direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C15×C22⋊C8, C22⋊2C120, C60.250D4, C23.3C60, C30.44M4(2), (C2×C6)⋊1C40, (C2×C30)⋊5C8, (C2×C40)⋊3C6, (C2×C8)⋊1C30, (C2×C10)⋊6C24, (C2×C120)⋊7C2, (C2×C24)⋊3C10, (C2×C4).3C60, C30.73(C2×C8), (C2×C60).36C4, C2.1(C2×C120), C6.11(C2×C40), (C2×C12).7C20, C12.65(C5×D4), C20.65(C3×D4), C4.16(D4×C15), C10.20(C2×C24), (C2×C20).18C12, (C22×C4).4C30, C22.8(C2×C60), (C22×C60).5C2, (C22×C6).3C20, (C22×C20).7C6, C6.8(C5×M4(2)), (C22×C30).13C4, (C22×C12).3C10, C2.2(C15×M4(2)), (C2×C60).588C22, (C22×C10).10C12, C10.13(C3×M4(2)), C30.124(C22⋊C4), (C2×C4).32(C2×C30), (C2×C6).38(C2×C20), C2.2(C15×C22⋊C4), C6.20(C5×C22⋊C4), (C2×C30).206(C2×C4), (C2×C20).134(C2×C6), (C2×C10).58(C2×C12), C10.31(C3×C22⋊C4), (C2×C12).135(C2×C10), SmallGroup(480,201)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C15×C22⋊C8
G = < a,b,c,d | a15=b2=c2=d8=1, ab=ba, ac=ca, ad=da, dbd-1=bc=cb, cd=dc >
Subgroups: 136 in 100 conjugacy classes, 64 normal (40 characteristic)
C1, C2, C2, C3, C4, C4, C22, C22, C22, C5, C6, C6, C8, C2×C4, C2×C4, C23, C10, C10, C12, C12, C2×C6, C2×C6, C2×C6, C15, C2×C8, C22×C4, C20, C20, C2×C10, C2×C10, C2×C10, C24, C2×C12, C2×C12, C22×C6, C30, C30, C22⋊C8, C40, C2×C20, C2×C20, C22×C10, C2×C24, C22×C12, C60, C60, C2×C30, C2×C30, C2×C30, C2×C40, C22×C20, C3×C22⋊C8, C120, C2×C60, C2×C60, C22×C30, C5×C22⋊C8, C2×C120, C22×C60, C15×C22⋊C8
Quotients: C1, C2, C3, C4, C22, C5, C6, C8, C2×C4, D4, C10, C12, C2×C6, C15, C22⋊C4, C2×C8, M4(2), C20, C2×C10, C24, C2×C12, C3×D4, C30, C22⋊C8, C40, C2×C20, C5×D4, C3×C22⋊C4, C2×C24, C3×M4(2), C60, C2×C30, C5×C22⋊C4, C2×C40, C5×M4(2), C3×C22⋊C8, C120, C2×C60, D4×C15, C5×C22⋊C8, C15×C22⋊C4, C2×C120, C15×M4(2), C15×C22⋊C8
►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)
(16 230)(17 231)(18 232)(19 233)(20 234)(21 235)(22 236)(23 237)(24 238)(25 239)(26 240)(27 226)(28 227)(29 228)(30 229)(31 104)(32 105)(33 91)(34 92)(35 93)(36 94)(37 95)(38 96)(39 97)(40 98)(41 99)(42 100)(43 101)(44 102)(45 103)(46 217)(47 218)(48 219)(49 220)(50 221)(51 222)(52 223)(53 224)(54 225)(55 211)(56 212)(57 213)(58 214)(59 215)(60 216)(61 173)(62 174)(63 175)(64 176)(65 177)(66 178)(67 179)(68 180)(69 166)(70 167)(71 168)(72 169)(73 170)(74 171)(75 172)
(1 106)(2 107)(3 108)(4 109)(5 110)(6 111)(7 112)(8 113)(9 114)(10 115)(11 116)(12 117)(13 118)(14 119)(15 120)(16 230)(17 231)(18 232)(19 233)(20 234)(21 235)(22 236)(23 237)(24 238)(25 239)(26 240)(27 226)(28 227)(29 228)(30 229)(31 104)(32 105)(33 91)(34 92)(35 93)(36 94)(37 95)(38 96)(39 97)(40 98)(41 99)(42 100)(43 101)(44 102)(45 103)(46 217)(47 218)(48 219)(49 220)(50 221)(51 222)(52 223)(53 224)(54 225)(55 211)(56 212)(57 213)(58 214)(59 215)(60 216)(61 173)(62 174)(63 175)(64 176)(65 177)(66 178)(67 179)(68 180)(69 166)(70 167)(71 168)(72 169)(73 170)(74 171)(75 172)(76 165)(77 151)(78 152)(79 153)(80 154)(81 155)(82 156)(83 157)(84 158)(85 159)(86 160)(87 161)(88 162)(89 163)(90 164)(121 185)(122 186)(123 187)(124 188)(125 189)(126 190)(127 191)(128 192)(129 193)(130 194)(131 195)(132 181)(133 182)(134 183)(135 184)(136 204)(137 205)(138 206)(139 207)(140 208)(141 209)(142 210)(143 196)(144 197)(145 198)(146 199)(147 200)(148 201)(149 202)(150 203)
(1 65 187 239 138 92 165 218)(2 66 188 240 139 93 151 219)(3 67 189 226 140 94 152 220)(4 68 190 227 141 95 153 221)(5 69 191 228 142 96 154 222)(6 70 192 229 143 97 155 223)(7 71 193 230 144 98 156 224)(8 72 194 231 145 99 157 225)(9 73 195 232 146 100 158 211)(10 74 181 233 147 101 159 212)(11 75 182 234 148 102 160 213)(12 61 183 235 149 103 161 214)(13 62 184 236 150 104 162 215)(14 63 185 237 136 105 163 216)(15 64 186 238 137 91 164 217)(16 197 40 82 53 112 168 129)(17 198 41 83 54 113 169 130)(18 199 42 84 55 114 170 131)(19 200 43 85 56 115 171 132)(20 201 44 86 57 116 172 133)(21 202 45 87 58 117 173 134)(22 203 31 88 59 118 174 135)(23 204 32 89 60 119 175 121)(24 205 33 90 46 120 176 122)(25 206 34 76 47 106 177 123)(26 207 35 77 48 107 178 124)(27 208 36 78 49 108 179 125)(28 209 37 79 50 109 180 126)(29 210 38 80 51 110 166 127)(30 196 39 81 52 111 167 128)
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), (16,230)(17,231)(18,232)(19,233)(20,234)(21,235)(22,236)(23,237)(24,238)(25,239)(26,240)(27,226)(28,227)(29,228)(30,229)(31,104)(32,105)(33,91)(34,92)(35,93)(36,94)(37,95)(38,96)(39,97)(40,98)(41,99)(42,100)(43,101)(44,102)(45,103)(46,217)(47,218)(48,219)(49,220)(50,221)(51,222)(52,223)(53,224)(54,225)(55,211)(56,212)(57,213)(58,214)(59,215)(60,216)(61,173)(62,174)(63,175)(64,176)(65,177)(66,178)(67,179)(68,180)(69,166)(70,167)(71,168)(72,169)(73,170)(74,171)(75,172), (1,106)(2,107)(3,108)(4,109)(5,110)(6,111)(7,112)(8,113)(9,114)(10,115)(11,116)(12,117)(13,118)(14,119)(15,120)(16,230)(17,231)(18,232)(19,233)(20,234)(21,235)(22,236)(23,237)(24,238)(25,239)(26,240)(27,226)(28,227)(29,228)(30,229)(31,104)(32,105)(33,91)(34,92)(35,93)(36,94)(37,95)(38,96)(39,97)(40,98)(41,99)(42,100)(43,101)(44,102)(45,103)(46,217)(47,218)(48,219)(49,220)(50,221)(51,222)(52,223)(53,224)(54,225)(55,211)(56,212)(57,213)(58,214)(59,215)(60,216)(61,173)(62,174)(63,175)(64,176)(65,177)(66,178)(67,179)(68,180)(69,166)(70,167)(71,168)(72,169)(73,170)(74,171)(75,172)(76,165)(77,151)(78,152)(79,153)(80,154)(81,155)(82,156)(83,157)(84,158)(85,159)(86,160)(87,161)(88,162)(89,163)(90,164)(121,185)(122,186)(123,187)(124,188)(125,189)(126,190)(127,191)(128,192)(129,193)(130,194)(131,195)(132,181)(133,182)(134,183)(135,184)(136,204)(137,205)(138,206)(139,207)(140,208)(141,209)(142,210)(143,196)(144,197)(145,198)(146,199)(147,200)(148,201)(149,202)(150,203), (1,65,187,239,138,92,165,218)(2,66,188,240,139,93,151,219)(3,67,189,226,140,94,152,220)(4,68,190,227,141,95,153,221)(5,69,191,228,142,96,154,222)(6,70,192,229,143,97,155,223)(7,71,193,230,144,98,156,224)(8,72,194,231,145,99,157,225)(9,73,195,232,146,100,158,211)(10,74,181,233,147,101,159,212)(11,75,182,234,148,102,160,213)(12,61,183,235,149,103,161,214)(13,62,184,236,150,104,162,215)(14,63,185,237,136,105,163,216)(15,64,186,238,137,91,164,217)(16,197,40,82,53,112,168,129)(17,198,41,83,54,113,169,130)(18,199,42,84,55,114,170,131)(19,200,43,85,56,115,171,132)(20,201,44,86,57,116,172,133)(21,202,45,87,58,117,173,134)(22,203,31,88,59,118,174,135)(23,204,32,89,60,119,175,121)(24,205,33,90,46,120,176,122)(25,206,34,76,47,106,177,123)(26,207,35,77,48,107,178,124)(27,208,36,78,49,108,179,125)(28,209,37,79,50,109,180,126)(29,210,38,80,51,110,166,127)(30,196,39,81,52,111,167,128)>;
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), (16,230)(17,231)(18,232)(19,233)(20,234)(21,235)(22,236)(23,237)(24,238)(25,239)(26,240)(27,226)(28,227)(29,228)(30,229)(31,104)(32,105)(33,91)(34,92)(35,93)(36,94)(37,95)(38,96)(39,97)(40,98)(41,99)(42,100)(43,101)(44,102)(45,103)(46,217)(47,218)(48,219)(49,220)(50,221)(51,222)(52,223)(53,224)(54,225)(55,211)(56,212)(57,213)(58,214)(59,215)(60,216)(61,173)(62,174)(63,175)(64,176)(65,177)(66,178)(67,179)(68,180)(69,166)(70,167)(71,168)(72,169)(73,170)(74,171)(75,172), (1,106)(2,107)(3,108)(4,109)(5,110)(6,111)(7,112)(8,113)(9,114)(10,115)(11,116)(12,117)(13,118)(14,119)(15,120)(16,230)(17,231)(18,232)(19,233)(20,234)(21,235)(22,236)(23,237)(24,238)(25,239)(26,240)(27,226)(28,227)(29,228)(30,229)(31,104)(32,105)(33,91)(34,92)(35,93)(36,94)(37,95)(38,96)(39,97)(40,98)(41,99)(42,100)(43,101)(44,102)(45,103)(46,217)(47,218)(48,219)(49,220)(50,221)(51,222)(52,223)(53,224)(54,225)(55,211)(56,212)(57,213)(58,214)(59,215)(60,216)(61,173)(62,174)(63,175)(64,176)(65,177)(66,178)(67,179)(68,180)(69,166)(70,167)(71,168)(72,169)(73,170)(74,171)(75,172)(76,165)(77,151)(78,152)(79,153)(80,154)(81,155)(82,156)(83,157)(84,158)(85,159)(86,160)(87,161)(88,162)(89,163)(90,164)(121,185)(122,186)(123,187)(124,188)(125,189)(126,190)(127,191)(128,192)(129,193)(130,194)(131,195)(132,181)(133,182)(134,183)(135,184)(136,204)(137,205)(138,206)(139,207)(140,208)(141,209)(142,210)(143,196)(144,197)(145,198)(146,199)(147,200)(148,201)(149,202)(150,203), (1,65,187,239,138,92,165,218)(2,66,188,240,139,93,151,219)(3,67,189,226,140,94,152,220)(4,68,190,227,141,95,153,221)(5,69,191,228,142,96,154,222)(6,70,192,229,143,97,155,223)(7,71,193,230,144,98,156,224)(8,72,194,231,145,99,157,225)(9,73,195,232,146,100,158,211)(10,74,181,233,147,101,159,212)(11,75,182,234,148,102,160,213)(12,61,183,235,149,103,161,214)(13,62,184,236,150,104,162,215)(14,63,185,237,136,105,163,216)(15,64,186,238,137,91,164,217)(16,197,40,82,53,112,168,129)(17,198,41,83,54,113,169,130)(18,199,42,84,55,114,170,131)(19,200,43,85,56,115,171,132)(20,201,44,86,57,116,172,133)(21,202,45,87,58,117,173,134)(22,203,31,88,59,118,174,135)(23,204,32,89,60,119,175,121)(24,205,33,90,46,120,176,122)(25,206,34,76,47,106,177,123)(26,207,35,77,48,107,178,124)(27,208,36,78,49,108,179,125)(28,209,37,79,50,109,180,126)(29,210,38,80,51,110,166,127)(30,196,39,81,52,111,167,128) );
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)], [(16,230),(17,231),(18,232),(19,233),(20,234),(21,235),(22,236),(23,237),(24,238),(25,239),(26,240),(27,226),(28,227),(29,228),(30,229),(31,104),(32,105),(33,91),(34,92),(35,93),(36,94),(37,95),(38,96),(39,97),(40,98),(41,99),(42,100),(43,101),(44,102),(45,103),(46,217),(47,218),(48,219),(49,220),(50,221),(51,222),(52,223),(53,224),(54,225),(55,211),(56,212),(57,213),(58,214),(59,215),(60,216),(61,173),(62,174),(63,175),(64,176),(65,177),(66,178),(67,179),(68,180),(69,166),(70,167),(71,168),(72,169),(73,170),(74,171),(75,172)], [(1,106),(2,107),(3,108),(4,109),(5,110),(6,111),(7,112),(8,113),(9,114),(10,115),(11,116),(12,117),(13,118),(14,119),(15,120),(16,230),(17,231),(18,232),(19,233),(20,234),(21,235),(22,236),(23,237),(24,238),(25,239),(26,240),(27,226),(28,227),(29,228),(30,229),(31,104),(32,105),(33,91),(34,92),(35,93),(36,94),(37,95),(38,96),(39,97),(40,98),(41,99),(42,100),(43,101),(44,102),(45,103),(46,217),(47,218),(48,219),(49,220),(50,221),(51,222),(52,223),(53,224),(54,225),(55,211),(56,212),(57,213),(58,214),(59,215),(60,216),(61,173),(62,174),(63,175),(64,176),(65,177),(66,178),(67,179),(68,180),(69,166),(70,167),(71,168),(72,169),(73,170),(74,171),(75,172),(76,165),(77,151),(78,152),(79,153),(80,154),(81,155),(82,156),(83,157),(84,158),(85,159),(86,160),(87,161),(88,162),(89,163),(90,164),(121,185),(122,186),(123,187),(124,188),(125,189),(126,190),(127,191),(128,192),(129,193),(130,194),(131,195),(132,181),(133,182),(134,183),(135,184),(136,204),(137,205),(138,206),(139,207),(140,208),(141,209),(142,210),(143,196),(144,197),(145,198),(146,199),(147,200),(148,201),(149,202),(150,203)], [(1,65,187,239,138,92,165,218),(2,66,188,240,139,93,151,219),(3,67,189,226,140,94,152,220),(4,68,190,227,141,95,153,221),(5,69,191,228,142,96,154,222),(6,70,192,229,143,97,155,223),(7,71,193,230,144,98,156,224),(8,72,194,231,145,99,157,225),(9,73,195,232,146,100,158,211),(10,74,181,233,147,101,159,212),(11,75,182,234,148,102,160,213),(12,61,183,235,149,103,161,214),(13,62,184,236,150,104,162,215),(14,63,185,237,136,105,163,216),(15,64,186,238,137,91,164,217),(16,197,40,82,53,112,168,129),(17,198,41,83,54,113,169,130),(18,199,42,84,55,114,170,131),(19,200,43,85,56,115,171,132),(20,201,44,86,57,116,172,133),(21,202,45,87,58,117,173,134),(22,203,31,88,59,118,174,135),(23,204,32,89,60,119,175,121),(24,205,33,90,46,120,176,122),(25,206,34,76,47,106,177,123),(26,207,35,77,48,107,178,124),(27,208,36,78,49,108,179,125),(28,209,37,79,50,109,180,126),(29,210,38,80,51,110,166,127),(30,196,39,81,52,111,167,128)]])
300 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 3A | 3B | 4A | 4B | 4C | 4D | 4E | 4F | 5A | 5B | 5C | 5D | 6A | ··· | 6F | 6G | 6H | 6I | 6J | 8A | ··· | 8H | 10A | ··· | 10L | 10M | ··· | 10T | 12A | ··· | 12H | 12I | 12J | 12K | 12L | 15A | ··· | 15H | 20A | ··· | 20P | 20Q | ··· | 20X | 24A | ··· | 24P | 30A | ··· | 30X | 30Y | ··· | 30AN | 40A | ··· | 40AF | 60A | ··· | 60AF | 60AG | ··· | 60AV | 120A | ··· | 120BL |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 5 | 5 | 6 | ··· | 6 | 6 | 6 | 6 | 6 | 8 | ··· | 8 | 10 | ··· | 10 | 10 | ··· | 10 | 12 | ··· | 12 | 12 | 12 | 12 | 12 | 15 | ··· | 15 | 20 | ··· | 20 | 20 | ··· | 20 | 24 | ··· | 24 | 30 | ··· | 30 | 30 | ··· | 30 | 40 | ··· | 40 | 60 | ··· | 60 | 60 | ··· | 60 | 120 | ··· | 120 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 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 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | ||||||||||||||||||||||||||||
| image | C1 | C2 | C2 | C3 | C4 | C4 | C5 | C6 | C6 | C8 | C10 | C10 | C12 | C12 | C15 | C20 | C20 | C24 | C30 | C30 | C40 | C60 | C60 | C120 | D4 | M4(2) | C3×D4 | C5×D4 | C3×M4(2) | C5×M4(2) | D4×C15 | C15×M4(2) |
| kernel | C15×C22⋊C8 | C2×C120 | C22×C60 | C5×C22⋊C8 | C2×C60 | C22×C30 | C3×C22⋊C8 | C2×C40 | C22×C20 | C2×C30 | C2×C24 | C22×C12 | C2×C20 | C22×C10 | C22⋊C8 | C2×C12 | C22×C6 | C2×C10 | C2×C8 | C22×C4 | C2×C6 | C2×C4 | C23 | C22 | C60 | C30 | C20 | C12 | C10 | C6 | C4 | C2 |
| # reps | 1 | 2 | 1 | 2 | 2 | 2 | 4 | 4 | 2 | 8 | 8 | 4 | 4 | 4 | 8 | 8 | 8 | 16 | 16 | 8 | 32 | 16 | 16 | 64 | 2 | 2 | 4 | 8 | 4 | 8 | 16 | 16 |
Matrix representation of C15×C22⋊C8 ►in GL4(𝔽241) generated by
| 87 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 15 | 0 |
| 0 | 0 | 0 | 15 |
| 240 | 0 | 0 | 0 |
| 0 | 240 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 240 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 240 | 0 |
| 0 | 0 | 0 | 240 |
| 240 | 0 | 0 | 0 |
| 0 | 30 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 240 | 0 |
G:=sub<GL(4,GF(241))| [87,0,0,0,0,1,0,0,0,0,15,0,0,0,0,15],[240,0,0,0,0,240,0,0,0,0,1,0,0,0,0,240],[1,0,0,0,0,1,0,0,0,0,240,0,0,0,0,240],[240,0,0,0,0,30,0,0,0,0,0,240,0,0,1,0] >;
C15×C22⋊C8 in GAP, Magma, Sage, TeX
C_{15}\times C_2^2\rtimes C_8 % in TeX
G:=Group("C15xC2^2:C8"); // GroupNames label
G:=SmallGroup(480,201);
// by ID
G=gap.SmallGroup(480,201);
# by ID
G:=PCGroup([7,-2,-2,-3,-5,-2,-2,-2,840,869,124]);
// Polycyclic
G:=Group<a,b,c,d|a^15=b^2=c^2=d^8=1,a*b=b*a,a*c=c*a,a*d=d*a,d*b*d^-1=b*c=c*b,c*d=d*c>;
// generators/relations