metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D8⋊3D15, C8.8D30, D4.1D30, C40.22D6, Dic60⋊7C2, D30.17D4, C24.22D10, C60.66C23, C120.13C22, Dic15.49D4, Dic30.22C22, (C5×D8)⋊3S3, (C3×D8)⋊3D5, (C8×D15)⋊2C2, (C15×D8)⋊3C2, C15⋊28(C4○D8), C5⋊4(D8⋊3S3), C3⋊4(D8⋊3D5), (C5×D4).13D6, C2.17(D4×D15), C6.110(D4×D5), D4⋊2D15⋊9C2, D4.D15⋊10C2, (C3×D4).13D10, C10.112(S3×D4), C30.317(C2×D4), C4.3(C22×D15), C20.104(C22×S3), C15⋊3C8.31C22, (C4×D15).43C22, (D4×C15).20C22, C12.104(C22×D5), SmallGroup(480,877)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D8⋊3D15
G = < a,b,c,d | a8=b2=c15=d2=1, bab=a-1, ac=ca, ad=da, bc=cb, dbd=a4b, dcd=c-1 >
Subgroups: 724 in 124 conjugacy classes, 41 normal (27 characteristic)
C1, C2, C2, C3, C4, C4, C22, C5, S3, C6, C6, C8, C8, C2×C4, D4, D4, Q8, D5, C10, C10, Dic3, C12, D6, C2×C6, C15, C2×C8, D8, SD16, Q16, C4○D4, Dic5, C20, D10, C2×C10, C3⋊C8, C24, Dic6, C4×S3, C2×Dic3, C3⋊D4, C3×D4, D15, C30, C30, C4○D8, C5⋊2C8, C40, Dic10, C4×D5, C2×Dic5, C5⋊D4, C5×D4, S3×C8, Dic12, D4.S3, C3×D8, D4⋊2S3, Dic15, Dic15, C60, D30, C2×C30, C8×D5, Dic20, D4.D5, C5×D8, D4⋊2D5, D8⋊3S3, C15⋊3C8, C120, Dic30, C4×D15, C2×Dic15, C15⋊7D4, D4×C15, D8⋊3D5, C8×D15, Dic60, D4.D15, C15×D8, D4⋊2D15, D8⋊3D15
Quotients: C1, C2, C22, S3, D4, C23, D5, D6, C2×D4, D10, C22×S3, D15, C4○D8, C22×D5, S3×D4, D30, D4×D5, D8⋊3S3, C22×D15, D8⋊3D5, D4×D15, D8⋊3D15
►On 240 points
Generators in S240
(1 219 31 208 17 230 50 182)(2 220 32 209 18 231 51 183)(3 221 33 210 19 232 52 184)(4 222 34 196 20 233 53 185)(5 223 35 197 21 234 54 186)(6 224 36 198 22 235 55 187)(7 225 37 199 23 236 56 188)(8 211 38 200 24 237 57 189)(9 212 39 201 25 238 58 190)(10 213 40 202 26 239 59 191)(11 214 41 203 27 240 60 192)(12 215 42 204 28 226 46 193)(13 216 43 205 29 227 47 194)(14 217 44 206 30 228 48 195)(15 218 45 207 16 229 49 181)(61 170 113 143 76 155 91 128)(62 171 114 144 77 156 92 129)(63 172 115 145 78 157 93 130)(64 173 116 146 79 158 94 131)(65 174 117 147 80 159 95 132)(66 175 118 148 81 160 96 133)(67 176 119 149 82 161 97 134)(68 177 120 150 83 162 98 135)(69 178 106 136 84 163 99 121)(70 179 107 137 85 164 100 122)(71 180 108 138 86 165 101 123)(72 166 109 139 87 151 102 124)(73 167 110 140 88 152 103 125)(74 168 111 141 89 153 104 126)(75 169 112 142 90 154 105 127)
(1 121)(2 122)(3 123)(4 124)(5 125)(6 126)(7 127)(8 128)(9 129)(10 130)(11 131)(12 132)(13 133)(14 134)(15 135)(16 150)(17 136)(18 137)(19 138)(20 139)(21 140)(22 141)(23 142)(24 143)(25 144)(26 145)(27 146)(28 147)(29 148)(30 149)(31 163)(32 164)(33 165)(34 151)(35 152)(36 153)(37 154)(38 155)(39 156)(40 157)(41 158)(42 159)(43 160)(44 161)(45 162)(46 174)(47 175)(48 176)(49 177)(50 178)(51 179)(52 180)(53 166)(54 167)(55 168)(56 169)(57 170)(58 171)(59 172)(60 173)(61 189)(62 190)(63 191)(64 192)(65 193)(66 194)(67 195)(68 181)(69 182)(70 183)(71 184)(72 185)(73 186)(74 187)(75 188)(76 200)(77 201)(78 202)(79 203)(80 204)(81 205)(82 206)(83 207)(84 208)(85 209)(86 210)(87 196)(88 197)(89 198)(90 199)(91 211)(92 212)(93 213)(94 214)(95 215)(96 216)(97 217)(98 218)(99 219)(100 220)(101 221)(102 222)(103 223)(104 224)(105 225)(106 230)(107 231)(108 232)(109 233)(110 234)(111 235)(112 236)(113 237)(114 238)(115 239)(116 240)(117 226)(118 227)(119 228)(120 229)
(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 15)(2 14)(3 13)(4 12)(5 11)(6 10)(7 9)(16 17)(18 30)(19 29)(20 28)(21 27)(22 26)(23 25)(31 45)(32 44)(33 43)(34 42)(35 41)(36 40)(37 39)(46 53)(47 52)(48 51)(49 50)(54 60)(55 59)(56 58)(61 76)(62 90)(63 89)(64 88)(65 87)(66 86)(67 85)(68 84)(69 83)(70 82)(71 81)(72 80)(73 79)(74 78)(75 77)(91 113)(92 112)(93 111)(94 110)(95 109)(96 108)(97 107)(98 106)(99 120)(100 119)(101 118)(102 117)(103 116)(104 115)(105 114)(121 150)(122 149)(123 148)(124 147)(125 146)(126 145)(127 144)(128 143)(129 142)(130 141)(131 140)(132 139)(133 138)(134 137)(135 136)(151 174)(152 173)(153 172)(154 171)(155 170)(156 169)(157 168)(158 167)(159 166)(160 180)(161 179)(162 178)(163 177)(164 176)(165 175)(181 182)(183 195)(184 194)(185 193)(186 192)(187 191)(188 190)(196 204)(197 203)(198 202)(199 201)(205 210)(206 209)(207 208)(212 225)(213 224)(214 223)(215 222)(216 221)(217 220)(218 219)(226 233)(227 232)(228 231)(229 230)(234 240)(235 239)(236 238)
G:=sub<Sym(240)| (1,219,31,208,17,230,50,182)(2,220,32,209,18,231,51,183)(3,221,33,210,19,232,52,184)(4,222,34,196,20,233,53,185)(5,223,35,197,21,234,54,186)(6,224,36,198,22,235,55,187)(7,225,37,199,23,236,56,188)(8,211,38,200,24,237,57,189)(9,212,39,201,25,238,58,190)(10,213,40,202,26,239,59,191)(11,214,41,203,27,240,60,192)(12,215,42,204,28,226,46,193)(13,216,43,205,29,227,47,194)(14,217,44,206,30,228,48,195)(15,218,45,207,16,229,49,181)(61,170,113,143,76,155,91,128)(62,171,114,144,77,156,92,129)(63,172,115,145,78,157,93,130)(64,173,116,146,79,158,94,131)(65,174,117,147,80,159,95,132)(66,175,118,148,81,160,96,133)(67,176,119,149,82,161,97,134)(68,177,120,150,83,162,98,135)(69,178,106,136,84,163,99,121)(70,179,107,137,85,164,100,122)(71,180,108,138,86,165,101,123)(72,166,109,139,87,151,102,124)(73,167,110,140,88,152,103,125)(74,168,111,141,89,153,104,126)(75,169,112,142,90,154,105,127), (1,121)(2,122)(3,123)(4,124)(5,125)(6,126)(7,127)(8,128)(9,129)(10,130)(11,131)(12,132)(13,133)(14,134)(15,135)(16,150)(17,136)(18,137)(19,138)(20,139)(21,140)(22,141)(23,142)(24,143)(25,144)(26,145)(27,146)(28,147)(29,148)(30,149)(31,163)(32,164)(33,165)(34,151)(35,152)(36,153)(37,154)(38,155)(39,156)(40,157)(41,158)(42,159)(43,160)(44,161)(45,162)(46,174)(47,175)(48,176)(49,177)(50,178)(51,179)(52,180)(53,166)(54,167)(55,168)(56,169)(57,170)(58,171)(59,172)(60,173)(61,189)(62,190)(63,191)(64,192)(65,193)(66,194)(67,195)(68,181)(69,182)(70,183)(71,184)(72,185)(73,186)(74,187)(75,188)(76,200)(77,201)(78,202)(79,203)(80,204)(81,205)(82,206)(83,207)(84,208)(85,209)(86,210)(87,196)(88,197)(89,198)(90,199)(91,211)(92,212)(93,213)(94,214)(95,215)(96,216)(97,217)(98,218)(99,219)(100,220)(101,221)(102,222)(103,223)(104,224)(105,225)(106,230)(107,231)(108,232)(109,233)(110,234)(111,235)(112,236)(113,237)(114,238)(115,239)(116,240)(117,226)(118,227)(119,228)(120,229), (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), (1,15)(2,14)(3,13)(4,12)(5,11)(6,10)(7,9)(16,17)(18,30)(19,29)(20,28)(21,27)(22,26)(23,25)(31,45)(32,44)(33,43)(34,42)(35,41)(36,40)(37,39)(46,53)(47,52)(48,51)(49,50)(54,60)(55,59)(56,58)(61,76)(62,90)(63,89)(64,88)(65,87)(66,86)(67,85)(68,84)(69,83)(70,82)(71,81)(72,80)(73,79)(74,78)(75,77)(91,113)(92,112)(93,111)(94,110)(95,109)(96,108)(97,107)(98,106)(99,120)(100,119)(101,118)(102,117)(103,116)(104,115)(105,114)(121,150)(122,149)(123,148)(124,147)(125,146)(126,145)(127,144)(128,143)(129,142)(130,141)(131,140)(132,139)(133,138)(134,137)(135,136)(151,174)(152,173)(153,172)(154,171)(155,170)(156,169)(157,168)(158,167)(159,166)(160,180)(161,179)(162,178)(163,177)(164,176)(165,175)(181,182)(183,195)(184,194)(185,193)(186,192)(187,191)(188,190)(196,204)(197,203)(198,202)(199,201)(205,210)(206,209)(207,208)(212,225)(213,224)(214,223)(215,222)(216,221)(217,220)(218,219)(226,233)(227,232)(228,231)(229,230)(234,240)(235,239)(236,238)>;
G:=Group( (1,219,31,208,17,230,50,182)(2,220,32,209,18,231,51,183)(3,221,33,210,19,232,52,184)(4,222,34,196,20,233,53,185)(5,223,35,197,21,234,54,186)(6,224,36,198,22,235,55,187)(7,225,37,199,23,236,56,188)(8,211,38,200,24,237,57,189)(9,212,39,201,25,238,58,190)(10,213,40,202,26,239,59,191)(11,214,41,203,27,240,60,192)(12,215,42,204,28,226,46,193)(13,216,43,205,29,227,47,194)(14,217,44,206,30,228,48,195)(15,218,45,207,16,229,49,181)(61,170,113,143,76,155,91,128)(62,171,114,144,77,156,92,129)(63,172,115,145,78,157,93,130)(64,173,116,146,79,158,94,131)(65,174,117,147,80,159,95,132)(66,175,118,148,81,160,96,133)(67,176,119,149,82,161,97,134)(68,177,120,150,83,162,98,135)(69,178,106,136,84,163,99,121)(70,179,107,137,85,164,100,122)(71,180,108,138,86,165,101,123)(72,166,109,139,87,151,102,124)(73,167,110,140,88,152,103,125)(74,168,111,141,89,153,104,126)(75,169,112,142,90,154,105,127), (1,121)(2,122)(3,123)(4,124)(5,125)(6,126)(7,127)(8,128)(9,129)(10,130)(11,131)(12,132)(13,133)(14,134)(15,135)(16,150)(17,136)(18,137)(19,138)(20,139)(21,140)(22,141)(23,142)(24,143)(25,144)(26,145)(27,146)(28,147)(29,148)(30,149)(31,163)(32,164)(33,165)(34,151)(35,152)(36,153)(37,154)(38,155)(39,156)(40,157)(41,158)(42,159)(43,160)(44,161)(45,162)(46,174)(47,175)(48,176)(49,177)(50,178)(51,179)(52,180)(53,166)(54,167)(55,168)(56,169)(57,170)(58,171)(59,172)(60,173)(61,189)(62,190)(63,191)(64,192)(65,193)(66,194)(67,195)(68,181)(69,182)(70,183)(71,184)(72,185)(73,186)(74,187)(75,188)(76,200)(77,201)(78,202)(79,203)(80,204)(81,205)(82,206)(83,207)(84,208)(85,209)(86,210)(87,196)(88,197)(89,198)(90,199)(91,211)(92,212)(93,213)(94,214)(95,215)(96,216)(97,217)(98,218)(99,219)(100,220)(101,221)(102,222)(103,223)(104,224)(105,225)(106,230)(107,231)(108,232)(109,233)(110,234)(111,235)(112,236)(113,237)(114,238)(115,239)(116,240)(117,226)(118,227)(119,228)(120,229), (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), (1,15)(2,14)(3,13)(4,12)(5,11)(6,10)(7,9)(16,17)(18,30)(19,29)(20,28)(21,27)(22,26)(23,25)(31,45)(32,44)(33,43)(34,42)(35,41)(36,40)(37,39)(46,53)(47,52)(48,51)(49,50)(54,60)(55,59)(56,58)(61,76)(62,90)(63,89)(64,88)(65,87)(66,86)(67,85)(68,84)(69,83)(70,82)(71,81)(72,80)(73,79)(74,78)(75,77)(91,113)(92,112)(93,111)(94,110)(95,109)(96,108)(97,107)(98,106)(99,120)(100,119)(101,118)(102,117)(103,116)(104,115)(105,114)(121,150)(122,149)(123,148)(124,147)(125,146)(126,145)(127,144)(128,143)(129,142)(130,141)(131,140)(132,139)(133,138)(134,137)(135,136)(151,174)(152,173)(153,172)(154,171)(155,170)(156,169)(157,168)(158,167)(159,166)(160,180)(161,179)(162,178)(163,177)(164,176)(165,175)(181,182)(183,195)(184,194)(185,193)(186,192)(187,191)(188,190)(196,204)(197,203)(198,202)(199,201)(205,210)(206,209)(207,208)(212,225)(213,224)(214,223)(215,222)(216,221)(217,220)(218,219)(226,233)(227,232)(228,231)(229,230)(234,240)(235,239)(236,238) );
G=PermutationGroup([[(1,219,31,208,17,230,50,182),(2,220,32,209,18,231,51,183),(3,221,33,210,19,232,52,184),(4,222,34,196,20,233,53,185),(5,223,35,197,21,234,54,186),(6,224,36,198,22,235,55,187),(7,225,37,199,23,236,56,188),(8,211,38,200,24,237,57,189),(9,212,39,201,25,238,58,190),(10,213,40,202,26,239,59,191),(11,214,41,203,27,240,60,192),(12,215,42,204,28,226,46,193),(13,216,43,205,29,227,47,194),(14,217,44,206,30,228,48,195),(15,218,45,207,16,229,49,181),(61,170,113,143,76,155,91,128),(62,171,114,144,77,156,92,129),(63,172,115,145,78,157,93,130),(64,173,116,146,79,158,94,131),(65,174,117,147,80,159,95,132),(66,175,118,148,81,160,96,133),(67,176,119,149,82,161,97,134),(68,177,120,150,83,162,98,135),(69,178,106,136,84,163,99,121),(70,179,107,137,85,164,100,122),(71,180,108,138,86,165,101,123),(72,166,109,139,87,151,102,124),(73,167,110,140,88,152,103,125),(74,168,111,141,89,153,104,126),(75,169,112,142,90,154,105,127)], [(1,121),(2,122),(3,123),(4,124),(5,125),(6,126),(7,127),(8,128),(9,129),(10,130),(11,131),(12,132),(13,133),(14,134),(15,135),(16,150),(17,136),(18,137),(19,138),(20,139),(21,140),(22,141),(23,142),(24,143),(25,144),(26,145),(27,146),(28,147),(29,148),(30,149),(31,163),(32,164),(33,165),(34,151),(35,152),(36,153),(37,154),(38,155),(39,156),(40,157),(41,158),(42,159),(43,160),(44,161),(45,162),(46,174),(47,175),(48,176),(49,177),(50,178),(51,179),(52,180),(53,166),(54,167),(55,168),(56,169),(57,170),(58,171),(59,172),(60,173),(61,189),(62,190),(63,191),(64,192),(65,193),(66,194),(67,195),(68,181),(69,182),(70,183),(71,184),(72,185),(73,186),(74,187),(75,188),(76,200),(77,201),(78,202),(79,203),(80,204),(81,205),(82,206),(83,207),(84,208),(85,209),(86,210),(87,196),(88,197),(89,198),(90,199),(91,211),(92,212),(93,213),(94,214),(95,215),(96,216),(97,217),(98,218),(99,219),(100,220),(101,221),(102,222),(103,223),(104,224),(105,225),(106,230),(107,231),(108,232),(109,233),(110,234),(111,235),(112,236),(113,237),(114,238),(115,239),(116,240),(117,226),(118,227),(119,228),(120,229)], [(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)], [(1,15),(2,14),(3,13),(4,12),(5,11),(6,10),(7,9),(16,17),(18,30),(19,29),(20,28),(21,27),(22,26),(23,25),(31,45),(32,44),(33,43),(34,42),(35,41),(36,40),(37,39),(46,53),(47,52),(48,51),(49,50),(54,60),(55,59),(56,58),(61,76),(62,90),(63,89),(64,88),(65,87),(66,86),(67,85),(68,84),(69,83),(70,82),(71,81),(72,80),(73,79),(74,78),(75,77),(91,113),(92,112),(93,111),(94,110),(95,109),(96,108),(97,107),(98,106),(99,120),(100,119),(101,118),(102,117),(103,116),(104,115),(105,114),(121,150),(122,149),(123,148),(124,147),(125,146),(126,145),(127,144),(128,143),(129,142),(130,141),(131,140),(132,139),(133,138),(134,137),(135,136),(151,174),(152,173),(153,172),(154,171),(155,170),(156,169),(157,168),(158,167),(159,166),(160,180),(161,179),(162,178),(163,177),(164,176),(165,175),(181,182),(183,195),(184,194),(185,193),(186,192),(187,191),(188,190),(196,204),(197,203),(198,202),(199,201),(205,210),(206,209),(207,208),(212,225),(213,224),(214,223),(215,222),(216,221),(217,220),(218,219),(226,233),(227,232),(228,231),(229,230),(234,240),(235,239),(236,238)]])
63 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 3 | 4A | 4B | 4C | 4D | 4E | 5A | 5B | 6A | 6B | 6C | 8A | 8B | 8C | 8D | 10A | 10B | 10C | 10D | 10E | 10F | 12 | 15A | 15B | 15C | 15D | 20A | 20B | 24A | 24B | 30A | 30B | 30C | 30D | 30E | ··· | 30L | 40A | 40B | 40C | 40D | 60A | 60B | 60C | 60D | 120A | ··· | 120H |
| order | 1 | 2 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 8 | 8 | 8 | 8 | 10 | 10 | 10 | 10 | 10 | 10 | 12 | 15 | 15 | 15 | 15 | 20 | 20 | 24 | 24 | 30 | 30 | 30 | 30 | 30 | ··· | 30 | 40 | 40 | 40 | 40 | 60 | 60 | 60 | 60 | 120 | ··· | 120 |
| size | 1 | 1 | 4 | 4 | 30 | 2 | 2 | 15 | 15 | 60 | 60 | 2 | 2 | 2 | 8 | 8 | 2 | 2 | 30 | 30 | 2 | 2 | 8 | 8 | 8 | 8 | 4 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 2 | 2 | 2 | 2 | 8 | ··· | 8 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 |
63 irreducible representations
| dim | 1 | 1 | 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 | C2 | C2 | S3 | D4 | D4 | D5 | D6 | D6 | D10 | D10 | D15 | C4○D8 | D30 | D30 | S3×D4 | D4×D5 | D8⋊3S3 | D8⋊3D5 | D4×D15 | D8⋊3D15 |
| kernel | D8⋊3D15 | C8×D15 | Dic60 | D4.D15 | C15×D8 | D4⋊2D15 | C5×D8 | Dic15 | D30 | C3×D8 | C40 | C5×D4 | C24 | C3×D4 | D8 | C15 | C8 | D4 | C10 | C6 | C5 | C3 | C2 | C1 |
| # reps | 1 | 1 | 1 | 2 | 1 | 2 | 1 | 1 | 1 | 2 | 1 | 2 | 2 | 4 | 4 | 4 | 4 | 8 | 1 | 2 | 2 | 4 | 4 | 8 |
Matrix representation of D8⋊3D15 ►in GL4(𝔽241) generated by
| 240 | 0 | 0 | 0 |
| 0 | 240 | 0 | 0 |
| 0 | 0 | 211 | 0 |
| 0 | 0 | 0 | 8 |
| 240 | 0 | 0 | 0 |
| 0 | 240 | 0 | 0 |
| 0 | 0 | 0 | 8 |
| 0 | 0 | 211 | 0 |
| 94 | 110 | 0 | 0 |
| 131 | 161 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 94 | 110 | 0 | 0 |
| 84 | 147 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 240 |
G:=sub<GL(4,GF(241))| [240,0,0,0,0,240,0,0,0,0,211,0,0,0,0,8],[240,0,0,0,0,240,0,0,0,0,0,211,0,0,8,0],[94,131,0,0,110,161,0,0,0,0,1,0,0,0,0,1],[94,84,0,0,110,147,0,0,0,0,1,0,0,0,0,240] >;
D8⋊3D15 in GAP, Magma, Sage, TeX
D_8\rtimes_3D_{15} % in TeX
G:=Group("D8:3D15"); // GroupNames label
G:=SmallGroup(480,877);
// by ID
G=gap.SmallGroup(480,877);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,253,422,135,346,185,80,2693,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^8=b^2=c^15=d^2=1,b*a*b=a^-1,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d=a^4*b,d*c*d=c^-1>;
// generators/relations