direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C2×D15⋊2C8, D30⋊5C8, C60.182C23, C6⋊1(C8×D5), C10⋊3(S3×C8), C30⋊7(C2×C8), C3⋊C8⋊32D10, D15⋊4(C2×C8), C5⋊2C8⋊32D6, C15⋊9(C22×C8), C20.73(C4×S3), C12.41(C4×D5), C60.149(C2×C4), (C4×D15).13C4, D30.36(C2×C4), (C2×C20).329D6, (C2×C12).333D10, (C2×C60).231C22, C4.22(D30.C2), C30.104(C22×C4), C20.179(C22×S3), (C2×Dic15).21C4, Dic15.44(C2×C4), (C4×D15).64C22, (C22×D15).12C4, C12.179(C22×D5), C22.13(D30.C2), C5⋊5(S3×C2×C8), C3⋊2(D5×C2×C8), (C2×C3⋊C8)⋊13D5, (C10×C3⋊C8)⋊12C2, C6.38(C2×C4×D5), C10.71(S3×C2×C4), (C6×C5⋊2C8)⋊12C2, C4.152(C2×S3×D5), (C2×C5⋊2C8)⋊13S3, (C5×C3⋊C8)⋊35C22, (C2×C4×D15).20C2, (C2×C6).20(C4×D5), (C2×C10).44(C4×S3), (C2×C4).234(S3×D5), C2.1(C2×D30.C2), (C2×C30).101(C2×C4), (C3×C5⋊2C8)⋊35C22, SmallGroup(480,365)
Series: Derived ►Chief ►Lower central ►Upper central
| C15 — C2×D15⋊2C8 |
Generators and relations for C2×D15⋊2C8
G = < a,b,c,d | a2=b15=c2=d8=1, ab=ba, ac=ca, ad=da, cbc=b-1, dbd-1=b11, dcd-1=b10c >
Subgroups: 668 in 152 conjugacy classes, 68 normal (32 characteristic)
C1, C2, C2, C2, C3, C4, C4, C22, C22, C5, S3, C6, C6, C8, C2×C4, 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⋊2C8, C40, C4×D5, C2×Dic5, C2×C20, C22×D5, S3×C8, C2×C3⋊C8, C2×C24, S3×C2×C4, Dic15, C60, D30, C2×C30, C8×D5, C2×C5⋊2C8, C2×C40, C2×C4×D5, S3×C2×C8, C5×C3⋊C8, C3×C5⋊2C8, C4×D15, C2×Dic15, C2×C60, C22×D15, D5×C2×C8, D15⋊2C8, C6×C5⋊2C8, C10×C3⋊C8, C2×C4×D15, C2×D15⋊2C8
Quotients: C1, C2, C4, C22, S3, C8, C2×C4, C23, D5, D6, C2×C8, C22×C4, D10, C4×S3, C22×S3, C22×C8, C4×D5, C22×D5, S3×C8, S3×C2×C4, S3×D5, C8×D5, C2×C4×D5, S3×C2×C8, D30.C2, C2×S3×D5, D5×C2×C8, D15⋊2C8, C2×D30.C2, C2×D15⋊2C8
►On 240 points
Generators in S240
(1 74)(2 75)(3 61)(4 62)(5 63)(6 64)(7 65)(8 66)(9 67)(10 68)(11 69)(12 70)(13 71)(14 72)(15 73)(16 89)(17 90)(18 76)(19 77)(20 78)(21 79)(22 80)(23 81)(24 82)(25 83)(26 84)(27 85)(28 86)(29 87)(30 88)(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)(46 117)(47 118)(48 119)(49 120)(50 106)(51 107)(52 108)(53 109)(54 110)(55 111)(56 112)(57 113)(58 114)(59 115)(60 116)(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)(136 205)(137 206)(138 207)(139 208)(140 209)(141 210)(142 196)(143 197)(144 198)(145 199)(146 200)(147 201)(148 202)(149 203)(150 204)(151 215)(152 216)(153 217)(154 218)(155 219)(156 220)(157 221)(158 222)(159 223)(160 224)(161 225)(162 211)(163 212)(164 213)(165 214)(166 230)(167 231)(168 232)(169 233)(170 234)(171 235)(172 236)(173 237)(174 238)(175 239)(176 240)(177 226)(178 227)(179 228)(180 229)
(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 73)(2 72)(3 71)(4 70)(5 69)(6 68)(7 67)(8 66)(9 65)(10 64)(11 63)(12 62)(13 61)(14 75)(15 74)(16 80)(17 79)(18 78)(19 77)(20 76)(21 90)(22 89)(23 88)(24 87)(25 86)(26 85)(27 84)(28 83)(29 82)(30 81)(31 95)(32 94)(33 93)(34 92)(35 91)(36 105)(37 104)(38 103)(39 102)(40 101)(41 100)(42 99)(43 98)(44 97)(45 96)(46 108)(47 107)(48 106)(49 120)(50 119)(51 118)(52 117)(53 116)(54 115)(55 114)(56 113)(57 112)(58 111)(59 110)(60 109)(121 193)(122 192)(123 191)(124 190)(125 189)(126 188)(127 187)(128 186)(129 185)(130 184)(131 183)(132 182)(133 181)(134 195)(135 194)(136 204)(137 203)(138 202)(139 201)(140 200)(141 199)(142 198)(143 197)(144 196)(145 210)(146 209)(147 208)(148 207)(149 206)(150 205)(151 217)(152 216)(153 215)(154 214)(155 213)(156 212)(157 211)(158 225)(159 224)(160 223)(161 222)(162 221)(163 220)(164 219)(165 218)(166 228)(167 227)(168 226)(169 240)(170 239)(171 238)(172 237)(173 236)(174 235)(175 234)(176 233)(177 232)(178 231)(179 230)(180 229)
(1 173 57 136 27 160 42 121)(2 169 58 147 28 156 43 132)(3 180 59 143 29 152 44 128)(4 176 60 139 30 163 45 124)(5 172 46 150 16 159 31 135)(6 168 47 146 17 155 32 131)(7 179 48 142 18 151 33 127)(8 175 49 138 19 162 34 123)(9 171 50 149 20 158 35 134)(10 167 51 145 21 154 36 130)(11 178 52 141 22 165 37 126)(12 174 53 137 23 161 38 122)(13 170 54 148 24 157 39 133)(14 166 55 144 25 153 40 129)(15 177 56 140 26 164 41 125)(61 229 115 197 87 216 102 186)(62 240 116 208 88 212 103 182)(63 236 117 204 89 223 104 193)(64 232 118 200 90 219 105 189)(65 228 119 196 76 215 91 185)(66 239 120 207 77 211 92 181)(67 235 106 203 78 222 93 192)(68 231 107 199 79 218 94 188)(69 227 108 210 80 214 95 184)(70 238 109 206 81 225 96 195)(71 234 110 202 82 221 97 191)(72 230 111 198 83 217 98 187)(73 226 112 209 84 213 99 183)(74 237 113 205 85 224 100 194)(75 233 114 201 86 220 101 190)
G:=sub<Sym(240)| (1,74)(2,75)(3,61)(4,62)(5,63)(6,64)(7,65)(8,66)(9,67)(10,68)(11,69)(12,70)(13,71)(14,72)(15,73)(16,89)(17,90)(18,76)(19,77)(20,78)(21,79)(22,80)(23,81)(24,82)(25,83)(26,84)(27,85)(28,86)(29,87)(30,88)(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)(46,117)(47,118)(48,119)(49,120)(50,106)(51,107)(52,108)(53,109)(54,110)(55,111)(56,112)(57,113)(58,114)(59,115)(60,116)(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)(136,205)(137,206)(138,207)(139,208)(140,209)(141,210)(142,196)(143,197)(144,198)(145,199)(146,200)(147,201)(148,202)(149,203)(150,204)(151,215)(152,216)(153,217)(154,218)(155,219)(156,220)(157,221)(158,222)(159,223)(160,224)(161,225)(162,211)(163,212)(164,213)(165,214)(166,230)(167,231)(168,232)(169,233)(170,234)(171,235)(172,236)(173,237)(174,238)(175,239)(176,240)(177,226)(178,227)(179,228)(180,229), (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), (1,73)(2,72)(3,71)(4,70)(5,69)(6,68)(7,67)(8,66)(9,65)(10,64)(11,63)(12,62)(13,61)(14,75)(15,74)(16,80)(17,79)(18,78)(19,77)(20,76)(21,90)(22,89)(23,88)(24,87)(25,86)(26,85)(27,84)(28,83)(29,82)(30,81)(31,95)(32,94)(33,93)(34,92)(35,91)(36,105)(37,104)(38,103)(39,102)(40,101)(41,100)(42,99)(43,98)(44,97)(45,96)(46,108)(47,107)(48,106)(49,120)(50,119)(51,118)(52,117)(53,116)(54,115)(55,114)(56,113)(57,112)(58,111)(59,110)(60,109)(121,193)(122,192)(123,191)(124,190)(125,189)(126,188)(127,187)(128,186)(129,185)(130,184)(131,183)(132,182)(133,181)(134,195)(135,194)(136,204)(137,203)(138,202)(139,201)(140,200)(141,199)(142,198)(143,197)(144,196)(145,210)(146,209)(147,208)(148,207)(149,206)(150,205)(151,217)(152,216)(153,215)(154,214)(155,213)(156,212)(157,211)(158,225)(159,224)(160,223)(161,222)(162,221)(163,220)(164,219)(165,218)(166,228)(167,227)(168,226)(169,240)(170,239)(171,238)(172,237)(173,236)(174,235)(175,234)(176,233)(177,232)(178,231)(179,230)(180,229), (1,173,57,136,27,160,42,121)(2,169,58,147,28,156,43,132)(3,180,59,143,29,152,44,128)(4,176,60,139,30,163,45,124)(5,172,46,150,16,159,31,135)(6,168,47,146,17,155,32,131)(7,179,48,142,18,151,33,127)(8,175,49,138,19,162,34,123)(9,171,50,149,20,158,35,134)(10,167,51,145,21,154,36,130)(11,178,52,141,22,165,37,126)(12,174,53,137,23,161,38,122)(13,170,54,148,24,157,39,133)(14,166,55,144,25,153,40,129)(15,177,56,140,26,164,41,125)(61,229,115,197,87,216,102,186)(62,240,116,208,88,212,103,182)(63,236,117,204,89,223,104,193)(64,232,118,200,90,219,105,189)(65,228,119,196,76,215,91,185)(66,239,120,207,77,211,92,181)(67,235,106,203,78,222,93,192)(68,231,107,199,79,218,94,188)(69,227,108,210,80,214,95,184)(70,238,109,206,81,225,96,195)(71,234,110,202,82,221,97,191)(72,230,111,198,83,217,98,187)(73,226,112,209,84,213,99,183)(74,237,113,205,85,224,100,194)(75,233,114,201,86,220,101,190)>;
G:=Group( (1,74)(2,75)(3,61)(4,62)(5,63)(6,64)(7,65)(8,66)(9,67)(10,68)(11,69)(12,70)(13,71)(14,72)(15,73)(16,89)(17,90)(18,76)(19,77)(20,78)(21,79)(22,80)(23,81)(24,82)(25,83)(26,84)(27,85)(28,86)(29,87)(30,88)(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)(46,117)(47,118)(48,119)(49,120)(50,106)(51,107)(52,108)(53,109)(54,110)(55,111)(56,112)(57,113)(58,114)(59,115)(60,116)(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)(136,205)(137,206)(138,207)(139,208)(140,209)(141,210)(142,196)(143,197)(144,198)(145,199)(146,200)(147,201)(148,202)(149,203)(150,204)(151,215)(152,216)(153,217)(154,218)(155,219)(156,220)(157,221)(158,222)(159,223)(160,224)(161,225)(162,211)(163,212)(164,213)(165,214)(166,230)(167,231)(168,232)(169,233)(170,234)(171,235)(172,236)(173,237)(174,238)(175,239)(176,240)(177,226)(178,227)(179,228)(180,229), (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), (1,73)(2,72)(3,71)(4,70)(5,69)(6,68)(7,67)(8,66)(9,65)(10,64)(11,63)(12,62)(13,61)(14,75)(15,74)(16,80)(17,79)(18,78)(19,77)(20,76)(21,90)(22,89)(23,88)(24,87)(25,86)(26,85)(27,84)(28,83)(29,82)(30,81)(31,95)(32,94)(33,93)(34,92)(35,91)(36,105)(37,104)(38,103)(39,102)(40,101)(41,100)(42,99)(43,98)(44,97)(45,96)(46,108)(47,107)(48,106)(49,120)(50,119)(51,118)(52,117)(53,116)(54,115)(55,114)(56,113)(57,112)(58,111)(59,110)(60,109)(121,193)(122,192)(123,191)(124,190)(125,189)(126,188)(127,187)(128,186)(129,185)(130,184)(131,183)(132,182)(133,181)(134,195)(135,194)(136,204)(137,203)(138,202)(139,201)(140,200)(141,199)(142,198)(143,197)(144,196)(145,210)(146,209)(147,208)(148,207)(149,206)(150,205)(151,217)(152,216)(153,215)(154,214)(155,213)(156,212)(157,211)(158,225)(159,224)(160,223)(161,222)(162,221)(163,220)(164,219)(165,218)(166,228)(167,227)(168,226)(169,240)(170,239)(171,238)(172,237)(173,236)(174,235)(175,234)(176,233)(177,232)(178,231)(179,230)(180,229), (1,173,57,136,27,160,42,121)(2,169,58,147,28,156,43,132)(3,180,59,143,29,152,44,128)(4,176,60,139,30,163,45,124)(5,172,46,150,16,159,31,135)(6,168,47,146,17,155,32,131)(7,179,48,142,18,151,33,127)(8,175,49,138,19,162,34,123)(9,171,50,149,20,158,35,134)(10,167,51,145,21,154,36,130)(11,178,52,141,22,165,37,126)(12,174,53,137,23,161,38,122)(13,170,54,148,24,157,39,133)(14,166,55,144,25,153,40,129)(15,177,56,140,26,164,41,125)(61,229,115,197,87,216,102,186)(62,240,116,208,88,212,103,182)(63,236,117,204,89,223,104,193)(64,232,118,200,90,219,105,189)(65,228,119,196,76,215,91,185)(66,239,120,207,77,211,92,181)(67,235,106,203,78,222,93,192)(68,231,107,199,79,218,94,188)(69,227,108,210,80,214,95,184)(70,238,109,206,81,225,96,195)(71,234,110,202,82,221,97,191)(72,230,111,198,83,217,98,187)(73,226,112,209,84,213,99,183)(74,237,113,205,85,224,100,194)(75,233,114,201,86,220,101,190) );
G=PermutationGroup([[(1,74),(2,75),(3,61),(4,62),(5,63),(6,64),(7,65),(8,66),(9,67),(10,68),(11,69),(12,70),(13,71),(14,72),(15,73),(16,89),(17,90),(18,76),(19,77),(20,78),(21,79),(22,80),(23,81),(24,82),(25,83),(26,84),(27,85),(28,86),(29,87),(30,88),(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),(46,117),(47,118),(48,119),(49,120),(50,106),(51,107),(52,108),(53,109),(54,110),(55,111),(56,112),(57,113),(58,114),(59,115),(60,116),(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),(136,205),(137,206),(138,207),(139,208),(140,209),(141,210),(142,196),(143,197),(144,198),(145,199),(146,200),(147,201),(148,202),(149,203),(150,204),(151,215),(152,216),(153,217),(154,218),(155,219),(156,220),(157,221),(158,222),(159,223),(160,224),(161,225),(162,211),(163,212),(164,213),(165,214),(166,230),(167,231),(168,232),(169,233),(170,234),(171,235),(172,236),(173,237),(174,238),(175,239),(176,240),(177,226),(178,227),(179,228),(180,229)], [(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)], [(1,73),(2,72),(3,71),(4,70),(5,69),(6,68),(7,67),(8,66),(9,65),(10,64),(11,63),(12,62),(13,61),(14,75),(15,74),(16,80),(17,79),(18,78),(19,77),(20,76),(21,90),(22,89),(23,88),(24,87),(25,86),(26,85),(27,84),(28,83),(29,82),(30,81),(31,95),(32,94),(33,93),(34,92),(35,91),(36,105),(37,104),(38,103),(39,102),(40,101),(41,100),(42,99),(43,98),(44,97),(45,96),(46,108),(47,107),(48,106),(49,120),(50,119),(51,118),(52,117),(53,116),(54,115),(55,114),(56,113),(57,112),(58,111),(59,110),(60,109),(121,193),(122,192),(123,191),(124,190),(125,189),(126,188),(127,187),(128,186),(129,185),(130,184),(131,183),(132,182),(133,181),(134,195),(135,194),(136,204),(137,203),(138,202),(139,201),(140,200),(141,199),(142,198),(143,197),(144,196),(145,210),(146,209),(147,208),(148,207),(149,206),(150,205),(151,217),(152,216),(153,215),(154,214),(155,213),(156,212),(157,211),(158,225),(159,224),(160,223),(161,222),(162,221),(163,220),(164,219),(165,218),(166,228),(167,227),(168,226),(169,240),(170,239),(171,238),(172,237),(173,236),(174,235),(175,234),(176,233),(177,232),(178,231),(179,230),(180,229)], [(1,173,57,136,27,160,42,121),(2,169,58,147,28,156,43,132),(3,180,59,143,29,152,44,128),(4,176,60,139,30,163,45,124),(5,172,46,150,16,159,31,135),(6,168,47,146,17,155,32,131),(7,179,48,142,18,151,33,127),(8,175,49,138,19,162,34,123),(9,171,50,149,20,158,35,134),(10,167,51,145,21,154,36,130),(11,178,52,141,22,165,37,126),(12,174,53,137,23,161,38,122),(13,170,54,148,24,157,39,133),(14,166,55,144,25,153,40,129),(15,177,56,140,26,164,41,125),(61,229,115,197,87,216,102,186),(62,240,116,208,88,212,103,182),(63,236,117,204,89,223,104,193),(64,232,118,200,90,219,105,189),(65,228,119,196,76,215,91,185),(66,239,120,207,77,211,92,181),(67,235,106,203,78,222,93,192),(68,231,107,199,79,218,94,188),(69,227,108,210,80,214,95,184),(70,238,109,206,81,225,96,195),(71,234,110,202,82,221,97,191),(72,230,111,198,83,217,98,187),(73,226,112,209,84,213,99,183),(74,237,113,205,85,224,100,194),(75,233,114,201,86,220,101,190)]])
96 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 5A | 5B | 6A | 6B | 6C | 8A | ··· | 8H | 8I | ··· | 8P | 10A | ··· | 10F | 12A | 12B | 12C | 12D | 15A | 15B | 20A | ··· | 20H | 24A | ··· | 24H | 30A | ··· | 30F | 40A | ··· | 40P | 60A | ··· | 60H |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 8 | ··· | 8 | 8 | ··· | 8 | 10 | ··· | 10 | 12 | 12 | 12 | 12 | 15 | 15 | 20 | ··· | 20 | 24 | ··· | 24 | 30 | ··· | 30 | 40 | ··· | 40 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 15 | 15 | 15 | 15 | 2 | 1 | 1 | 1 | 1 | 15 | 15 | 15 | 15 | 2 | 2 | 2 | 2 | 2 | 3 | ··· | 3 | 5 | ··· | 5 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 2 | ··· | 2 | 10 | ··· | 10 | 4 | ··· | 4 | 6 | ··· | 6 | 4 | ··· | 4 |
96 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |||||||||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | C4 | C4 | C8 | S3 | D5 | D6 | D6 | D10 | D10 | C4×S3 | C4×S3 | C4×D5 | C4×D5 | S3×C8 | C8×D5 | S3×D5 | D30.C2 | C2×S3×D5 | D30.C2 | D15⋊2C8 |
| kernel | C2×D15⋊2C8 | D15⋊2C8 | C6×C5⋊2C8 | C10×C3⋊C8 | C2×C4×D15 | C4×D15 | C2×Dic15 | C22×D15 | D30 | C2×C5⋊2C8 | C2×C3⋊C8 | C5⋊2C8 | C2×C20 | C3⋊C8 | C2×C12 | C20 | C2×C10 | C12 | C2×C6 | C10 | C6 | C2×C4 | C4 | C4 | C22 | C2 |
| # reps | 1 | 4 | 1 | 1 | 1 | 4 | 2 | 2 | 16 | 1 | 2 | 2 | 1 | 4 | 2 | 2 | 2 | 4 | 4 | 8 | 16 | 2 | 2 | 2 | 2 | 8 |
Matrix representation of C2×D15⋊2C8 ►in GL5(𝔽241)
| 240 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 189 | 190 | 0 | 0 |
| 0 | 52 | 0 | 0 | 0 |
| 0 | 0 | 0 | 240 | 240 |
| 0 | 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 52 | 1 | 0 | 0 |
| 0 | 189 | 189 | 0 | 0 |
| 0 | 0 | 0 | 240 | 240 |
| 0 | 0 | 0 | 0 | 1 |
| 240 | 0 | 0 | 0 | 0 |
| 0 | 233 | 0 | 0 | 0 |
| 0 | 0 | 233 | 0 | 0 |
| 0 | 0 | 0 | 8 | 0 |
| 0 | 0 | 0 | 233 | 233 |
G:=sub<GL(5,GF(241))| [240,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,189,52,0,0,0,190,0,0,0,0,0,0,240,1,0,0,0,240,0],[1,0,0,0,0,0,52,189,0,0,0,1,189,0,0,0,0,0,240,0,0,0,0,240,1],[240,0,0,0,0,0,233,0,0,0,0,0,233,0,0,0,0,0,8,233,0,0,0,0,233] >;
C2×D15⋊2C8 in GAP, Magma, Sage, TeX
C_2\times D_{15}\rtimes_2C_8 % in TeX
G:=Group("C2xD15:2C8"); // GroupNames label
G:=SmallGroup(480,365);
// by ID
G=gap.SmallGroup(480,365);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,56,64,80,1356,18822]);
// 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^11,d*c*d^-1=b^10*c>;
// generators/relations