metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D8.D15, C60.4D4, C8.5D30, C30.40D8, C40.13D6, C15⋊10SD32, Dic60⋊6C2, C24.13D10, C120.10C22, C5⋊3(D8.S3), C3⋊3(D8.D5), (C3×D8).1D5, (C5×D8).1S3, C15⋊3C16⋊2C2, (C15×D8).1C2, C2.5(D4⋊D15), C6.18(D4⋊D5), C4.2(C15⋊7D4), C10.18(D4⋊S3), C12.18(C5⋊D4), C20.16(C3⋊D4), SmallGroup(480,187)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D8.D15
G = < a,b,c,d | a8=b2=c15=1, d2=a4, bab=dad-1=a-1, ac=ca, bc=cb, dbd-1=a5b, dcd-1=c-1 >
Smallest permutation representation of D8.D15
►On 240 points
Generators in S240
(1 91 31 77 17 110 50 62)(2 92 32 78 18 111 51 63)(3 93 33 79 19 112 52 64)(4 94 34 80 20 113 53 65)(5 95 35 81 21 114 54 66)(6 96 36 82 22 115 55 67)(7 97 37 83 23 116 56 68)(8 98 38 84 24 117 57 69)(9 99 39 85 25 118 58 70)(10 100 40 86 26 119 59 71)(11 101 41 87 27 120 60 72)(12 102 42 88 28 106 46 73)(13 103 43 89 29 107 47 74)(14 104 44 90 30 108 48 75)(15 105 45 76 16 109 49 61)(121 192 170 233 149 209 153 219)(122 193 171 234 150 210 154 220)(123 194 172 235 136 196 155 221)(124 195 173 236 137 197 156 222)(125 181 174 237 138 198 157 223)(126 182 175 238 139 199 158 224)(127 183 176 239 140 200 159 225)(128 184 177 240 141 201 160 211)(129 185 178 226 142 202 161 212)(130 186 179 227 143 203 162 213)(131 187 180 228 144 204 163 214)(132 188 166 229 145 205 164 215)(133 189 167 230 146 206 165 216)(134 190 168 231 147 207 151 217)(135 191 169 232 148 208 152 218)
(1 62)(2 63)(3 64)(4 65)(5 66)(6 67)(7 68)(8 69)(9 70)(10 71)(11 72)(12 73)(13 74)(14 75)(15 61)(16 76)(17 77)(18 78)(19 79)(20 80)(21 81)(22 82)(23 83)(24 84)(25 85)(26 86)(27 87)(28 88)(29 89)(30 90)(31 110)(32 111)(33 112)(34 113)(35 114)(36 115)(37 116)(38 117)(39 118)(40 119)(41 120)(42 106)(43 107)(44 108)(45 109)(46 102)(47 103)(48 104)(49 105)(50 91)(51 92)(52 93)(53 94)(54 95)(55 96)(56 97)(57 98)(58 99)(59 100)(60 101)(121 153)(122 154)(123 155)(124 156)(125 157)(126 158)(127 159)(128 160)(129 161)(130 162)(131 163)(132 164)(133 165)(134 151)(135 152)(136 172)(137 173)(138 174)(139 175)(140 176)(141 177)(142 178)(143 179)(144 180)(145 166)(146 167)(147 168)(148 169)(149 170)(150 171)(181 198)(182 199)(183 200)(184 201)(185 202)(186 203)(187 204)(188 205)(189 206)(190 207)(191 208)(192 209)(193 210)(194 196)(195 197)
(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)
(1 137 17 124)(2 136 18 123)(3 150 19 122)(4 149 20 121)(5 148 21 135)(6 147 22 134)(7 146 23 133)(8 145 24 132)(9 144 25 131)(10 143 26 130)(11 142 27 129)(12 141 28 128)(13 140 29 127)(14 139 30 126)(15 138 16 125)(31 173 50 156)(32 172 51 155)(33 171 52 154)(34 170 53 153)(35 169 54 152)(36 168 55 151)(37 167 56 165)(38 166 57 164)(39 180 58 163)(40 179 59 162)(41 178 60 161)(42 177 46 160)(43 176 47 159)(44 175 48 158)(45 174 49 157)(61 198 76 181)(62 197 77 195)(63 196 78 194)(64 210 79 193)(65 209 80 192)(66 208 81 191)(67 207 82 190)(68 206 83 189)(69 205 84 188)(70 204 85 187)(71 203 86 186)(72 202 87 185)(73 201 88 184)(74 200 89 183)(75 199 90 182)(91 236 110 222)(92 235 111 221)(93 234 112 220)(94 233 113 219)(95 232 114 218)(96 231 115 217)(97 230 116 216)(98 229 117 215)(99 228 118 214)(100 227 119 213)(101 226 120 212)(102 240 106 211)(103 239 107 225)(104 238 108 224)(105 237 109 223)
G:=sub<Sym(240)| (1,91,31,77,17,110,50,62)(2,92,32,78,18,111,51,63)(3,93,33,79,19,112,52,64)(4,94,34,80,20,113,53,65)(5,95,35,81,21,114,54,66)(6,96,36,82,22,115,55,67)(7,97,37,83,23,116,56,68)(8,98,38,84,24,117,57,69)(9,99,39,85,25,118,58,70)(10,100,40,86,26,119,59,71)(11,101,41,87,27,120,60,72)(12,102,42,88,28,106,46,73)(13,103,43,89,29,107,47,74)(14,104,44,90,30,108,48,75)(15,105,45,76,16,109,49,61)(121,192,170,233,149,209,153,219)(122,193,171,234,150,210,154,220)(123,194,172,235,136,196,155,221)(124,195,173,236,137,197,156,222)(125,181,174,237,138,198,157,223)(126,182,175,238,139,199,158,224)(127,183,176,239,140,200,159,225)(128,184,177,240,141,201,160,211)(129,185,178,226,142,202,161,212)(130,186,179,227,143,203,162,213)(131,187,180,228,144,204,163,214)(132,188,166,229,145,205,164,215)(133,189,167,230,146,206,165,216)(134,190,168,231,147,207,151,217)(135,191,169,232,148,208,152,218), (1,62)(2,63)(3,64)(4,65)(5,66)(6,67)(7,68)(8,69)(9,70)(10,71)(11,72)(12,73)(13,74)(14,75)(15,61)(16,76)(17,77)(18,78)(19,79)(20,80)(21,81)(22,82)(23,83)(24,84)(25,85)(26,86)(27,87)(28,88)(29,89)(30,90)(31,110)(32,111)(33,112)(34,113)(35,114)(36,115)(37,116)(38,117)(39,118)(40,119)(41,120)(42,106)(43,107)(44,108)(45,109)(46,102)(47,103)(48,104)(49,105)(50,91)(51,92)(52,93)(53,94)(54,95)(55,96)(56,97)(57,98)(58,99)(59,100)(60,101)(121,153)(122,154)(123,155)(124,156)(125,157)(126,158)(127,159)(128,160)(129,161)(130,162)(131,163)(132,164)(133,165)(134,151)(135,152)(136,172)(137,173)(138,174)(139,175)(140,176)(141,177)(142,178)(143,179)(144,180)(145,166)(146,167)(147,168)(148,169)(149,170)(150,171)(181,198)(182,199)(183,200)(184,201)(185,202)(186,203)(187,204)(188,205)(189,206)(190,207)(191,208)(192,209)(193,210)(194,196)(195,197), (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), (1,137,17,124)(2,136,18,123)(3,150,19,122)(4,149,20,121)(5,148,21,135)(6,147,22,134)(7,146,23,133)(8,145,24,132)(9,144,25,131)(10,143,26,130)(11,142,27,129)(12,141,28,128)(13,140,29,127)(14,139,30,126)(15,138,16,125)(31,173,50,156)(32,172,51,155)(33,171,52,154)(34,170,53,153)(35,169,54,152)(36,168,55,151)(37,167,56,165)(38,166,57,164)(39,180,58,163)(40,179,59,162)(41,178,60,161)(42,177,46,160)(43,176,47,159)(44,175,48,158)(45,174,49,157)(61,198,76,181)(62,197,77,195)(63,196,78,194)(64,210,79,193)(65,209,80,192)(66,208,81,191)(67,207,82,190)(68,206,83,189)(69,205,84,188)(70,204,85,187)(71,203,86,186)(72,202,87,185)(73,201,88,184)(74,200,89,183)(75,199,90,182)(91,236,110,222)(92,235,111,221)(93,234,112,220)(94,233,113,219)(95,232,114,218)(96,231,115,217)(97,230,116,216)(98,229,117,215)(99,228,118,214)(100,227,119,213)(101,226,120,212)(102,240,106,211)(103,239,107,225)(104,238,108,224)(105,237,109,223)>;
G:=Group( (1,91,31,77,17,110,50,62)(2,92,32,78,18,111,51,63)(3,93,33,79,19,112,52,64)(4,94,34,80,20,113,53,65)(5,95,35,81,21,114,54,66)(6,96,36,82,22,115,55,67)(7,97,37,83,23,116,56,68)(8,98,38,84,24,117,57,69)(9,99,39,85,25,118,58,70)(10,100,40,86,26,119,59,71)(11,101,41,87,27,120,60,72)(12,102,42,88,28,106,46,73)(13,103,43,89,29,107,47,74)(14,104,44,90,30,108,48,75)(15,105,45,76,16,109,49,61)(121,192,170,233,149,209,153,219)(122,193,171,234,150,210,154,220)(123,194,172,235,136,196,155,221)(124,195,173,236,137,197,156,222)(125,181,174,237,138,198,157,223)(126,182,175,238,139,199,158,224)(127,183,176,239,140,200,159,225)(128,184,177,240,141,201,160,211)(129,185,178,226,142,202,161,212)(130,186,179,227,143,203,162,213)(131,187,180,228,144,204,163,214)(132,188,166,229,145,205,164,215)(133,189,167,230,146,206,165,216)(134,190,168,231,147,207,151,217)(135,191,169,232,148,208,152,218), (1,62)(2,63)(3,64)(4,65)(5,66)(6,67)(7,68)(8,69)(9,70)(10,71)(11,72)(12,73)(13,74)(14,75)(15,61)(16,76)(17,77)(18,78)(19,79)(20,80)(21,81)(22,82)(23,83)(24,84)(25,85)(26,86)(27,87)(28,88)(29,89)(30,90)(31,110)(32,111)(33,112)(34,113)(35,114)(36,115)(37,116)(38,117)(39,118)(40,119)(41,120)(42,106)(43,107)(44,108)(45,109)(46,102)(47,103)(48,104)(49,105)(50,91)(51,92)(52,93)(53,94)(54,95)(55,96)(56,97)(57,98)(58,99)(59,100)(60,101)(121,153)(122,154)(123,155)(124,156)(125,157)(126,158)(127,159)(128,160)(129,161)(130,162)(131,163)(132,164)(133,165)(134,151)(135,152)(136,172)(137,173)(138,174)(139,175)(140,176)(141,177)(142,178)(143,179)(144,180)(145,166)(146,167)(147,168)(148,169)(149,170)(150,171)(181,198)(182,199)(183,200)(184,201)(185,202)(186,203)(187,204)(188,205)(189,206)(190,207)(191,208)(192,209)(193,210)(194,196)(195,197), (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), (1,137,17,124)(2,136,18,123)(3,150,19,122)(4,149,20,121)(5,148,21,135)(6,147,22,134)(7,146,23,133)(8,145,24,132)(9,144,25,131)(10,143,26,130)(11,142,27,129)(12,141,28,128)(13,140,29,127)(14,139,30,126)(15,138,16,125)(31,173,50,156)(32,172,51,155)(33,171,52,154)(34,170,53,153)(35,169,54,152)(36,168,55,151)(37,167,56,165)(38,166,57,164)(39,180,58,163)(40,179,59,162)(41,178,60,161)(42,177,46,160)(43,176,47,159)(44,175,48,158)(45,174,49,157)(61,198,76,181)(62,197,77,195)(63,196,78,194)(64,210,79,193)(65,209,80,192)(66,208,81,191)(67,207,82,190)(68,206,83,189)(69,205,84,188)(70,204,85,187)(71,203,86,186)(72,202,87,185)(73,201,88,184)(74,200,89,183)(75,199,90,182)(91,236,110,222)(92,235,111,221)(93,234,112,220)(94,233,113,219)(95,232,114,218)(96,231,115,217)(97,230,116,216)(98,229,117,215)(99,228,118,214)(100,227,119,213)(101,226,120,212)(102,240,106,211)(103,239,107,225)(104,238,108,224)(105,237,109,223) );
G=PermutationGroup([[(1,91,31,77,17,110,50,62),(2,92,32,78,18,111,51,63),(3,93,33,79,19,112,52,64),(4,94,34,80,20,113,53,65),(5,95,35,81,21,114,54,66),(6,96,36,82,22,115,55,67),(7,97,37,83,23,116,56,68),(8,98,38,84,24,117,57,69),(9,99,39,85,25,118,58,70),(10,100,40,86,26,119,59,71),(11,101,41,87,27,120,60,72),(12,102,42,88,28,106,46,73),(13,103,43,89,29,107,47,74),(14,104,44,90,30,108,48,75),(15,105,45,76,16,109,49,61),(121,192,170,233,149,209,153,219),(122,193,171,234,150,210,154,220),(123,194,172,235,136,196,155,221),(124,195,173,236,137,197,156,222),(125,181,174,237,138,198,157,223),(126,182,175,238,139,199,158,224),(127,183,176,239,140,200,159,225),(128,184,177,240,141,201,160,211),(129,185,178,226,142,202,161,212),(130,186,179,227,143,203,162,213),(131,187,180,228,144,204,163,214),(132,188,166,229,145,205,164,215),(133,189,167,230,146,206,165,216),(134,190,168,231,147,207,151,217),(135,191,169,232,148,208,152,218)], [(1,62),(2,63),(3,64),(4,65),(5,66),(6,67),(7,68),(8,69),(9,70),(10,71),(11,72),(12,73),(13,74),(14,75),(15,61),(16,76),(17,77),(18,78),(19,79),(20,80),(21,81),(22,82),(23,83),(24,84),(25,85),(26,86),(27,87),(28,88),(29,89),(30,90),(31,110),(32,111),(33,112),(34,113),(35,114),(36,115),(37,116),(38,117),(39,118),(40,119),(41,120),(42,106),(43,107),(44,108),(45,109),(46,102),(47,103),(48,104),(49,105),(50,91),(51,92),(52,93),(53,94),(54,95),(55,96),(56,97),(57,98),(58,99),(59,100),(60,101),(121,153),(122,154),(123,155),(124,156),(125,157),(126,158),(127,159),(128,160),(129,161),(130,162),(131,163),(132,164),(133,165),(134,151),(135,152),(136,172),(137,173),(138,174),(139,175),(140,176),(141,177),(142,178),(143,179),(144,180),(145,166),(146,167),(147,168),(148,169),(149,170),(150,171),(181,198),(182,199),(183,200),(184,201),(185,202),(186,203),(187,204),(188,205),(189,206),(190,207),(191,208),(192,209),(193,210),(194,196),(195,197)], [(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)], [(1,137,17,124),(2,136,18,123),(3,150,19,122),(4,149,20,121),(5,148,21,135),(6,147,22,134),(7,146,23,133),(8,145,24,132),(9,144,25,131),(10,143,26,130),(11,142,27,129),(12,141,28,128),(13,140,29,127),(14,139,30,126),(15,138,16,125),(31,173,50,156),(32,172,51,155),(33,171,52,154),(34,170,53,153),(35,169,54,152),(36,168,55,151),(37,167,56,165),(38,166,57,164),(39,180,58,163),(40,179,59,162),(41,178,60,161),(42,177,46,160),(43,176,47,159),(44,175,48,158),(45,174,49,157),(61,198,76,181),(62,197,77,195),(63,196,78,194),(64,210,79,193),(65,209,80,192),(66,208,81,191),(67,207,82,190),(68,206,83,189),(69,205,84,188),(70,204,85,187),(71,203,86,186),(72,202,87,185),(73,201,88,184),(74,200,89,183),(75,199,90,182),(91,236,110,222),(92,235,111,221),(93,234,112,220),(94,233,113,219),(95,232,114,218),(96,231,115,217),(97,230,116,216),(98,229,117,215),(99,228,118,214),(100,227,119,213),(101,226,120,212),(102,240,106,211),(103,239,107,225),(104,238,108,224),(105,237,109,223)]])
60 conjugacy classes
| class | 1 | 2A | 2B | 3 | 4A | 4B | 5A | 5B | 6A | 6B | 6C | 8A | 8B | 10A | 10B | 10C | 10D | 10E | 10F | 12 | 15A | 15B | 15C | 15D | 16A | 16B | 16C | 16D | 20A | 20B | 24A | 24B | 30A | 30B | 30C | 30D | 30E | ··· | 30L | 40A | 40B | 40C | 40D | 60A | 60B | 60C | 60D | 120A | ··· | 120H |
| order | 1 | 2 | 2 | 3 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 8 | 8 | 10 | 10 | 10 | 10 | 10 | 10 | 12 | 15 | 15 | 15 | 15 | 16 | 16 | 16 | 16 | 20 | 20 | 24 | 24 | 30 | 30 | 30 | 30 | 30 | ··· | 30 | 40 | 40 | 40 | 40 | 60 | 60 | 60 | 60 | 120 | ··· | 120 |
| size | 1 | 1 | 8 | 2 | 2 | 120 | 2 | 2 | 2 | 8 | 8 | 2 | 2 | 2 | 2 | 8 | 8 | 8 | 8 | 4 | 2 | 2 | 2 | 2 | 30 | 30 | 30 | 30 | 4 | 4 | 4 | 4 | 2 | 2 | 2 | 2 | 8 | ··· | 8 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 |
60 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 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 | C3⋊D4 | D15 | SD32 | C5⋊D4 | D30 | C15⋊7D4 | D4⋊S3 | D4⋊D5 | D8.S3 | D8.D5 | D4⋊D15 | D8.D15 |
| kernel | D8.D15 | C15⋊3C16 | Dic60 | C15×D8 | C5×D8 | C60 | C3×D8 | C40 | C30 | C24 | C20 | D8 | C15 | C12 | C8 | C4 | C10 | C6 | C5 | C3 | C2 | C1 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 8 | 1 | 2 | 2 | 4 | 4 | 8 |
Matrix representation of D8.D15 ►in GL4(𝔽241) generated by
| 240 | 0 | 0 | 0 |
| 0 | 240 | 0 | 0 |
| 0 | 0 | 0 | 168 |
| 0 | 0 | 208 | 22 |
| 240 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 168 |
| 0 | 0 | 33 | 0 |
| 100 | 0 | 0 | 0 |
| 0 | 94 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 94 | 0 | 0 |
| 100 | 0 | 0 | 0 |
| 0 | 0 | 62 | 92 |
| 0 | 0 | 118 | 179 |
G:=sub<GL(4,GF(241))| [240,0,0,0,0,240,0,0,0,0,0,208,0,0,168,22],[240,0,0,0,0,1,0,0,0,0,0,33,0,0,168,0],[100,0,0,0,0,94,0,0,0,0,1,0,0,0,0,1],[0,100,0,0,94,0,0,0,0,0,62,118,0,0,92,179] >;
D8.D15 in GAP, Magma, Sage, TeX
D_8.D_{15} % in TeX
G:=Group("D8.D15"); // GroupNames label
G:=SmallGroup(480,187);
// by ID
G=gap.SmallGroup(480,187);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,112,85,254,135,142,675,346,80,2693,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^8=b^2=c^15=1,d^2=a^4,b*a*b=d*a*d^-1=a^-1,a*c=c*a,b*c=c*b,d*b*d^-1=a^5*b,d*c*d^-1=c^-1>;
// generators/relations
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