,97),(29,108,41,120),(30,107,42,119),(31,106,43,118),(32,105,44,117),(33,104,45,116),(34,103,46,115),(35,102,47,114),(36,101,48,113),(49,136,61,124),(50,135,62,123),(51,134,63,122),(52,133,64,121),(53,132,65,144),(54,131,66,143),(55,130,67,142),(56,129,68,141),(57,128,69,140),(58,127,70,139),(59,126,71,138),(60,125,72,137),(145,197,157,209),(146,196,158,208),(147,195,159,207),(148,194,160,206),(149,193,161,205),(150,216,162,204),(151,215,163,203),(152,214,164,202),(153,213,165,201),(154,212,166,200),(155,211,167,199),(156,210,168,198),(169,238,181,226),(170,237,182,225),(171,236,183,224),(172,235,184,223),(173,234,185,222),(174,233,186,221),(175,232,187,220),(176,231,188,219),(177,230,189,218),(178,229,190,217),(179,228,191,240),(180,227,192,239)], [(1,166,46,69,222),(2,167,47,70,223),(3,168,48,71,224),(4,145,25,72,225),(5,146,26,49,226),(6,147,27,50,227),(7,148,28,51,228),(8,149,29,52,229),(9,150,30,53,230),(10,151,31,54,231),(11,152,32,55,232),(12,153,33,56,233),(13,154,34,57,234),(14,155,35,58,235),(15,156,36,59,236),(16,157,37,60,237),(17,158,38,61,238),(18,159,39,62,239),(19,160,40,63,240),(20,161,41,64,217),(21,162,42,65,218),(22,163,43,66,219),(23,164,44,67,220),(24,165,45,68,221),(73,216,107,132,189),(74,193,108,133,190),(75,194,109,134,191),(76,195,110,135,192),(77,196,111,136,169),(78,197,112,137,170),(79,198,113,138,171),(80,199,114,139,172),(81,200,115,140,173),(82,201,116,141,174),(83,202,117,142,175),(84,203,118,143,176),(85,204,119,144,177),(86,205,120,121,178),(87,206,97,122,179),(88,207,98,123,180),(89,208,99,124,181),(90,209,100,125,182),(91,210,101,126,183),(92,211,102,127,184),(93,212,103,128,185),(94,213,104,129,186),(95,214,105,130,187),(96,215,106,131,188)], [(1,222),(2,221),(3,220),(4,219),(5,218),(6,217),(7,240),(8,239),(9,238),(10,237),(11,236),(12,235),(13,234),(14,233),(15,232),(16,231),(17,230),(18,229),(19,228),(20,227),(21,226),(22,225),(23,224),(24,223),(25,43),(26,42),(27,41),(28,40),(29,39),(30,38),(31,37),(32,36),(33,35),(44,48),(45,47),(49,162),(50,161),(51,160),(52,159),(53,158),(54,157),(55,156),(56,155),(57,154),(58,153),(59,152),(60,151),(61,150),(62,149),(63,148),(64,147),(65,146),(66,145),(67,168),(68,167),(69,166),(70,165),(71,164),(72,163),(73,184),(74,183),(75,182),(76,181),(77,180),(78,179),(79,178),(80,177),(81,176),(82,175),(83,174),(84,173),(85,172),(86,171),(87,170),(88,169),(89,192),(90,191),(91,190),(92,189),(93,188),(94,187),(95,186),(96,185),(97,112),(98,111),(99,110),(100,109),(101,108),(102,107),(103,106),(104,105),(113,120),(114,119),(115,118),(116,117),(121,198),(122,197),(123,196),(124,195),(125,194),(126,193),(127,216),(128,215),(129,214),(130,213),(131,212),(132,211),(133,210),(134,209),(135,208),(136,207),(137,206),(138,205),(139,204),(140,203),(141,202),(142,201),(143,200),(144,199)]])
57 conjugacy classes
| class | 1 | 2A | 2B | 3 | 4A | 4B | 5A | 5B | 6 | 8A | 8B | 10A | 10B | 12A | 12B | 15A | 15B | 16A | 16B | 16C | 16D | 20A | 20B | 20C | 20D | 20E | 20F | 24A | 24B | 24C | 24D | 30A | 30B | 40A | 40B | 40C | 40D | 48A | ··· | 48H | 60A | 60B | 60C | 60D | 120A | ··· | 120H |
| order | 1 | 2 | 2 | 3 | 4 | 4 | 5 | 5 | 6 | 8 | 8 | 10 | 10 | 12 | 12 | 15 | 15 | 16 | 16 | 16 | 16 | 20 | 20 | 20 | 20 | 20 | 20 | 24 | 24 | 24 | 24 | 30 | 30 | 40 | 40 | 40 | 40 | 48 | ··· | 48 | 60 | 60 | 60 | 60 | 120 | ··· | 120 |
| size | 1 | 1 | 120 | 2 | 2 | 24 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 10 | 10 | 10 | 10 | 4 | 4 | 24 | 24 | 24 | 24 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 10 | ··· | 10 | 4 | 4 | 4 | 4 | 4 | ··· | 4 |
57 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |||
| image | C1 | C2 | C2 | C2 | S3 | D4 | D5 | D6 | D8 | D10 | D12 | SD32 | C5⋊D4 | D24 | C48⋊C2 | S3×D5 | D4⋊D5 | C5⋊D12 | C5⋊SD32 | C5⋊D24 | Dic12⋊D5 |
| kernel | Dic12⋊D5 | C3×C5⋊2C16 | C5×Dic12 | D120 | C5⋊2C16 | C60 | Dic12 | C40 | C30 | C24 | C20 | C15 | C12 | C10 | C5 | C8 | C6 | C4 | C3 | C2 | C1 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 8 | 2 | 2 | 2 | 4 | 4 | 8 |
Matrix representation of Dic12⋊D5 ►in GL4(𝔽241) generated by
| 145 | 213 | 0 | 0 |
| 157 | 219 | 0 | 0 |
| 0 | 0 | 240 | 0 |
| 0 | 0 | 0 | 240 |
| 230 | 44 | 0 | 0 |
| 52 | 11 | 0 | 0 |
| 0 | 0 | 165 | 103 |
| 0 | 0 | 89 | 76 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 240 | 1 |
| 0 | 0 | 50 | 190 |
| 240 | 0 | 0 | 0 |
| 192 | 1 | 0 | 0 |
| 0 | 0 | 240 | 0 |
| 0 | 0 | 50 | 1 |
G:=sub<GL(4,GF(241))| [145,157,0,0,213,219,0,0,0,0,240,0,0,0,0,240],[230,52,0,0,44,11,0,0,0,0,165,89,0,0,103,76],[1,0,0,0,0,1,0,0,0,0,240,50,0,0,1,190],[240,192,0,0,0,1,0,0,0,0,240,50,0,0,0,1] >;
Dic12⋊D5 in GAP, Magma, Sage, TeX
{\rm Dic}_{12}\rtimes D_5 % in TeX
G:=Group("Dic12:D5"); // GroupNames label
G:=SmallGroup(480,21);
// by ID
G=gap.SmallGroup(480,21);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,28,309,120,135,142,346,80,1356,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^24=c^5=d^2=1,b^2=a^12,b*a*b^-1=d*a*d=a^-1,a*c=c*a,b*c=c*b,d*b*d=a^21*b,d*c*d=c^-1>;
// generators/relations
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