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## G = (C4×Dic15)⋊C2order 480 = 25·3·5

### 8th semidirect product of C4×Dic15 and C2 acting faithfully

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C30 — (C4×Dic15)⋊C2
 Chief series C1 — C5 — C15 — C30 — C2×C30 — D5×C2×C6 — D10⋊Dic3 — (C4×Dic15)⋊C2
 Lower central C15 — C2×C30 — (C4×Dic15)⋊C2
 Upper central C1 — C22 — C2×C4

Generators and relations for (C4×Dic15)⋊C2
G = < a,b,c,d | a4=b30=d2=1, c2=b15, ab=ba, ac=ca, dad=a-1b15, cbc-1=b-1, dbd=b19, dcd=a2c >

Subgroups: 556 in 120 conjugacy classes, 44 normal (all characteristic)
C1, C2 [×3], C2, C3, C4 [×6], C22, C22 [×3], C5, C6 [×3], C6, C2×C4, C2×C4 [×5], C23, D5, C10 [×3], Dic3 [×4], C12 [×2], C2×C6, C2×C6 [×3], C15, C42, C22⋊C4 [×3], C4⋊C4 [×3], Dic5 [×3], C20 [×3], D10 [×3], C2×C10, C2×Dic3 [×2], C2×Dic3 [×2], C2×C12, C2×C12, C22×C6, C3×D5, C30 [×3], C422C2, C2×Dic5, C2×Dic5 [×2], C2×C20, C2×C20 [×2], C22×D5, C4×Dic3, Dic3⋊C4, Dic3⋊C4, C4⋊Dic3, C6.D4 [×2], C3×C22⋊C4, C5×Dic3 [×2], C3×Dic5, Dic15 [×2], C60, C6×D5 [×3], C2×C30, C4×Dic5, C10.D4, C4⋊Dic5, D10⋊C4, D10⋊C4 [×2], C5×C4⋊C4, C23.8D6, C6×Dic5, C10×Dic3 [×2], C2×Dic15 [×2], C2×C60, D5×C2×C6, C4⋊C4⋊D5, D10⋊Dic3 [×2], C30.Q8, C6.Dic10, C3×D10⋊C4, C5×Dic3⋊C4, C4×Dic15, (C4×Dic15)⋊C2
Quotients: C1, C2 [×7], C22 [×7], S3, C23, D5, D6 [×3], C4○D4 [×3], D10 [×3], C22×S3, C422C2, C22×D5, C4○D12, D42S3 [×2], S3×D5, C4○D20, D42D5, Q82D5, C23.8D6, C2×S3×D5, C4⋊C4⋊D5, D20⋊S3, D6.D10, C30.C23, (C4×Dic15)⋊C2

Smallest permutation representation of (C4×Dic15)⋊C2
On 240 points
Generators in S240
(1 130 80 52)(2 131 81 53)(3 132 82 54)(4 133 83 55)(5 134 84 56)(6 135 85 57)(7 136 86 58)(8 137 87 59)(9 138 88 60)(10 139 89 31)(11 140 90 32)(12 141 61 33)(13 142 62 34)(14 143 63 35)(15 144 64 36)(16 145 65 37)(17 146 66 38)(18 147 67 39)(19 148 68 40)(20 149 69 41)(21 150 70 42)(22 121 71 43)(23 122 72 44)(24 123 73 45)(25 124 74 46)(26 125 75 47)(27 126 76 48)(28 127 77 49)(29 128 78 50)(30 129 79 51)(91 167 233 194)(92 168 234 195)(93 169 235 196)(94 170 236 197)(95 171 237 198)(96 172 238 199)(97 173 239 200)(98 174 240 201)(99 175 211 202)(100 176 212 203)(101 177 213 204)(102 178 214 205)(103 179 215 206)(104 180 216 207)(105 151 217 208)(106 152 218 209)(107 153 219 210)(108 154 220 181)(109 155 221 182)(110 156 222 183)(111 157 223 184)(112 158 224 185)(113 159 225 186)(114 160 226 187)(115 161 227 188)(116 162 228 189)(117 163 229 190)(118 164 230 191)(119 165 231 192)(120 166 232 193)
(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)
(1 172 16 157)(2 171 17 156)(3 170 18 155)(4 169 19 154)(5 168 20 153)(6 167 21 152)(7 166 22 151)(8 165 23 180)(9 164 24 179)(10 163 25 178)(11 162 26 177)(12 161 27 176)(13 160 28 175)(14 159 29 174)(15 158 30 173)(31 117 46 102)(32 116 47 101)(33 115 48 100)(34 114 49 99)(35 113 50 98)(36 112 51 97)(37 111 52 96)(38 110 53 95)(39 109 54 94)(40 108 55 93)(41 107 56 92)(42 106 57 91)(43 105 58 120)(44 104 59 119)(45 103 60 118)(61 188 76 203)(62 187 77 202)(63 186 78 201)(64 185 79 200)(65 184 80 199)(66 183 81 198)(67 182 82 197)(68 181 83 196)(69 210 84 195)(70 209 85 194)(71 208 86 193)(72 207 87 192)(73 206 88 191)(74 205 89 190)(75 204 90 189)(121 217 136 232)(122 216 137 231)(123 215 138 230)(124 214 139 229)(125 213 140 228)(126 212 141 227)(127 211 142 226)(128 240 143 225)(129 239 144 224)(130 238 145 223)(131 237 146 222)(132 236 147 221)(133 235 148 220)(134 234 149 219)(135 233 150 218)
(2 20)(3 9)(4 28)(5 17)(7 25)(8 14)(10 22)(12 30)(13 19)(15 27)(18 24)(23 29)(31 136)(32 125)(33 144)(34 133)(35 122)(36 141)(37 130)(38 149)(39 138)(40 127)(41 146)(42 135)(43 124)(44 143)(45 132)(46 121)(47 140)(48 129)(49 148)(50 137)(51 126)(52 145)(53 134)(54 123)(55 142)(56 131)(57 150)(58 139)(59 128)(60 147)(61 79)(62 68)(63 87)(64 76)(66 84)(67 73)(69 81)(71 89)(72 78)(74 86)(77 83)(82 88)(91 106)(92 95)(93 114)(94 103)(96 111)(97 100)(98 119)(99 108)(101 116)(102 105)(104 113)(107 110)(109 118)(112 115)(117 120)(151 190)(152 209)(153 198)(154 187)(155 206)(156 195)(157 184)(158 203)(159 192)(160 181)(161 200)(162 189)(163 208)(164 197)(165 186)(166 205)(167 194)(168 183)(169 202)(170 191)(171 210)(172 199)(173 188)(174 207)(175 196)(176 185)(177 204)(178 193)(179 182)(180 201)(211 220)(212 239)(213 228)(214 217)(215 236)(216 225)(218 233)(219 222)(221 230)(223 238)(224 227)(226 235)(229 232)(231 240)(234 237)

G:=sub<Sym(240)| (1,130,80,52)(2,131,81,53)(3,132,82,54)(4,133,83,55)(5,134,84,56)(6,135,85,57)(7,136,86,58)(8,137,87,59)(9,138,88,60)(10,139,89,31)(11,140,90,32)(12,141,61,33)(13,142,62,34)(14,143,63,35)(15,144,64,36)(16,145,65,37)(17,146,66,38)(18,147,67,39)(19,148,68,40)(20,149,69,41)(21,150,70,42)(22,121,71,43)(23,122,72,44)(24,123,73,45)(25,124,74,46)(26,125,75,47)(27,126,76,48)(28,127,77,49)(29,128,78,50)(30,129,79,51)(91,167,233,194)(92,168,234,195)(93,169,235,196)(94,170,236,197)(95,171,237,198)(96,172,238,199)(97,173,239,200)(98,174,240,201)(99,175,211,202)(100,176,212,203)(101,177,213,204)(102,178,214,205)(103,179,215,206)(104,180,216,207)(105,151,217,208)(106,152,218,209)(107,153,219,210)(108,154,220,181)(109,155,221,182)(110,156,222,183)(111,157,223,184)(112,158,224,185)(113,159,225,186)(114,160,226,187)(115,161,227,188)(116,162,228,189)(117,163,229,190)(118,164,230,191)(119,165,231,192)(120,166,232,193), (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), (1,172,16,157)(2,171,17,156)(3,170,18,155)(4,169,19,154)(5,168,20,153)(6,167,21,152)(7,166,22,151)(8,165,23,180)(9,164,24,179)(10,163,25,178)(11,162,26,177)(12,161,27,176)(13,160,28,175)(14,159,29,174)(15,158,30,173)(31,117,46,102)(32,116,47,101)(33,115,48,100)(34,114,49,99)(35,113,50,98)(36,112,51,97)(37,111,52,96)(38,110,53,95)(39,109,54,94)(40,108,55,93)(41,107,56,92)(42,106,57,91)(43,105,58,120)(44,104,59,119)(45,103,60,118)(61,188,76,203)(62,187,77,202)(63,186,78,201)(64,185,79,200)(65,184,80,199)(66,183,81,198)(67,182,82,197)(68,181,83,196)(69,210,84,195)(70,209,85,194)(71,208,86,193)(72,207,87,192)(73,206,88,191)(74,205,89,190)(75,204,90,189)(121,217,136,232)(122,216,137,231)(123,215,138,230)(124,214,139,229)(125,213,140,228)(126,212,141,227)(127,211,142,226)(128,240,143,225)(129,239,144,224)(130,238,145,223)(131,237,146,222)(132,236,147,221)(133,235,148,220)(134,234,149,219)(135,233,150,218), (2,20)(3,9)(4,28)(5,17)(7,25)(8,14)(10,22)(12,30)(13,19)(15,27)(18,24)(23,29)(31,136)(32,125)(33,144)(34,133)(35,122)(36,141)(37,130)(38,149)(39,138)(40,127)(41,146)(42,135)(43,124)(44,143)(45,132)(46,121)(47,140)(48,129)(49,148)(50,137)(51,126)(52,145)(53,134)(54,123)(55,142)(56,131)(57,150)(58,139)(59,128)(60,147)(61,79)(62,68)(63,87)(64,76)(66,84)(67,73)(69,81)(71,89)(72,78)(74,86)(77,83)(82,88)(91,106)(92,95)(93,114)(94,103)(96,111)(97,100)(98,119)(99,108)(101,116)(102,105)(104,113)(107,110)(109,118)(112,115)(117,120)(151,190)(152,209)(153,198)(154,187)(155,206)(156,195)(157,184)(158,203)(159,192)(160,181)(161,200)(162,189)(163,208)(164,197)(165,186)(166,205)(167,194)(168,183)(169,202)(170,191)(171,210)(172,199)(173,188)(174,207)(175,196)(176,185)(177,204)(178,193)(179,182)(180,201)(211,220)(212,239)(213,228)(214,217)(215,236)(216,225)(218,233)(219,222)(221,230)(223,238)(224,227)(226,235)(229,232)(231,240)(234,237)>;

G:=Group( (1,130,80,52)(2,131,81,53)(3,132,82,54)(4,133,83,55)(5,134,84,56)(6,135,85,57)(7,136,86,58)(8,137,87,59)(9,138,88,60)(10,139,89,31)(11,140,90,32)(12,141,61,33)(13,142,62,34)(14,143,63,35)(15,144,64,36)(16,145,65,37)(17,146,66,38)(18,147,67,39)(19,148,68,40)(20,149,69,41)(21,150,70,42)(22,121,71,43)(23,122,72,44)(24,123,73,45)(25,124,74,46)(26,125,75,47)(27,126,76,48)(28,127,77,49)(29,128,78,50)(30,129,79,51)(91,167,233,194)(92,168,234,195)(93,169,235,196)(94,170,236,197)(95,171,237,198)(96,172,238,199)(97,173,239,200)(98,174,240,201)(99,175,211,202)(100,176,212,203)(101,177,213,204)(102,178,214,205)(103,179,215,206)(104,180,216,207)(105,151,217,208)(106,152,218,209)(107,153,219,210)(108,154,220,181)(109,155,221,182)(110,156,222,183)(111,157,223,184)(112,158,224,185)(113,159,225,186)(114,160,226,187)(115,161,227,188)(116,162,228,189)(117,163,229,190)(118,164,230,191)(119,165,231,192)(120,166,232,193), (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), (1,172,16,157)(2,171,17,156)(3,170,18,155)(4,169,19,154)(5,168,20,153)(6,167,21,152)(7,166,22,151)(8,165,23,180)(9,164,24,179)(10,163,25,178)(11,162,26,177)(12,161,27,176)(13,160,28,175)(14,159,29,174)(15,158,30,173)(31,117,46,102)(32,116,47,101)(33,115,48,100)(34,114,49,99)(35,113,50,98)(36,112,51,97)(37,111,52,96)(38,110,53,95)(39,109,54,94)(40,108,55,93)(41,107,56,92)(42,106,57,91)(43,105,58,120)(44,104,59,119)(45,103,60,118)(61,188,76,203)(62,187,77,202)(63,186,78,201)(64,185,79,200)(65,184,80,199)(66,183,81,198)(67,182,82,197)(68,181,83,196)(69,210,84,195)(70,209,85,194)(71,208,86,193)(72,207,87,192)(73,206,88,191)(74,205,89,190)(75,204,90,189)(121,217,136,232)(122,216,137,231)(123,215,138,230)(124,214,139,229)(125,213,140,228)(126,212,141,227)(127,211,142,226)(128,240,143,225)(129,239,144,224)(130,238,145,223)(131,237,146,222)(132,236,147,221)(133,235,148,220)(134,234,149,219)(135,233,150,218), (2,20)(3,9)(4,28)(5,17)(7,25)(8,14)(10,22)(12,30)(13,19)(15,27)(18,24)(23,29)(31,136)(32,125)(33,144)(34,133)(35,122)(36,141)(37,130)(38,149)(39,138)(40,127)(41,146)(42,135)(43,124)(44,143)(45,132)(46,121)(47,140)(48,129)(49,148)(50,137)(51,126)(52,145)(53,134)(54,123)(55,142)(56,131)(57,150)(58,139)(59,128)(60,147)(61,79)(62,68)(63,87)(64,76)(66,84)(67,73)(69,81)(71,89)(72,78)(74,86)(77,83)(82,88)(91,106)(92,95)(93,114)(94,103)(96,111)(97,100)(98,119)(99,108)(101,116)(102,105)(104,113)(107,110)(109,118)(112,115)(117,120)(151,190)(152,209)(153,198)(154,187)(155,206)(156,195)(157,184)(158,203)(159,192)(160,181)(161,200)(162,189)(163,208)(164,197)(165,186)(166,205)(167,194)(168,183)(169,202)(170,191)(171,210)(172,199)(173,188)(174,207)(175,196)(176,185)(177,204)(178,193)(179,182)(180,201)(211,220)(212,239)(213,228)(214,217)(215,236)(216,225)(218,233)(219,222)(221,230)(223,238)(224,227)(226,235)(229,232)(231,240)(234,237) );

G=PermutationGroup([(1,130,80,52),(2,131,81,53),(3,132,82,54),(4,133,83,55),(5,134,84,56),(6,135,85,57),(7,136,86,58),(8,137,87,59),(9,138,88,60),(10,139,89,31),(11,140,90,32),(12,141,61,33),(13,142,62,34),(14,143,63,35),(15,144,64,36),(16,145,65,37),(17,146,66,38),(18,147,67,39),(19,148,68,40),(20,149,69,41),(21,150,70,42),(22,121,71,43),(23,122,72,44),(24,123,73,45),(25,124,74,46),(26,125,75,47),(27,126,76,48),(28,127,77,49),(29,128,78,50),(30,129,79,51),(91,167,233,194),(92,168,234,195),(93,169,235,196),(94,170,236,197),(95,171,237,198),(96,172,238,199),(97,173,239,200),(98,174,240,201),(99,175,211,202),(100,176,212,203),(101,177,213,204),(102,178,214,205),(103,179,215,206),(104,180,216,207),(105,151,217,208),(106,152,218,209),(107,153,219,210),(108,154,220,181),(109,155,221,182),(110,156,222,183),(111,157,223,184),(112,158,224,185),(113,159,225,186),(114,160,226,187),(115,161,227,188),(116,162,228,189),(117,163,229,190),(118,164,230,191),(119,165,231,192),(120,166,232,193)], [(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)], [(1,172,16,157),(2,171,17,156),(3,170,18,155),(4,169,19,154),(5,168,20,153),(6,167,21,152),(7,166,22,151),(8,165,23,180),(9,164,24,179),(10,163,25,178),(11,162,26,177),(12,161,27,176),(13,160,28,175),(14,159,29,174),(15,158,30,173),(31,117,46,102),(32,116,47,101),(33,115,48,100),(34,114,49,99),(35,113,50,98),(36,112,51,97),(37,111,52,96),(38,110,53,95),(39,109,54,94),(40,108,55,93),(41,107,56,92),(42,106,57,91),(43,105,58,120),(44,104,59,119),(45,103,60,118),(61,188,76,203),(62,187,77,202),(63,186,78,201),(64,185,79,200),(65,184,80,199),(66,183,81,198),(67,182,82,197),(68,181,83,196),(69,210,84,195),(70,209,85,194),(71,208,86,193),(72,207,87,192),(73,206,88,191),(74,205,89,190),(75,204,90,189),(121,217,136,232),(122,216,137,231),(123,215,138,230),(124,214,139,229),(125,213,140,228),(126,212,141,227),(127,211,142,226),(128,240,143,225),(129,239,144,224),(130,238,145,223),(131,237,146,222),(132,236,147,221),(133,235,148,220),(134,234,149,219),(135,233,150,218)], [(2,20),(3,9),(4,28),(5,17),(7,25),(8,14),(10,22),(12,30),(13,19),(15,27),(18,24),(23,29),(31,136),(32,125),(33,144),(34,133),(35,122),(36,141),(37,130),(38,149),(39,138),(40,127),(41,146),(42,135),(43,124),(44,143),(45,132),(46,121),(47,140),(48,129),(49,148),(50,137),(51,126),(52,145),(53,134),(54,123),(55,142),(56,131),(57,150),(58,139),(59,128),(60,147),(61,79),(62,68),(63,87),(64,76),(66,84),(67,73),(69,81),(71,89),(72,78),(74,86),(77,83),(82,88),(91,106),(92,95),(93,114),(94,103),(96,111),(97,100),(98,119),(99,108),(101,116),(102,105),(104,113),(107,110),(109,118),(112,115),(117,120),(151,190),(152,209),(153,198),(154,187),(155,206),(156,195),(157,184),(158,203),(159,192),(160,181),(161,200),(162,189),(163,208),(164,197),(165,186),(166,205),(167,194),(168,183),(169,202),(170,191),(171,210),(172,199),(173,188),(174,207),(175,196),(176,185),(177,204),(178,193),(179,182),(180,201),(211,220),(212,239),(213,228),(214,217),(215,236),(216,225),(218,233),(219,222),(221,230),(223,238),(224,227),(226,235),(229,232),(231,240),(234,237)])

60 conjugacy classes

 class 1 2A 2B 2C 2D 3 4A 4B 4C 4D 4E 4F 4G 4H 4I 5A 5B 6A 6B 6C 6D 6E 10A ··· 10F 12A 12B 12C 12D 15A 15B 20A 20B 20C 20D 20E ··· 20L 30A ··· 30F 60A ··· 60H order 1 2 2 2 2 3 4 4 4 4 4 4 4 4 4 5 5 6 6 6 6 6 10 ··· 10 12 12 12 12 15 15 20 20 20 20 20 ··· 20 30 ··· 30 60 ··· 60 size 1 1 1 1 20 2 2 2 12 12 20 30 30 30 30 2 2 2 2 2 20 20 2 ··· 2 4 4 20 20 4 4 4 4 4 4 12 ··· 12 4 ··· 4 4 ··· 4

60 irreducible representations

 dim 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 type + + + + + + + + + + + + + + - + - + + - image C1 C2 C2 C2 C2 C2 C2 S3 D5 D6 D6 D6 C4○D4 D10 D10 C4○D12 C4○D20 D4⋊2S3 S3×D5 D4⋊2D5 Q8⋊2D5 C2×S3×D5 D20⋊S3 D6.D10 C30.C23 kernel (C4×Dic15)⋊C2 D10⋊Dic3 C30.Q8 C6.Dic10 C3×D10⋊C4 C5×Dic3⋊C4 C4×Dic15 D10⋊C4 Dic3⋊C4 C2×Dic5 C2×C20 C22×D5 C30 C2×Dic3 C2×C12 C10 C6 C10 C2×C4 C6 C6 C22 C2 C2 C2 # reps 1 2 1 1 1 1 1 1 2 1 1 1 6 4 2 4 8 2 2 2 2 2 4 4 4

Matrix representation of (C4×Dic15)⋊C2 in GL6(𝔽61)

 11 0 0 0 0 0 0 11 0 0 0 0 0 0 1 8 0 0 0 0 15 60 0 0 0 0 0 0 11 0 0 0 0 0 0 11
,
 43 1 0 0 0 0 42 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 14 39 0 0 0 0 0 48
,
 8 14 0 0 0 0 52 53 0 0 0 0 0 0 50 34 0 0 0 0 18 11 0 0 0 0 0 0 28 48 0 0 0 0 51 33
,
 43 1 0 0 0 0 43 18 0 0 0 0 0 0 1 8 0 0 0 0 0 60 0 0 0 0 0 0 1 30 0 0 0 0 0 60

G:=sub<GL(6,GF(61))| [11,0,0,0,0,0,0,11,0,0,0,0,0,0,1,15,0,0,0,0,8,60,0,0,0,0,0,0,11,0,0,0,0,0,0,11],[43,42,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,14,0,0,0,0,0,39,48],[8,52,0,0,0,0,14,53,0,0,0,0,0,0,50,18,0,0,0,0,34,11,0,0,0,0,0,0,28,51,0,0,0,0,48,33],[43,43,0,0,0,0,1,18,0,0,0,0,0,0,1,0,0,0,0,0,8,60,0,0,0,0,0,0,1,0,0,0,0,0,30,60] >;

(C4×Dic15)⋊C2 in GAP, Magma, Sage, TeX

(C_4\times {\rm Dic}_{15})\rtimes C_2
% in TeX

G:=Group("(C4xDic15):C2");
// GroupNames label

G:=SmallGroup(480,442);
// by ID

G=gap.SmallGroup(480,442);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,141,120,422,219,58,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^4=b^30=d^2=1,c^2=b^15,a*b=b*a,a*c=c*a,d*a*d=a^-1*b^15,c*b*c^-1=b^-1,d*b*d=b^19,d*c*d=a^2*c>;
// generators/relations

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