direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C15×C8○D4, D4.C60, Q8.2C60, M4(2)⋊5C30, C60.302C23, C120.113C22, (C2×C8)⋊7C30, (C2×C40)⋊15C6, C8.7(C2×C30), C4.5(C2×C60), (C2×C24)⋊15C10, (C2×C120)⋊31C2, C40.29(C2×C6), C4○D4.5C30, (D4×C15).6C4, (C5×D4).3C12, (C3×D4).2C20, (C3×Q8).2C20, (Q8×C15).6C4, (C5×Q8).6C12, C24.29(C2×C10), C60.229(C2×C4), C20.54(C2×C12), C12.33(C2×C20), C22.1(C2×C60), C2.7(C22×C60), (C5×M4(2))⋊11C6, C6.35(C22×C20), C4.12(C22×C30), C20.55(C22×C6), (C3×M4(2))⋊11C10, (C15×M4(2))⋊23C2, (C2×C60).581C22, C10.48(C22×C12), C30.242(C22×C4), C12.54(C22×C10), (C2×C6).8(C2×C20), (C2×C4).25(C2×C30), (C5×C4○D4).10C6, (C3×C4○D4).6C10, (C2×C20).127(C2×C6), (C2×C30).132(C2×C4), (C2×C10).28(C2×C12), (C15×C4○D4).12C2, (C2×C12).128(C2×C10), SmallGroup(480,936)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C15×C8○D4
G = < a,b,c,d | a15=b8=d2=1, c2=b4, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd=b4c >
Subgroups: 136 in 124 conjugacy classes, 112 normal (28 characteristic)
C1, C2, C2, C3, C4, C4, C22, C5, C6, C6, C8, C8, C2×C4, D4, Q8, C10, C10, C12, C12, C2×C6, C15, C2×C8, M4(2), C4○D4, C20, C20, C2×C10, C24, C24, C2×C12, C3×D4, C3×Q8, C30, C30, C8○D4, C40, C40, C2×C20, C5×D4, C5×Q8, C2×C24, C3×M4(2), C3×C4○D4, C60, C60, C2×C30, C2×C40, C5×M4(2), C5×C4○D4, C3×C8○D4, C120, C120, C2×C60, D4×C15, Q8×C15, C5×C8○D4, C2×C120, C15×M4(2), C15×C4○D4, C15×C8○D4
Quotients: C1, C2, C3, C4, C22, C5, C6, C2×C4, C23, C10, C12, C2×C6, C15, C22×C4, C20, C2×C10, C2×C12, C22×C6, C30, C8○D4, C2×C20, C22×C10, C22×C12, C60, C2×C30, C22×C20, C3×C8○D4, C2×C60, C22×C30, C5×C8○D4, C22×C60, C15×C8○D4
►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)
(1 171 191 111 238 210 80 162)(2 172 192 112 239 196 81 163)(3 173 193 113 240 197 82 164)(4 174 194 114 226 198 83 165)(5 175 195 115 227 199 84 151)(6 176 181 116 228 200 85 152)(7 177 182 117 229 201 86 153)(8 178 183 118 230 202 87 154)(9 179 184 119 231 203 88 155)(10 180 185 120 232 204 89 156)(11 166 186 106 233 205 90 157)(12 167 187 107 234 206 76 158)(13 168 188 108 235 207 77 159)(14 169 189 109 236 208 78 160)(15 170 190 110 237 209 79 161)(16 96 127 140 214 48 65 31)(17 97 128 141 215 49 66 32)(18 98 129 142 216 50 67 33)(19 99 130 143 217 51 68 34)(20 100 131 144 218 52 69 35)(21 101 132 145 219 53 70 36)(22 102 133 146 220 54 71 37)(23 103 134 147 221 55 72 38)(24 104 135 148 222 56 73 39)(25 105 121 149 223 57 74 40)(26 91 122 150 224 58 75 41)(27 92 123 136 225 59 61 42)(28 93 124 137 211 60 62 43)(29 94 125 138 212 46 63 44)(30 95 126 139 213 47 64 45)
(1 139 238 45)(2 140 239 31)(3 141 240 32)(4 142 226 33)(5 143 227 34)(6 144 228 35)(7 145 229 36)(8 146 230 37)(9 147 231 38)(10 148 232 39)(11 149 233 40)(12 150 234 41)(13 136 235 42)(14 137 236 43)(15 138 237 44)(16 172 214 196)(17 173 215 197)(18 174 216 198)(19 175 217 199)(20 176 218 200)(21 177 219 201)(22 178 220 202)(23 179 221 203)(24 180 222 204)(25 166 223 205)(26 167 224 206)(27 168 225 207)(28 169 211 208)(29 170 212 209)(30 171 213 210)(46 79 94 190)(47 80 95 191)(48 81 96 192)(49 82 97 193)(50 83 98 194)(51 84 99 195)(52 85 100 181)(53 86 101 182)(54 87 102 183)(55 88 103 184)(56 89 104 185)(57 90 105 186)(58 76 91 187)(59 77 92 188)(60 78 93 189)(61 159 123 108)(62 160 124 109)(63 161 125 110)(64 162 126 111)(65 163 127 112)(66 164 128 113)(67 165 129 114)(68 151 130 115)(69 152 131 116)(70 153 132 117)(71 154 133 118)(72 155 134 119)(73 156 135 120)(74 157 121 106)(75 158 122 107)
(16 214)(17 215)(18 216)(19 217)(20 218)(21 219)(22 220)(23 221)(24 222)(25 223)(26 224)(27 225)(28 211)(29 212)(30 213)(31 140)(32 141)(33 142)(34 143)(35 144)(36 145)(37 146)(38 147)(39 148)(40 149)(41 150)(42 136)(43 137)(44 138)(45 139)(46 94)(47 95)(48 96)(49 97)(50 98)(51 99)(52 100)(53 101)(54 102)(55 103)(56 104)(57 105)(58 91)(59 92)(60 93)(61 123)(62 124)(63 125)(64 126)(65 127)(66 128)(67 129)(68 130)(69 131)(70 132)(71 133)(72 134)(73 135)(74 121)(75 122)
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), (1,171,191,111,238,210,80,162)(2,172,192,112,239,196,81,163)(3,173,193,113,240,197,82,164)(4,174,194,114,226,198,83,165)(5,175,195,115,227,199,84,151)(6,176,181,116,228,200,85,152)(7,177,182,117,229,201,86,153)(8,178,183,118,230,202,87,154)(9,179,184,119,231,203,88,155)(10,180,185,120,232,204,89,156)(11,166,186,106,233,205,90,157)(12,167,187,107,234,206,76,158)(13,168,188,108,235,207,77,159)(14,169,189,109,236,208,78,160)(15,170,190,110,237,209,79,161)(16,96,127,140,214,48,65,31)(17,97,128,141,215,49,66,32)(18,98,129,142,216,50,67,33)(19,99,130,143,217,51,68,34)(20,100,131,144,218,52,69,35)(21,101,132,145,219,53,70,36)(22,102,133,146,220,54,71,37)(23,103,134,147,221,55,72,38)(24,104,135,148,222,56,73,39)(25,105,121,149,223,57,74,40)(26,91,122,150,224,58,75,41)(27,92,123,136,225,59,61,42)(28,93,124,137,211,60,62,43)(29,94,125,138,212,46,63,44)(30,95,126,139,213,47,64,45), (1,139,238,45)(2,140,239,31)(3,141,240,32)(4,142,226,33)(5,143,227,34)(6,144,228,35)(7,145,229,36)(8,146,230,37)(9,147,231,38)(10,148,232,39)(11,149,233,40)(12,150,234,41)(13,136,235,42)(14,137,236,43)(15,138,237,44)(16,172,214,196)(17,173,215,197)(18,174,216,198)(19,175,217,199)(20,176,218,200)(21,177,219,201)(22,178,220,202)(23,179,221,203)(24,180,222,204)(25,166,223,205)(26,167,224,206)(27,168,225,207)(28,169,211,208)(29,170,212,209)(30,171,213,210)(46,79,94,190)(47,80,95,191)(48,81,96,192)(49,82,97,193)(50,83,98,194)(51,84,99,195)(52,85,100,181)(53,86,101,182)(54,87,102,183)(55,88,103,184)(56,89,104,185)(57,90,105,186)(58,76,91,187)(59,77,92,188)(60,78,93,189)(61,159,123,108)(62,160,124,109)(63,161,125,110)(64,162,126,111)(65,163,127,112)(66,164,128,113)(67,165,129,114)(68,151,130,115)(69,152,131,116)(70,153,132,117)(71,154,133,118)(72,155,134,119)(73,156,135,120)(74,157,121,106)(75,158,122,107), (16,214)(17,215)(18,216)(19,217)(20,218)(21,219)(22,220)(23,221)(24,222)(25,223)(26,224)(27,225)(28,211)(29,212)(30,213)(31,140)(32,141)(33,142)(34,143)(35,144)(36,145)(37,146)(38,147)(39,148)(40,149)(41,150)(42,136)(43,137)(44,138)(45,139)(46,94)(47,95)(48,96)(49,97)(50,98)(51,99)(52,100)(53,101)(54,102)(55,103)(56,104)(57,105)(58,91)(59,92)(60,93)(61,123)(62,124)(63,125)(64,126)(65,127)(66,128)(67,129)(68,130)(69,131)(70,132)(71,133)(72,134)(73,135)(74,121)(75,122)>;
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), (1,171,191,111,238,210,80,162)(2,172,192,112,239,196,81,163)(3,173,193,113,240,197,82,164)(4,174,194,114,226,198,83,165)(5,175,195,115,227,199,84,151)(6,176,181,116,228,200,85,152)(7,177,182,117,229,201,86,153)(8,178,183,118,230,202,87,154)(9,179,184,119,231,203,88,155)(10,180,185,120,232,204,89,156)(11,166,186,106,233,205,90,157)(12,167,187,107,234,206,76,158)(13,168,188,108,235,207,77,159)(14,169,189,109,236,208,78,160)(15,170,190,110,237,209,79,161)(16,96,127,140,214,48,65,31)(17,97,128,141,215,49,66,32)(18,98,129,142,216,50,67,33)(19,99,130,143,217,51,68,34)(20,100,131,144,218,52,69,35)(21,101,132,145,219,53,70,36)(22,102,133,146,220,54,71,37)(23,103,134,147,221,55,72,38)(24,104,135,148,222,56,73,39)(25,105,121,149,223,57,74,40)(26,91,122,150,224,58,75,41)(27,92,123,136,225,59,61,42)(28,93,124,137,211,60,62,43)(29,94,125,138,212,46,63,44)(30,95,126,139,213,47,64,45), (1,139,238,45)(2,140,239,31)(3,141,240,32)(4,142,226,33)(5,143,227,34)(6,144,228,35)(7,145,229,36)(8,146,230,37)(9,147,231,38)(10,148,232,39)(11,149,233,40)(12,150,234,41)(13,136,235,42)(14,137,236,43)(15,138,237,44)(16,172,214,196)(17,173,215,197)(18,174,216,198)(19,175,217,199)(20,176,218,200)(21,177,219,201)(22,178,220,202)(23,179,221,203)(24,180,222,204)(25,166,223,205)(26,167,224,206)(27,168,225,207)(28,169,211,208)(29,170,212,209)(30,171,213,210)(46,79,94,190)(47,80,95,191)(48,81,96,192)(49,82,97,193)(50,83,98,194)(51,84,99,195)(52,85,100,181)(53,86,101,182)(54,87,102,183)(55,88,103,184)(56,89,104,185)(57,90,105,186)(58,76,91,187)(59,77,92,188)(60,78,93,189)(61,159,123,108)(62,160,124,109)(63,161,125,110)(64,162,126,111)(65,163,127,112)(66,164,128,113)(67,165,129,114)(68,151,130,115)(69,152,131,116)(70,153,132,117)(71,154,133,118)(72,155,134,119)(73,156,135,120)(74,157,121,106)(75,158,122,107), (16,214)(17,215)(18,216)(19,217)(20,218)(21,219)(22,220)(23,221)(24,222)(25,223)(26,224)(27,225)(28,211)(29,212)(30,213)(31,140)(32,141)(33,142)(34,143)(35,144)(36,145)(37,146)(38,147)(39,148)(40,149)(41,150)(42,136)(43,137)(44,138)(45,139)(46,94)(47,95)(48,96)(49,97)(50,98)(51,99)(52,100)(53,101)(54,102)(55,103)(56,104)(57,105)(58,91)(59,92)(60,93)(61,123)(62,124)(63,125)(64,126)(65,127)(66,128)(67,129)(68,130)(69,131)(70,132)(71,133)(72,134)(73,135)(74,121)(75,122) );
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)], [(1,171,191,111,238,210,80,162),(2,172,192,112,239,196,81,163),(3,173,193,113,240,197,82,164),(4,174,194,114,226,198,83,165),(5,175,195,115,227,199,84,151),(6,176,181,116,228,200,85,152),(7,177,182,117,229,201,86,153),(8,178,183,118,230,202,87,154),(9,179,184,119,231,203,88,155),(10,180,185,120,232,204,89,156),(11,166,186,106,233,205,90,157),(12,167,187,107,234,206,76,158),(13,168,188,108,235,207,77,159),(14,169,189,109,236,208,78,160),(15,170,190,110,237,209,79,161),(16,96,127,140,214,48,65,31),(17,97,128,141,215,49,66,32),(18,98,129,142,216,50,67,33),(19,99,130,143,217,51,68,34),(20,100,131,144,218,52,69,35),(21,101,132,145,219,53,70,36),(22,102,133,146,220,54,71,37),(23,103,134,147,221,55,72,38),(24,104,135,148,222,56,73,39),(25,105,121,149,223,57,74,40),(26,91,122,150,224,58,75,41),(27,92,123,136,225,59,61,42),(28,93,124,137,211,60,62,43),(29,94,125,138,212,46,63,44),(30,95,126,139,213,47,64,45)], [(1,139,238,45),(2,140,239,31),(3,141,240,32),(4,142,226,33),(5,143,227,34),(6,144,228,35),(7,145,229,36),(8,146,230,37),(9,147,231,38),(10,148,232,39),(11,149,233,40),(12,150,234,41),(13,136,235,42),(14,137,236,43),(15,138,237,44),(16,172,214,196),(17,173,215,197),(18,174,216,198),(19,175,217,199),(20,176,218,200),(21,177,219,201),(22,178,220,202),(23,179,221,203),(24,180,222,204),(25,166,223,205),(26,167,224,206),(27,168,225,207),(28,169,211,208),(29,170,212,209),(30,171,213,210),(46,79,94,190),(47,80,95,191),(48,81,96,192),(49,82,97,193),(50,83,98,194),(51,84,99,195),(52,85,100,181),(53,86,101,182),(54,87,102,183),(55,88,103,184),(56,89,104,185),(57,90,105,186),(58,76,91,187),(59,77,92,188),(60,78,93,189),(61,159,123,108),(62,160,124,109),(63,161,125,110),(64,162,126,111),(65,163,127,112),(66,164,128,113),(67,165,129,114),(68,151,130,115),(69,152,131,116),(70,153,132,117),(71,154,133,118),(72,155,134,119),(73,156,135,120),(74,157,121,106),(75,158,122,107)], [(16,214),(17,215),(18,216),(19,217),(20,218),(21,219),(22,220),(23,221),(24,222),(25,223),(26,224),(27,225),(28,211),(29,212),(30,213),(31,140),(32,141),(33,142),(34,143),(35,144),(36,145),(37,146),(38,147),(39,148),(40,149),(41,150),(42,136),(43,137),(44,138),(45,139),(46,94),(47,95),(48,96),(49,97),(50,98),(51,99),(52,100),(53,101),(54,102),(55,103),(56,104),(57,105),(58,91),(59,92),(60,93),(61,123),(62,124),(63,125),(64,126),(65,127),(66,128),(67,129),(68,130),(69,131),(70,132),(71,133),(72,134),(73,135),(74,121),(75,122)]])
300 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 3A | 3B | 4A | 4B | 4C | 4D | 4E | 5A | 5B | 5C | 5D | 6A | 6B | 6C | ··· | 6H | 8A | 8B | 8C | 8D | 8E | ··· | 8J | 10A | 10B | 10C | 10D | 10E | ··· | 10P | 12A | 12B | 12C | 12D | 12E | ··· | 12J | 15A | ··· | 15H | 20A | ··· | 20H | 20I | ··· | 20T | 24A | ··· | 24H | 24I | ··· | 24T | 30A | ··· | 30H | 30I | ··· | 30AF | 40A | ··· | 40P | 40Q | ··· | 40AN | 60A | ··· | 60P | 60Q | ··· | 60AN | 120A | ··· | 120AF | 120AG | ··· | 120CB |
| order | 1 | 2 | 2 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 5 | 5 | 6 | 6 | 6 | ··· | 6 | 8 | 8 | 8 | 8 | 8 | ··· | 8 | 10 | 10 | 10 | 10 | 10 | ··· | 10 | 12 | 12 | 12 | 12 | 12 | ··· | 12 | 15 | ··· | 15 | 20 | ··· | 20 | 20 | ··· | 20 | 24 | ··· | 24 | 24 | ··· | 24 | 30 | ··· | 30 | 30 | ··· | 30 | 40 | ··· | 40 | 40 | ··· | 40 | 60 | ··· | 60 | 60 | ··· | 60 | 120 | ··· | 120 | 120 | ··· | 120 |
| size | 1 | 1 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 |
300 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | ||||||||||||||||||||||||
| image | C1 | C2 | C2 | C2 | C3 | C4 | C4 | C5 | C6 | C6 | C6 | C10 | C10 | C10 | C12 | C12 | C15 | C20 | C20 | C30 | C30 | C30 | C60 | C60 | C8○D4 | C3×C8○D4 | C5×C8○D4 | C15×C8○D4 |
| kernel | C15×C8○D4 | C2×C120 | C15×M4(2) | C15×C4○D4 | C5×C8○D4 | D4×C15 | Q8×C15 | C3×C8○D4 | C2×C40 | C5×M4(2) | C5×C4○D4 | C2×C24 | C3×M4(2) | C3×C4○D4 | C5×D4 | C5×Q8 | C8○D4 | C3×D4 | C3×Q8 | C2×C8 | M4(2) | C4○D4 | D4 | Q8 | C15 | C5 | C3 | C1 |
| # reps | 1 | 3 | 3 | 1 | 2 | 6 | 2 | 4 | 6 | 6 | 2 | 12 | 12 | 4 | 12 | 4 | 8 | 24 | 8 | 24 | 24 | 8 | 48 | 16 | 4 | 8 | 16 | 32 |
Matrix representation of C15×C8○D4 ►in GL3(𝔽241) generated by
| 98 | 0 | 0 |
| 0 | 15 | 0 |
| 0 | 0 | 15 |
| 240 | 0 | 0 |
| 0 | 30 | 0 |
| 0 | 0 | 30 |
| 240 | 0 | 0 |
| 0 | 171 | 2 |
| 0 | 80 | 70 |
| 240 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 70 | 240 |
G:=sub<GL(3,GF(241))| [98,0,0,0,15,0,0,0,15],[240,0,0,0,30,0,0,0,30],[240,0,0,0,171,80,0,2,70],[240,0,0,0,1,70,0,0,240] >;
C15×C8○D4 in GAP, Magma, Sage, TeX
C_{15}\times C_8\circ D_4 % in TeX
G:=Group("C15xC8oD4"); // GroupNames label
G:=SmallGroup(480,936);
// by ID
G=gap.SmallGroup(480,936);
# by ID
G:=PCGroup([7,-2,-2,-2,-3,-5,-2,-2,840,2571,124]);
// Polycyclic
G:=Group<a,b,c,d|a^15=b^8=d^2=1,c^2=b^4,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d=b^4*c>;
// generators/relations