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G = C2×C15⋊D8order 480 = 25·3·5

Direct product of C2 and C15⋊D8

direct product, metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C2×C15⋊D8, C301D8, D2020D6, C60.80D4, D1220D10, C60.149C23, C154(C2×D8), C62(D4⋊D5), (C2×D12)⋊7D5, (C2×D20)⋊7S3, (C6×D20)⋊9C2, C102(D4⋊S3), (C10×D12)⋊9C2, (C2×C30).39D4, C30.71(C2×D4), (C2×C20).83D6, (C2×C12).84D10, C4.5(C15⋊D4), C153C837C22, (C3×D20)⋊27C22, (C5×D12)⋊27C22, C20.23(C3⋊D4), C12.25(C5⋊D4), C20.84(C22×S3), C12.84(C22×D5), (C2×C60).187C22, C22.19(C15⋊D4), C53(C2×D4⋊S3), C33(C2×D4⋊D5), C4.122(C2×S3×D5), (C2×C153C8)⋊15C2, C6.71(C2×C5⋊D4), C2.5(C2×C15⋊D4), (C2×C4).196(S3×D5), C10.72(C2×C3⋊D4), (C2×C6).51(C5⋊D4), (C2×C10).51(C3⋊D4), SmallGroup(480,372)

Series: Derived Chief Lower central Upper central

C1C60 — C2×C15⋊D8
C1C5C15C30C60C3×D20C15⋊D8 — C2×C15⋊D8
C15C30C60 — C2×C15⋊D8
C1C22C2×C4

Generators and relations for C2×C15⋊D8
 G = < a,b,c,d | a2=b15=c8=d2=1, ab=ba, ac=ca, ad=da, cbc-1=b-1, dbd=b4, dcd=c-1 >

Subgroups: 764 in 152 conjugacy classes, 52 normal (30 characteristic)
C1, C2, C2 [×2], C2 [×4], C3, C4 [×2], C22, C22 [×8], C5, S3 [×2], C6, C6 [×2], C6 [×2], C8 [×2], C2×C4, D4 [×6], C23 [×2], D5 [×2], C10, C10 [×2], C10 [×2], C12 [×2], D6 [×4], C2×C6, C2×C6 [×4], C15, C2×C8, D8 [×4], C2×D4 [×2], C20 [×2], D10 [×4], C2×C10, C2×C10 [×4], C3⋊C8 [×2], D12 [×2], D12, C2×C12, C3×D4 [×3], C22×S3, C22×C6, C5×S3 [×2], C3×D5 [×2], C30, C30 [×2], C2×D8, C52C8 [×2], D20 [×2], D20, C2×C20, C5×D4 [×3], C22×D5, C22×C10, C2×C3⋊C8, D4⋊S3 [×4], C2×D12, C6×D4, C60 [×2], C6×D5 [×4], S3×C10 [×4], C2×C30, C2×C52C8, D4⋊D5 [×4], C2×D20, D4×C10, C2×D4⋊S3, C153C8 [×2], C3×D20 [×2], C3×D20, C5×D12 [×2], C5×D12, C2×C60, D5×C2×C6, S3×C2×C10, C2×D4⋊D5, C15⋊D8 [×4], C2×C153C8, C6×D20, C10×D12, C2×C15⋊D8
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], D8 [×2], C2×D4, D10 [×3], C3⋊D4 [×2], C22×S3, C2×D8, C5⋊D4 [×2], C22×D5, D4⋊S3 [×2], C2×C3⋊D4, S3×D5, D4⋊D5 [×2], C2×C5⋊D4, C2×D4⋊S3, C15⋊D4 [×2], C2×S3×D5, C2×D4⋊D5, C15⋊D8 [×2], C2×C15⋊D4, C2×C15⋊D8

Smallest permutation representation of C2×C15⋊D8
On 240 points
Generators in S240
(1 69)(2 70)(3 71)(4 72)(5 73)(6 74)(7 75)(8 61)(9 62)(10 63)(11 64)(12 65)(13 66)(14 67)(15 68)(16 78)(17 79)(18 80)(19 81)(20 82)(21 83)(22 84)(23 85)(24 86)(25 87)(26 88)(27 89)(28 90)(29 76)(30 77)(31 98)(32 99)(33 100)(34 101)(35 102)(36 103)(37 104)(38 105)(39 91)(40 92)(41 93)(42 94)(43 95)(44 96)(45 97)(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)(121 183)(122 184)(123 185)(124 186)(125 187)(126 188)(127 189)(128 190)(129 191)(130 192)(131 193)(132 194)(133 195)(134 181)(135 182)(136 207)(137 208)(138 209)(139 210)(140 196)(141 197)(142 198)(143 199)(144 200)(145 201)(146 202)(147 203)(148 204)(149 205)(150 206)(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)(166 237)(167 238)(168 239)(169 240)(170 226)(171 227)(172 228)(173 229)(174 230)(175 231)(176 232)(177 233)(178 234)(179 235)(180 236)
(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)
(1 181 38 235 19 207 50 220)(2 195 39 234 20 206 51 219)(3 194 40 233 21 205 52 218)(4 193 41 232 22 204 53 217)(5 192 42 231 23 203 54 216)(6 191 43 230 24 202 55 215)(7 190 44 229 25 201 56 214)(8 189 45 228 26 200 57 213)(9 188 31 227 27 199 58 212)(10 187 32 226 28 198 59 211)(11 186 33 240 29 197 60 225)(12 185 34 239 30 196 46 224)(13 184 35 238 16 210 47 223)(14 183 36 237 17 209 48 222)(15 182 37 236 18 208 49 221)(61 127 97 172 88 144 113 153)(62 126 98 171 89 143 114 152)(63 125 99 170 90 142 115 151)(64 124 100 169 76 141 116 165)(65 123 101 168 77 140 117 164)(66 122 102 167 78 139 118 163)(67 121 103 166 79 138 119 162)(68 135 104 180 80 137 120 161)(69 134 105 179 81 136 106 160)(70 133 91 178 82 150 107 159)(71 132 92 177 83 149 108 158)(72 131 93 176 84 148 109 157)(73 130 94 175 85 147 110 156)(74 129 95 174 86 146 111 155)(75 128 96 173 87 145 112 154)
(1 69)(2 73)(3 62)(4 66)(5 70)(6 74)(7 63)(8 67)(9 71)(10 75)(11 64)(12 68)(13 72)(14 61)(15 65)(16 84)(17 88)(18 77)(19 81)(20 85)(21 89)(22 78)(23 82)(24 86)(25 90)(26 79)(27 83)(28 87)(29 76)(30 80)(31 108)(32 112)(33 116)(34 120)(35 109)(36 113)(37 117)(38 106)(39 110)(40 114)(41 118)(42 107)(43 111)(44 115)(45 119)(46 104)(47 93)(48 97)(49 101)(50 105)(51 94)(52 98)(53 102)(54 91)(55 95)(56 99)(57 103)(58 92)(59 96)(60 100)(121 213)(122 217)(123 221)(124 225)(125 214)(126 218)(127 222)(128 211)(129 215)(130 219)(131 223)(132 212)(133 216)(134 220)(135 224)(136 235)(137 239)(138 228)(139 232)(140 236)(141 240)(142 229)(143 233)(144 237)(145 226)(146 230)(147 234)(148 238)(149 227)(150 231)(151 190)(152 194)(153 183)(154 187)(155 191)(156 195)(157 184)(158 188)(159 192)(160 181)(161 185)(162 189)(163 193)(164 182)(165 186)(166 200)(167 204)(168 208)(169 197)(170 201)(171 205)(172 209)(173 198)(174 202)(175 206)(176 210)(177 199)(178 203)(179 207)(180 196)

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

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

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

60 conjugacy classes

class 1 2A2B2C2D2E2F2G 3 4A4B5A5B6A6B6C6D6E6F6G8A8B8C8D10A···10F10G···10N12A12B15A15B20A20B20C20D30A···30F60A···60H
order12222222344556666666888810···1010···10121215152020202030···3060···60
size1111121220202222222220202020303030302···212···12444444444···44···4

60 irreducible representations

dim1111122222222222224444444
type+++++++++++++++++-+-
imageC1C2C2C2C2S3D4D4D5D6D6D8D10D10C3⋊D4C3⋊D4C5⋊D4C5⋊D4D4⋊S3S3×D5D4⋊D5C15⋊D4C2×S3×D5C15⋊D4C15⋊D8
kernelC2×C15⋊D8C15⋊D8C2×C153C8C6×D20C10×D12C2×D20C60C2×C30C2×D12D20C2×C20C30D12C2×C12C20C2×C10C12C2×C6C10C2×C4C6C4C4C22C2
# reps1411111122144222442242228

Matrix representation of C2×C15⋊D8 in GL6(𝔽241)

24000000
02400000
001000
000100
00002400
00000240
,
100000
010000
0024019000
005119000
0000150
0000172225
,
230110000
2302300000
0016517200
001927600
00002193
0000226239
,
24000000
010000
0015100
00024000
00002400
00000240

G:=sub<GL(6,GF(241))| [240,0,0,0,0,0,0,240,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,240,0,0,0,0,0,0,240],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,240,51,0,0,0,0,190,190,0,0,0,0,0,0,15,172,0,0,0,0,0,225],[230,230,0,0,0,0,11,230,0,0,0,0,0,0,165,192,0,0,0,0,172,76,0,0,0,0,0,0,2,226,0,0,0,0,193,239],[240,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,51,240,0,0,0,0,0,0,240,0,0,0,0,0,0,240] >;

C2×C15⋊D8 in GAP, Magma, Sage, TeX

C_2\times C_{15}\rtimes D_8
% in TeX

G:=Group("C2xC15:D8");
// GroupNames label

G:=SmallGroup(480,372);
// by ID

G=gap.SmallGroup(480,372);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,141,675,346,80,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^2=b^15=c^8=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^-1,d*b*d=b^4,d*c*d=c^-1>;
// generators/relations

׿
×
𝔽