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## G = C2×D15⋊2C8order 480 = 25·3·5

### Direct product of C2 and D15⋊2C8

Series: Derived Chief Lower central Upper central

 Derived series C1 — C15 — C2×D15⋊2C8
 Chief series C1 — C5 — C15 — C30 — C60 — C3×C5⋊2C8 — D15⋊2C8 — C2×D15⋊2C8
 Lower central C15 — C2×D15⋊2C8
 Upper central C1 — C2×C4

Generators and relations for C2×D152C8
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 [×2], C2 [×4], C3, C4 [×2], C4 [×2], C22, C22 [×6], C5, S3 [×4], C6, C6 [×2], C8 [×4], C2×C4, C2×C4 [×5], C23, D5 [×4], C10, C10 [×2], Dic3 [×2], C12 [×2], D6 [×6], C2×C6, C15, C2×C8 [×6], C22×C4, Dic5 [×2], C20 [×2], D10 [×6], C2×C10, C3⋊C8 [×2], C24 [×2], C4×S3 [×4], C2×Dic3, C2×C12, C22×S3, D15 [×4], C30, C30 [×2], C22×C8, C52C8 [×2], C40 [×2], C4×D5 [×4], C2×Dic5, C2×C20, C22×D5, S3×C8 [×4], C2×C3⋊C8, C2×C24, S3×C2×C4, Dic15 [×2], C60 [×2], D30 [×6], C2×C30, C8×D5 [×4], C2×C52C8, C2×C40, C2×C4×D5, S3×C2×C8, C5×C3⋊C8 [×2], C3×C52C8 [×2], C4×D15 [×4], C2×Dic15, C2×C60, C22×D15, D5×C2×C8, D152C8 [×4], C6×C52C8, C10×C3⋊C8, C2×C4×D15, C2×D152C8
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], S3, C8 [×4], C2×C4 [×6], C23, D5, D6 [×3], C2×C8 [×6], C22×C4, D10 [×3], C4×S3 [×2], C22×S3, C22×C8, C4×D5 [×2], C22×D5, S3×C8 [×2], S3×C2×C4, S3×D5, C8×D5 [×2], C2×C4×D5, S3×C2×C8, D30.C2 [×2], C2×S3×D5, D5×C2×C8, D152C8 [×2], C2×D30.C2, C2×D152C8

Smallest permutation representation of C2×D152C8
On 240 points
Generators in S240
(1 71)(2 72)(3 73)(4 74)(5 75)(6 61)(7 62)(8 63)(9 64)(10 65)(11 66)(12 67)(13 68)(14 69)(15 70)(16 85)(17 86)(18 87)(19 88)(20 89)(21 90)(22 76)(23 77)(24 78)(25 79)(26 80)(27 81)(28 82)(29 83)(30 84)(31 101)(32 102)(33 103)(34 104)(35 105)(36 91)(37 92)(38 93)(39 94)(40 95)(41 96)(42 97)(43 98)(44 99)(45 100)(46 110)(47 111)(48 112)(49 113)(50 114)(51 115)(52 116)(53 117)(54 118)(55 119)(56 120)(57 106)(58 107)(59 108)(60 109)(121 190)(122 191)(123 192)(124 193)(125 194)(126 195)(127 181)(128 182)(129 183)(130 184)(131 185)(132 186)(133 187)(134 188)(135 189)(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)(151 211)(152 212)(153 213)(154 214)(155 215)(156 216)(157 217)(158 218)(159 219)(160 220)(161 221)(162 222)(163 223)(164 224)(165 225)(166 232)(167 233)(168 234)(169 235)(170 236)(171 237)(172 238)(173 239)(174 240)(175 226)(176 227)(177 228)(178 229)(179 230)(180 231)
(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 70)(2 69)(3 68)(4 67)(5 66)(6 65)(7 64)(8 63)(9 62)(10 61)(11 75)(12 74)(13 73)(14 72)(15 71)(16 81)(17 80)(18 79)(19 78)(20 77)(21 76)(22 90)(23 89)(24 88)(25 87)(26 86)(27 85)(28 84)(29 83)(30 82)(31 98)(32 97)(33 96)(34 95)(35 94)(36 93)(37 92)(38 91)(39 105)(40 104)(41 103)(42 102)(43 101)(44 100)(45 99)(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)(121 185)(122 184)(123 183)(124 182)(125 181)(126 195)(127 194)(128 193)(129 192)(130 191)(131 190)(132 189)(133 188)(134 187)(135 186)(136 202)(137 201)(138 200)(139 199)(140 198)(141 197)(142 196)(143 210)(144 209)(145 208)(146 207)(147 206)(148 205)(149 204)(150 203)(151 224)(152 223)(153 222)(154 221)(155 220)(156 219)(157 218)(158 217)(159 216)(160 215)(161 214)(162 213)(163 212)(164 211)(165 225)(166 234)(167 233)(168 232)(169 231)(170 230)(171 229)(172 228)(173 227)(174 226)(175 240)(176 239)(177 238)(178 237)(179 236)(180 235)
(1 175 53 143 22 158 45 134)(2 171 54 139 23 154 31 130)(3 167 55 150 24 165 32 126)(4 178 56 146 25 161 33 122)(5 174 57 142 26 157 34 133)(6 170 58 138 27 153 35 129)(7 166 59 149 28 164 36 125)(8 177 60 145 29 160 37 121)(9 173 46 141 30 156 38 132)(10 169 47 137 16 152 39 128)(11 180 48 148 17 163 40 124)(12 176 49 144 18 159 41 135)(13 172 50 140 19 155 42 131)(14 168 51 136 20 151 43 127)(15 179 52 147 21 162 44 123)(61 236 107 206 81 213 105 183)(62 232 108 202 82 224 91 194)(63 228 109 198 83 220 92 190)(64 239 110 209 84 216 93 186)(65 235 111 205 85 212 94 182)(66 231 112 201 86 223 95 193)(67 227 113 197 87 219 96 189)(68 238 114 208 88 215 97 185)(69 234 115 204 89 211 98 181)(70 230 116 200 90 222 99 192)(71 226 117 196 76 218 100 188)(72 237 118 207 77 214 101 184)(73 233 119 203 78 225 102 195)(74 229 120 199 79 221 103 191)(75 240 106 210 80 217 104 187)

G:=sub<Sym(240)| (1,71)(2,72)(3,73)(4,74)(5,75)(6,61)(7,62)(8,63)(9,64)(10,65)(11,66)(12,67)(13,68)(14,69)(15,70)(16,85)(17,86)(18,87)(19,88)(20,89)(21,90)(22,76)(23,77)(24,78)(25,79)(26,80)(27,81)(28,82)(29,83)(30,84)(31,101)(32,102)(33,103)(34,104)(35,105)(36,91)(37,92)(38,93)(39,94)(40,95)(41,96)(42,97)(43,98)(44,99)(45,100)(46,110)(47,111)(48,112)(49,113)(50,114)(51,115)(52,116)(53,117)(54,118)(55,119)(56,120)(57,106)(58,107)(59,108)(60,109)(121,190)(122,191)(123,192)(124,193)(125,194)(126,195)(127,181)(128,182)(129,183)(130,184)(131,185)(132,186)(133,187)(134,188)(135,189)(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)(151,211)(152,212)(153,213)(154,214)(155,215)(156,216)(157,217)(158,218)(159,219)(160,220)(161,221)(162,222)(163,223)(164,224)(165,225)(166,232)(167,233)(168,234)(169,235)(170,236)(171,237)(172,238)(173,239)(174,240)(175,226)(176,227)(177,228)(178,229)(179,230)(180,231), (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), (1,70)(2,69)(3,68)(4,67)(5,66)(6,65)(7,64)(8,63)(9,62)(10,61)(11,75)(12,74)(13,73)(14,72)(15,71)(16,81)(17,80)(18,79)(19,78)(20,77)(21,76)(22,90)(23,89)(24,88)(25,87)(26,86)(27,85)(28,84)(29,83)(30,82)(31,98)(32,97)(33,96)(34,95)(35,94)(36,93)(37,92)(38,91)(39,105)(40,104)(41,103)(42,102)(43,101)(44,100)(45,99)(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)(121,185)(122,184)(123,183)(124,182)(125,181)(126,195)(127,194)(128,193)(129,192)(130,191)(131,190)(132,189)(133,188)(134,187)(135,186)(136,202)(137,201)(138,200)(139,199)(140,198)(141,197)(142,196)(143,210)(144,209)(145,208)(146,207)(147,206)(148,205)(149,204)(150,203)(151,224)(152,223)(153,222)(154,221)(155,220)(156,219)(157,218)(158,217)(159,216)(160,215)(161,214)(162,213)(163,212)(164,211)(165,225)(166,234)(167,233)(168,232)(169,231)(170,230)(171,229)(172,228)(173,227)(174,226)(175,240)(176,239)(177,238)(178,237)(179,236)(180,235), (1,175,53,143,22,158,45,134)(2,171,54,139,23,154,31,130)(3,167,55,150,24,165,32,126)(4,178,56,146,25,161,33,122)(5,174,57,142,26,157,34,133)(6,170,58,138,27,153,35,129)(7,166,59,149,28,164,36,125)(8,177,60,145,29,160,37,121)(9,173,46,141,30,156,38,132)(10,169,47,137,16,152,39,128)(11,180,48,148,17,163,40,124)(12,176,49,144,18,159,41,135)(13,172,50,140,19,155,42,131)(14,168,51,136,20,151,43,127)(15,179,52,147,21,162,44,123)(61,236,107,206,81,213,105,183)(62,232,108,202,82,224,91,194)(63,228,109,198,83,220,92,190)(64,239,110,209,84,216,93,186)(65,235,111,205,85,212,94,182)(66,231,112,201,86,223,95,193)(67,227,113,197,87,219,96,189)(68,238,114,208,88,215,97,185)(69,234,115,204,89,211,98,181)(70,230,116,200,90,222,99,192)(71,226,117,196,76,218,100,188)(72,237,118,207,77,214,101,184)(73,233,119,203,78,225,102,195)(74,229,120,199,79,221,103,191)(75,240,106,210,80,217,104,187)>;

G:=Group( (1,71)(2,72)(3,73)(4,74)(5,75)(6,61)(7,62)(8,63)(9,64)(10,65)(11,66)(12,67)(13,68)(14,69)(15,70)(16,85)(17,86)(18,87)(19,88)(20,89)(21,90)(22,76)(23,77)(24,78)(25,79)(26,80)(27,81)(28,82)(29,83)(30,84)(31,101)(32,102)(33,103)(34,104)(35,105)(36,91)(37,92)(38,93)(39,94)(40,95)(41,96)(42,97)(43,98)(44,99)(45,100)(46,110)(47,111)(48,112)(49,113)(50,114)(51,115)(52,116)(53,117)(54,118)(55,119)(56,120)(57,106)(58,107)(59,108)(60,109)(121,190)(122,191)(123,192)(124,193)(125,194)(126,195)(127,181)(128,182)(129,183)(130,184)(131,185)(132,186)(133,187)(134,188)(135,189)(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)(151,211)(152,212)(153,213)(154,214)(155,215)(156,216)(157,217)(158,218)(159,219)(160,220)(161,221)(162,222)(163,223)(164,224)(165,225)(166,232)(167,233)(168,234)(169,235)(170,236)(171,237)(172,238)(173,239)(174,240)(175,226)(176,227)(177,228)(178,229)(179,230)(180,231), (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), (1,70)(2,69)(3,68)(4,67)(5,66)(6,65)(7,64)(8,63)(9,62)(10,61)(11,75)(12,74)(13,73)(14,72)(15,71)(16,81)(17,80)(18,79)(19,78)(20,77)(21,76)(22,90)(23,89)(24,88)(25,87)(26,86)(27,85)(28,84)(29,83)(30,82)(31,98)(32,97)(33,96)(34,95)(35,94)(36,93)(37,92)(38,91)(39,105)(40,104)(41,103)(42,102)(43,101)(44,100)(45,99)(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)(121,185)(122,184)(123,183)(124,182)(125,181)(126,195)(127,194)(128,193)(129,192)(130,191)(131,190)(132,189)(133,188)(134,187)(135,186)(136,202)(137,201)(138,200)(139,199)(140,198)(141,197)(142,196)(143,210)(144,209)(145,208)(146,207)(147,206)(148,205)(149,204)(150,203)(151,224)(152,223)(153,222)(154,221)(155,220)(156,219)(157,218)(158,217)(159,216)(160,215)(161,214)(162,213)(163,212)(164,211)(165,225)(166,234)(167,233)(168,232)(169,231)(170,230)(171,229)(172,228)(173,227)(174,226)(175,240)(176,239)(177,238)(178,237)(179,236)(180,235), (1,175,53,143,22,158,45,134)(2,171,54,139,23,154,31,130)(3,167,55,150,24,165,32,126)(4,178,56,146,25,161,33,122)(5,174,57,142,26,157,34,133)(6,170,58,138,27,153,35,129)(7,166,59,149,28,164,36,125)(8,177,60,145,29,160,37,121)(9,173,46,141,30,156,38,132)(10,169,47,137,16,152,39,128)(11,180,48,148,17,163,40,124)(12,176,49,144,18,159,41,135)(13,172,50,140,19,155,42,131)(14,168,51,136,20,151,43,127)(15,179,52,147,21,162,44,123)(61,236,107,206,81,213,105,183)(62,232,108,202,82,224,91,194)(63,228,109,198,83,220,92,190)(64,239,110,209,84,216,93,186)(65,235,111,205,85,212,94,182)(66,231,112,201,86,223,95,193)(67,227,113,197,87,219,96,189)(68,238,114,208,88,215,97,185)(69,234,115,204,89,211,98,181)(70,230,116,200,90,222,99,192)(71,226,117,196,76,218,100,188)(72,237,118,207,77,214,101,184)(73,233,119,203,78,225,102,195)(74,229,120,199,79,221,103,191)(75,240,106,210,80,217,104,187) );

G=PermutationGroup([(1,71),(2,72),(3,73),(4,74),(5,75),(6,61),(7,62),(8,63),(9,64),(10,65),(11,66),(12,67),(13,68),(14,69),(15,70),(16,85),(17,86),(18,87),(19,88),(20,89),(21,90),(22,76),(23,77),(24,78),(25,79),(26,80),(27,81),(28,82),(29,83),(30,84),(31,101),(32,102),(33,103),(34,104),(35,105),(36,91),(37,92),(38,93),(39,94),(40,95),(41,96),(42,97),(43,98),(44,99),(45,100),(46,110),(47,111),(48,112),(49,113),(50,114),(51,115),(52,116),(53,117),(54,118),(55,119),(56,120),(57,106),(58,107),(59,108),(60,109),(121,190),(122,191),(123,192),(124,193),(125,194),(126,195),(127,181),(128,182),(129,183),(130,184),(131,185),(132,186),(133,187),(134,188),(135,189),(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),(151,211),(152,212),(153,213),(154,214),(155,215),(156,216),(157,217),(158,218),(159,219),(160,220),(161,221),(162,222),(163,223),(164,224),(165,225),(166,232),(167,233),(168,234),(169,235),(170,236),(171,237),(172,238),(173,239),(174,240),(175,226),(176,227),(177,228),(178,229),(179,230),(180,231)], [(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)], [(1,70),(2,69),(3,68),(4,67),(5,66),(6,65),(7,64),(8,63),(9,62),(10,61),(11,75),(12,74),(13,73),(14,72),(15,71),(16,81),(17,80),(18,79),(19,78),(20,77),(21,76),(22,90),(23,89),(24,88),(25,87),(26,86),(27,85),(28,84),(29,83),(30,82),(31,98),(32,97),(33,96),(34,95),(35,94),(36,93),(37,92),(38,91),(39,105),(40,104),(41,103),(42,102),(43,101),(44,100),(45,99),(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),(121,185),(122,184),(123,183),(124,182),(125,181),(126,195),(127,194),(128,193),(129,192),(130,191),(131,190),(132,189),(133,188),(134,187),(135,186),(136,202),(137,201),(138,200),(139,199),(140,198),(141,197),(142,196),(143,210),(144,209),(145,208),(146,207),(147,206),(148,205),(149,204),(150,203),(151,224),(152,223),(153,222),(154,221),(155,220),(156,219),(157,218),(158,217),(159,216),(160,215),(161,214),(162,213),(163,212),(164,211),(165,225),(166,234),(167,233),(168,232),(169,231),(170,230),(171,229),(172,228),(173,227),(174,226),(175,240),(176,239),(177,238),(178,237),(179,236),(180,235)], [(1,175,53,143,22,158,45,134),(2,171,54,139,23,154,31,130),(3,167,55,150,24,165,32,126),(4,178,56,146,25,161,33,122),(5,174,57,142,26,157,34,133),(6,170,58,138,27,153,35,129),(7,166,59,149,28,164,36,125),(8,177,60,145,29,160,37,121),(9,173,46,141,30,156,38,132),(10,169,47,137,16,152,39,128),(11,180,48,148,17,163,40,124),(12,176,49,144,18,159,41,135),(13,172,50,140,19,155,42,131),(14,168,51,136,20,151,43,127),(15,179,52,147,21,162,44,123),(61,236,107,206,81,213,105,183),(62,232,108,202,82,224,91,194),(63,228,109,198,83,220,92,190),(64,239,110,209,84,216,93,186),(65,235,111,205,85,212,94,182),(66,231,112,201,86,223,95,193),(67,227,113,197,87,219,96,189),(68,238,114,208,88,215,97,185),(69,234,115,204,89,211,98,181),(70,230,116,200,90,222,99,192),(71,226,117,196,76,218,100,188),(72,237,118,207,77,214,101,184),(73,233,119,203,78,225,102,195),(74,229,120,199,79,221,103,191),(75,240,106,210,80,217,104,187)])

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×D152C8 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×D152C8 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

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