direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C2×D15⋊C8, D30⋊2C8, C5⋊C8⋊9D6, C10⋊1(S3×C8), C30⋊2(C2×C8), C6⋊1(D5⋊C8), D15⋊2(C2×C8), C15⋊3(C22×C8), C15⋊C8⋊8C22, D30.13(C2×C4), D30.C2.4C4, (C2×Dic3).9F5, C22.21(S3×F5), C6.25(C22×F5), C30.25(C22×C4), Dic5.29(C4×S3), (C10×Dic3).8C4, Dic3.15(C2×F5), (C22×D15).5C4, (C2×Dic5).149D6, D30.C2.16C22, Dic5.37(C22×S3), (C3×Dic5).35C23, (C6×Dic5).146C22, C5⋊2(S3×C2×C8), (C6×C5⋊C8)⋊5C2, (C2×C5⋊C8)⋊6S3, C3⋊2(C2×D5⋊C8), C2.5(C2×S3×F5), (C3×C5⋊C8)⋊8C22, C10.25(S3×C2×C4), (C2×C15⋊C8)⋊5C2, (C2×C6).23(C2×F5), (C2×C30).20(C2×C4), (C2×C10).20(C4×S3), (C2×D30.C2).11C2, (C5×Dic3).14(C2×C4), (C3×Dic5).27(C2×C4), SmallGroup(480,1006)
Series: Derived ►Chief ►Lower central ►Upper central
| C15 — C2×D15⋊C8 |
Generators and relations for C2×D15⋊C8
G = < a,b,c,d | a2=b15=c2=d8=1, ab=ba, ac=ca, ad=da, cbc=b-1, dbd-1=b13, dcd-1=b12c >
Subgroups: 692 in 152 conjugacy classes, 62 normal (26 characteristic)
C1, C2, C2, C2, C3, C4, C22, C22, C5, S3, C6, C6, C8, C2×C4, C23, D5, C10, C10, Dic3, C12, D6, C2×C6, C15, C2×C8, C22×C4, Dic5, C20, D10, C2×C10, C3⋊C8, C24, C4×S3, C2×Dic3, C2×C12, C22×S3, D15, C30, C30, C22×C8, C5⋊C8, C5⋊C8, C4×D5, C2×Dic5, C2×C20, C22×D5, S3×C8, C2×C3⋊C8, C2×C24, S3×C2×C4, C5×Dic3, C3×Dic5, D30, C2×C30, D5⋊C8, C2×C5⋊C8, C2×C5⋊C8, C2×C4×D5, S3×C2×C8, C3×C5⋊C8, C15⋊C8, D30.C2, C6×Dic5, C10×Dic3, C22×D15, C2×D5⋊C8, D15⋊C8, C6×C5⋊C8, C2×C15⋊C8, C2×D30.C2, C2×D15⋊C8
Quotients: C1, C2, C4, C22, S3, C8, C2×C4, C23, D6, C2×C8, C22×C4, F5, C4×S3, C22×S3, C22×C8, C2×F5, S3×C8, S3×C2×C4, D5⋊C8, C22×F5, S3×C2×C8, S3×F5, C2×D5⋊C8, D15⋊C8, C2×S3×F5, C2×D15⋊C8
►On 240 points
Generators in S240
(1 61)(2 62)(3 63)(4 64)(5 65)(6 66)(7 67)(8 68)(9 69)(10 70)(11 71)(12 72)(13 73)(14 74)(15 75)(16 82)(17 83)(18 84)(19 85)(20 86)(21 87)(22 88)(23 89)(24 90)(25 76)(26 77)(27 78)(28 79)(29 80)(30 81)(31 99)(32 100)(33 101)(34 102)(35 103)(36 104)(37 105)(38 91)(39 92)(40 93)(41 94)(42 95)(43 96)(44 97)(45 98)(46 111)(47 112)(48 113)(49 114)(50 115)(51 116)(52 117)(53 118)(54 119)(55 120)(56 106)(57 107)(58 108)(59 109)(60 110)(121 194)(122 195)(123 181)(124 182)(125 183)(126 184)(127 185)(128 186)(129 187)(130 188)(131 189)(132 190)(133 191)(134 192)(135 193)(136 208)(137 209)(138 210)(139 196)(140 197)(141 198)(142 199)(143 200)(144 201)(145 202)(146 203)(147 204)(148 205)(149 206)(150 207)(151 221)(152 222)(153 223)(154 224)(155 225)(156 211)(157 212)(158 213)(159 214)(160 215)(161 216)(162 217)(163 218)(164 219)(165 220)(166 231)(167 232)(168 233)(169 234)(170 235)(171 236)(172 237)(173 238)(174 239)(175 240)(176 226)(177 227)(178 228)(179 229)(180 230)
(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 20)(2 19)(3 18)(4 17)(5 16)(6 30)(7 29)(8 28)(9 27)(10 26)(11 25)(12 24)(13 23)(14 22)(15 21)(31 55)(32 54)(33 53)(34 52)(35 51)(36 50)(37 49)(38 48)(39 47)(40 46)(41 60)(42 59)(43 58)(44 57)(45 56)(61 86)(62 85)(63 84)(64 83)(65 82)(66 81)(67 80)(68 79)(69 78)(70 77)(71 76)(72 90)(73 89)(74 88)(75 87)(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)(121 146)(122 145)(123 144)(124 143)(125 142)(126 141)(127 140)(128 139)(129 138)(130 137)(131 136)(132 150)(133 149)(134 148)(135 147)(151 175)(152 174)(153 173)(154 172)(155 171)(156 170)(157 169)(158 168)(159 167)(160 166)(161 180)(162 179)(163 178)(164 177)(165 176)(181 201)(182 200)(183 199)(184 198)(185 197)(186 196)(187 210)(188 209)(189 208)(190 207)(191 206)(192 205)(193 204)(194 203)(195 202)(211 235)(212 234)(213 233)(214 232)(215 231)(216 230)(217 229)(218 228)(219 227)(220 226)(221 240)(222 239)(223 238)(224 237)(225 236)
(1 176 58 137 21 151 44 131)(2 168 47 150 22 158 33 129)(3 175 51 148 23 165 37 127)(4 167 55 146 24 157 41 125)(5 174 59 144 25 164 45 123)(6 166 48 142 26 156 34 121)(7 173 52 140 27 163 38 134)(8 180 56 138 28 155 42 132)(9 172 60 136 29 162 31 130)(10 179 49 149 30 154 35 128)(11 171 53 147 16 161 39 126)(12 178 57 145 17 153 43 124)(13 170 46 143 18 160 32 122)(14 177 50 141 19 152 36 135)(15 169 54 139 20 159 40 133)(61 226 108 209 87 221 97 189)(62 233 112 207 88 213 101 187)(63 240 116 205 89 220 105 185)(64 232 120 203 90 212 94 183)(65 239 109 201 76 219 98 181)(66 231 113 199 77 211 102 194)(67 238 117 197 78 218 91 192)(68 230 106 210 79 225 95 190)(69 237 110 208 80 217 99 188)(70 229 114 206 81 224 103 186)(71 236 118 204 82 216 92 184)(72 228 107 202 83 223 96 182)(73 235 111 200 84 215 100 195)(74 227 115 198 85 222 104 193)(75 234 119 196 86 214 93 191)
G:=sub<Sym(240)| (1,61)(2,62)(3,63)(4,64)(5,65)(6,66)(7,67)(8,68)(9,69)(10,70)(11,71)(12,72)(13,73)(14,74)(15,75)(16,82)(17,83)(18,84)(19,85)(20,86)(21,87)(22,88)(23,89)(24,90)(25,76)(26,77)(27,78)(28,79)(29,80)(30,81)(31,99)(32,100)(33,101)(34,102)(35,103)(36,104)(37,105)(38,91)(39,92)(40,93)(41,94)(42,95)(43,96)(44,97)(45,98)(46,111)(47,112)(48,113)(49,114)(50,115)(51,116)(52,117)(53,118)(54,119)(55,120)(56,106)(57,107)(58,108)(59,109)(60,110)(121,194)(122,195)(123,181)(124,182)(125,183)(126,184)(127,185)(128,186)(129,187)(130,188)(131,189)(132,190)(133,191)(134,192)(135,193)(136,208)(137,209)(138,210)(139,196)(140,197)(141,198)(142,199)(143,200)(144,201)(145,202)(146,203)(147,204)(148,205)(149,206)(150,207)(151,221)(152,222)(153,223)(154,224)(155,225)(156,211)(157,212)(158,213)(159,214)(160,215)(161,216)(162,217)(163,218)(164,219)(165,220)(166,231)(167,232)(168,233)(169,234)(170,235)(171,236)(172,237)(173,238)(174,239)(175,240)(176,226)(177,227)(178,228)(179,229)(180,230), (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), (1,20)(2,19)(3,18)(4,17)(5,16)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(31,55)(32,54)(33,53)(34,52)(35,51)(36,50)(37,49)(38,48)(39,47)(40,46)(41,60)(42,59)(43,58)(44,57)(45,56)(61,86)(62,85)(63,84)(64,83)(65,82)(66,81)(67,80)(68,79)(69,78)(70,77)(71,76)(72,90)(73,89)(74,88)(75,87)(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)(121,146)(122,145)(123,144)(124,143)(125,142)(126,141)(127,140)(128,139)(129,138)(130,137)(131,136)(132,150)(133,149)(134,148)(135,147)(151,175)(152,174)(153,173)(154,172)(155,171)(156,170)(157,169)(158,168)(159,167)(160,166)(161,180)(162,179)(163,178)(164,177)(165,176)(181,201)(182,200)(183,199)(184,198)(185,197)(186,196)(187,210)(188,209)(189,208)(190,207)(191,206)(192,205)(193,204)(194,203)(195,202)(211,235)(212,234)(213,233)(214,232)(215,231)(216,230)(217,229)(218,228)(219,227)(220,226)(221,240)(222,239)(223,238)(224,237)(225,236), (1,176,58,137,21,151,44,131)(2,168,47,150,22,158,33,129)(3,175,51,148,23,165,37,127)(4,167,55,146,24,157,41,125)(5,174,59,144,25,164,45,123)(6,166,48,142,26,156,34,121)(7,173,52,140,27,163,38,134)(8,180,56,138,28,155,42,132)(9,172,60,136,29,162,31,130)(10,179,49,149,30,154,35,128)(11,171,53,147,16,161,39,126)(12,178,57,145,17,153,43,124)(13,170,46,143,18,160,32,122)(14,177,50,141,19,152,36,135)(15,169,54,139,20,159,40,133)(61,226,108,209,87,221,97,189)(62,233,112,207,88,213,101,187)(63,240,116,205,89,220,105,185)(64,232,120,203,90,212,94,183)(65,239,109,201,76,219,98,181)(66,231,113,199,77,211,102,194)(67,238,117,197,78,218,91,192)(68,230,106,210,79,225,95,190)(69,237,110,208,80,217,99,188)(70,229,114,206,81,224,103,186)(71,236,118,204,82,216,92,184)(72,228,107,202,83,223,96,182)(73,235,111,200,84,215,100,195)(74,227,115,198,85,222,104,193)(75,234,119,196,86,214,93,191)>;
G:=Group( (1,61)(2,62)(3,63)(4,64)(5,65)(6,66)(7,67)(8,68)(9,69)(10,70)(11,71)(12,72)(13,73)(14,74)(15,75)(16,82)(17,83)(18,84)(19,85)(20,86)(21,87)(22,88)(23,89)(24,90)(25,76)(26,77)(27,78)(28,79)(29,80)(30,81)(31,99)(32,100)(33,101)(34,102)(35,103)(36,104)(37,105)(38,91)(39,92)(40,93)(41,94)(42,95)(43,96)(44,97)(45,98)(46,111)(47,112)(48,113)(49,114)(50,115)(51,116)(52,117)(53,118)(54,119)(55,120)(56,106)(57,107)(58,108)(59,109)(60,110)(121,194)(122,195)(123,181)(124,182)(125,183)(126,184)(127,185)(128,186)(129,187)(130,188)(131,189)(132,190)(133,191)(134,192)(135,193)(136,208)(137,209)(138,210)(139,196)(140,197)(141,198)(142,199)(143,200)(144,201)(145,202)(146,203)(147,204)(148,205)(149,206)(150,207)(151,221)(152,222)(153,223)(154,224)(155,225)(156,211)(157,212)(158,213)(159,214)(160,215)(161,216)(162,217)(163,218)(164,219)(165,220)(166,231)(167,232)(168,233)(169,234)(170,235)(171,236)(172,237)(173,238)(174,239)(175,240)(176,226)(177,227)(178,228)(179,229)(180,230), (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), (1,20)(2,19)(3,18)(4,17)(5,16)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(31,55)(32,54)(33,53)(34,52)(35,51)(36,50)(37,49)(38,48)(39,47)(40,46)(41,60)(42,59)(43,58)(44,57)(45,56)(61,86)(62,85)(63,84)(64,83)(65,82)(66,81)(67,80)(68,79)(69,78)(70,77)(71,76)(72,90)(73,89)(74,88)(75,87)(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)(121,146)(122,145)(123,144)(124,143)(125,142)(126,141)(127,140)(128,139)(129,138)(130,137)(131,136)(132,150)(133,149)(134,148)(135,147)(151,175)(152,174)(153,173)(154,172)(155,171)(156,170)(157,169)(158,168)(159,167)(160,166)(161,180)(162,179)(163,178)(164,177)(165,176)(181,201)(182,200)(183,199)(184,198)(185,197)(186,196)(187,210)(188,209)(189,208)(190,207)(191,206)(192,205)(193,204)(194,203)(195,202)(211,235)(212,234)(213,233)(214,232)(215,231)(216,230)(217,229)(218,228)(219,227)(220,226)(221,240)(222,239)(223,238)(224,237)(225,236), (1,176,58,137,21,151,44,131)(2,168,47,150,22,158,33,129)(3,175,51,148,23,165,37,127)(4,167,55,146,24,157,41,125)(5,174,59,144,25,164,45,123)(6,166,48,142,26,156,34,121)(7,173,52,140,27,163,38,134)(8,180,56,138,28,155,42,132)(9,172,60,136,29,162,31,130)(10,179,49,149,30,154,35,128)(11,171,53,147,16,161,39,126)(12,178,57,145,17,153,43,124)(13,170,46,143,18,160,32,122)(14,177,50,141,19,152,36,135)(15,169,54,139,20,159,40,133)(61,226,108,209,87,221,97,189)(62,233,112,207,88,213,101,187)(63,240,116,205,89,220,105,185)(64,232,120,203,90,212,94,183)(65,239,109,201,76,219,98,181)(66,231,113,199,77,211,102,194)(67,238,117,197,78,218,91,192)(68,230,106,210,79,225,95,190)(69,237,110,208,80,217,99,188)(70,229,114,206,81,224,103,186)(71,236,118,204,82,216,92,184)(72,228,107,202,83,223,96,182)(73,235,111,200,84,215,100,195)(74,227,115,198,85,222,104,193)(75,234,119,196,86,214,93,191) );
G=PermutationGroup([[(1,61),(2,62),(3,63),(4,64),(5,65),(6,66),(7,67),(8,68),(9,69),(10,70),(11,71),(12,72),(13,73),(14,74),(15,75),(16,82),(17,83),(18,84),(19,85),(20,86),(21,87),(22,88),(23,89),(24,90),(25,76),(26,77),(27,78),(28,79),(29,80),(30,81),(31,99),(32,100),(33,101),(34,102),(35,103),(36,104),(37,105),(38,91),(39,92),(40,93),(41,94),(42,95),(43,96),(44,97),(45,98),(46,111),(47,112),(48,113),(49,114),(50,115),(51,116),(52,117),(53,118),(54,119),(55,120),(56,106),(57,107),(58,108),(59,109),(60,110),(121,194),(122,195),(123,181),(124,182),(125,183),(126,184),(127,185),(128,186),(129,187),(130,188),(131,189),(132,190),(133,191),(134,192),(135,193),(136,208),(137,209),(138,210),(139,196),(140,197),(141,198),(142,199),(143,200),(144,201),(145,202),(146,203),(147,204),(148,205),(149,206),(150,207),(151,221),(152,222),(153,223),(154,224),(155,225),(156,211),(157,212),(158,213),(159,214),(160,215),(161,216),(162,217),(163,218),(164,219),(165,220),(166,231),(167,232),(168,233),(169,234),(170,235),(171,236),(172,237),(173,238),(174,239),(175,240),(176,226),(177,227),(178,228),(179,229),(180,230)], [(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)], [(1,20),(2,19),(3,18),(4,17),(5,16),(6,30),(7,29),(8,28),(9,27),(10,26),(11,25),(12,24),(13,23),(14,22),(15,21),(31,55),(32,54),(33,53),(34,52),(35,51),(36,50),(37,49),(38,48),(39,47),(40,46),(41,60),(42,59),(43,58),(44,57),(45,56),(61,86),(62,85),(63,84),(64,83),(65,82),(66,81),(67,80),(68,79),(69,78),(70,77),(71,76),(72,90),(73,89),(74,88),(75,87),(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),(121,146),(122,145),(123,144),(124,143),(125,142),(126,141),(127,140),(128,139),(129,138),(130,137),(131,136),(132,150),(133,149),(134,148),(135,147),(151,175),(152,174),(153,173),(154,172),(155,171),(156,170),(157,169),(158,168),(159,167),(160,166),(161,180),(162,179),(163,178),(164,177),(165,176),(181,201),(182,200),(183,199),(184,198),(185,197),(186,196),(187,210),(188,209),(189,208),(190,207),(191,206),(192,205),(193,204),(194,203),(195,202),(211,235),(212,234),(213,233),(214,232),(215,231),(216,230),(217,229),(218,228),(219,227),(220,226),(221,240),(222,239),(223,238),(224,237),(225,236)], [(1,176,58,137,21,151,44,131),(2,168,47,150,22,158,33,129),(3,175,51,148,23,165,37,127),(4,167,55,146,24,157,41,125),(5,174,59,144,25,164,45,123),(6,166,48,142,26,156,34,121),(7,173,52,140,27,163,38,134),(8,180,56,138,28,155,42,132),(9,172,60,136,29,162,31,130),(10,179,49,149,30,154,35,128),(11,171,53,147,16,161,39,126),(12,178,57,145,17,153,43,124),(13,170,46,143,18,160,32,122),(14,177,50,141,19,152,36,135),(15,169,54,139,20,159,40,133),(61,226,108,209,87,221,97,189),(62,233,112,207,88,213,101,187),(63,240,116,205,89,220,105,185),(64,232,120,203,90,212,94,183),(65,239,109,201,76,219,98,181),(66,231,113,199,77,211,102,194),(67,238,117,197,78,218,91,192),(68,230,106,210,79,225,95,190),(69,237,110,208,80,217,99,188),(70,229,114,206,81,224,103,186),(71,236,118,204,82,216,92,184),(72,228,107,202,83,223,96,182),(73,235,111,200,84,215,100,195),(74,227,115,198,85,222,104,193),(75,234,119,196,86,214,93,191)]])
60 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 5 | 6A | 6B | 6C | 8A | ··· | 8H | 8I | ··· | 8P | 10A | 10B | 10C | 12A | 12B | 12C | 12D | 15 | 20A | 20B | 20C | 20D | 24A | ··· | 24H | 30A | 30B | 30C |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 6 | 6 | 6 | 8 | ··· | 8 | 8 | ··· | 8 | 10 | 10 | 10 | 12 | 12 | 12 | 12 | 15 | 20 | 20 | 20 | 20 | 24 | ··· | 24 | 30 | 30 | 30 |
| size | 1 | 1 | 1 | 1 | 15 | 15 | 15 | 15 | 2 | 3 | 3 | 3 | 3 | 5 | 5 | 5 | 5 | 4 | 2 | 2 | 2 | 5 | ··· | 5 | 15 | ··· | 15 | 4 | 4 | 4 | 10 | 10 | 10 | 10 | 8 | 12 | 12 | 12 | 12 | 10 | ··· | 10 | 8 | 8 | 8 |
60 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 8 | 8 | 8 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||||||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | C4 | C4 | C8 | S3 | D6 | D6 | C4×S3 | C4×S3 | S3×C8 | F5 | C2×F5 | C2×F5 | D5⋊C8 | S3×F5 | D15⋊C8 | C2×S3×F5 |
| kernel | C2×D15⋊C8 | D15⋊C8 | C6×C5⋊C8 | C2×C15⋊C8 | C2×D30.C2 | D30.C2 | C10×Dic3 | C22×D15 | D30 | C2×C5⋊C8 | C5⋊C8 | C2×Dic5 | Dic5 | C2×C10 | C10 | C2×Dic3 | Dic3 | C2×C6 | C6 | C22 | C2 | C2 |
| # reps | 1 | 4 | 1 | 1 | 1 | 4 | 2 | 2 | 16 | 1 | 2 | 1 | 2 | 2 | 8 | 1 | 2 | 1 | 4 | 1 | 2 | 1 |
Matrix representation of C2×D15⋊C8 ►in GL6(𝔽241)
| 240 | 0 | 0 | 0 | 0 | 0 |
| 0 | 240 | 0 | 0 | 0 | 0 |
| 0 | 0 | 240 | 0 | 0 | 0 |
| 0 | 0 | 0 | 240 | 0 | 0 |
| 0 | 0 | 0 | 0 | 240 | 0 |
| 0 | 0 | 0 | 0 | 0 | 240 |
| 0 | 240 | 0 | 0 | 0 | 0 |
| 1 | 240 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 240 | 1 | 0 |
| 0 | 0 | 0 | 240 | 0 | 1 |
| 0 | 0 | 0 | 240 | 0 | 0 |
| 0 | 0 | 1 | 240 | 0 | 0 |
| 1 | 240 | 0 | 0 | 0 | 0 |
| 0 | 240 | 0 | 0 | 0 | 0 |
| 0 | 0 | 240 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 240 |
| 0 | 0 | 0 | 1 | 240 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 149 | 92 | 93 | 0 |
| 0 | 0 | 1 | 92 | 0 | 149 |
| 0 | 0 | 149 | 0 | 92 | 1 |
| 0 | 0 | 0 | 93 | 92 | 149 |
G:=sub<GL(6,GF(241))| [240,0,0,0,0,0,0,240,0,0,0,0,0,0,240,0,0,0,0,0,0,240,0,0,0,0,0,0,240,0,0,0,0,0,0,240],[0,1,0,0,0,0,240,240,0,0,0,0,0,0,0,0,0,1,0,0,240,240,240,240,0,0,1,0,0,0,0,0,0,1,0,0],[1,0,0,0,0,0,240,240,0,0,0,0,0,0,240,0,0,0,0,0,1,1,1,1,0,0,0,0,0,240,0,0,0,0,240,0],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,149,1,149,0,0,0,92,92,0,93,0,0,93,0,92,92,0,0,0,149,1,149] >;
C2×D15⋊C8 in GAP, Magma, Sage, TeX
C_2\times D_{15}\rtimes C_8 % in TeX
G:=Group("C2xD15:C8"); // GroupNames label
G:=SmallGroup(480,1006);
// by ID
G=gap.SmallGroup(480,1006);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,56,120,80,1356,9414,2379]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^15=c^2=d^8=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c=b^-1,d*b*d^-1=b^13,d*c*d^-1=b^12*c>;
// generators/relations