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G = C2×C15⋊SD16order 480 = 25·3·5

Direct product of C2 and C15⋊SD16

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

Aliases: C2×C15⋊SD16, C304SD16, C60.41D4, C12.16D20, Dic1017D6, C60.107C23, D60.45C22, C3⋊C827D10, C157(C2×SD16), C62(C40⋊C2), C6.52(C2×D20), (C2×C30).57D4, C30.89(C2×D4), (C2×C6).41D20, (C2×Dic10)⋊1S3, (C6×Dic10)⋊4C2, (C2×D60).13C2, (C2×C20).287D6, C4.7(C3⋊D20), C101(Q82S3), (C2×C12).100D10, C20.55(C3⋊D4), C12.98(C22×D5), C20.157(C22×S3), (C2×C60).106C22, (C3×Dic10)⋊19C22, C22.21(C3⋊D20), (C2×C3⋊C8)⋊8D5, (C10×C3⋊C8)⋊8C2, C33(C2×C40⋊C2), C51(C2×Q82S3), C4.106(C2×S3×D5), (C5×C3⋊C8)⋊31C22, (C2×C4).97(S3×D5), C10.7(C2×C3⋊D4), C2.11(C2×C3⋊D20), (C2×C10).33(C3⋊D4), SmallGroup(480,390)

Series: Derived Chief Lower central Upper central

C1C60 — C2×C15⋊SD16
C1C5C15C30C60C3×Dic10C15⋊SD16 — C2×C15⋊SD16
C15C30C60 — C2×C15⋊SD16
C1C22C2×C4

Generators and relations for C2×C15⋊SD16
 G = < a,b,c,d | a2=b15=c8=d2=1, ab=ba, ac=ca, ad=da, cbc-1=b11, dbd=b-1, dcd=c3 >

Subgroups: 956 in 136 conjugacy classes, 52 normal (30 characteristic)
C1, C2, C2 [×2], C2 [×2], C3, C4 [×2], C4 [×2], C22, C22 [×4], C5, S3 [×2], C6, C6 [×2], C8 [×2], C2×C4, C2×C4, D4 [×3], Q8 [×3], C23, D5 [×2], C10, C10 [×2], C12 [×2], C12 [×2], D6 [×4], C2×C6, C15, C2×C8, SD16 [×4], C2×D4, C2×Q8, Dic5 [×2], C20 [×2], D10 [×4], C2×C10, C3⋊C8 [×2], D12 [×3], C2×C12, C2×C12, C3×Q8 [×3], C22×S3, D15 [×2], C30, C30 [×2], C2×SD16, C40 [×2], Dic10 [×2], Dic10, D20 [×3], C2×Dic5, C2×C20, C22×D5, C2×C3⋊C8, Q82S3 [×4], C2×D12, C6×Q8, C3×Dic5 [×2], C60 [×2], D30 [×4], C2×C30, C40⋊C2 [×4], C2×C40, C2×Dic10, C2×D20, C2×Q82S3, C5×C3⋊C8 [×2], C3×Dic10 [×2], C3×Dic10, C6×Dic5, D60 [×2], D60, C2×C60, C22×D15, C2×C40⋊C2, C15⋊SD16 [×4], C10×C3⋊C8, C6×Dic10, C2×D60, C2×C15⋊SD16
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], SD16 [×2], C2×D4, D10 [×3], C3⋊D4 [×2], C22×S3, C2×SD16, D20 [×2], C22×D5, Q82S3 [×2], C2×C3⋊D4, S3×D5, C40⋊C2 [×2], C2×D20, C2×Q82S3, C3⋊D20 [×2], C2×S3×D5, C2×C40⋊C2, C15⋊SD16 [×2], C2×C3⋊D20, C2×C15⋊SD16

Smallest permutation representation of C2×C15⋊SD16
On 240 points
Generators in S240
(1 75)(2 61)(3 62)(4 63)(5 64)(6 65)(7 66)(8 67)(9 68)(10 69)(11 70)(12 71)(13 72)(14 73)(15 74)(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)(31 102)(32 103)(33 104)(34 105)(35 91)(36 92)(37 93)(38 94)(39 95)(40 96)(41 97)(42 98)(43 99)(44 100)(45 101)(46 118)(47 119)(48 120)(49 106)(50 107)(51 108)(52 109)(53 110)(54 111)(55 112)(56 113)(57 114)(58 115)(59 116)(60 117)(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)(136 196)(137 197)(138 198)(139 199)(140 200)(141 201)(142 202)(143 203)(144 204)(145 205)(146 206)(147 207)(148 208)(149 209)(150 210)(151 213)(152 214)(153 215)(154 216)(155 217)(156 218)(157 219)(158 220)(159 221)(160 222)(161 223)(162 224)(163 225)(164 211)(165 212)(166 226)(167 227)(168 228)(169 229)(170 230)(171 231)(172 232)(173 233)(174 234)(175 235)(176 236)(177 237)(178 238)(179 239)(180 240)
(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)
(1 145 43 173 18 132 46 158)(2 141 44 169 19 128 47 154)(3 137 45 180 20 124 48 165)(4 148 31 176 21 135 49 161)(5 144 32 172 22 131 50 157)(6 140 33 168 23 127 51 153)(7 136 34 179 24 123 52 164)(8 147 35 175 25 134 53 160)(9 143 36 171 26 130 54 156)(10 139 37 167 27 126 55 152)(11 150 38 178 28 122 56 163)(12 146 39 174 29 133 57 159)(13 142 40 170 30 129 58 155)(14 138 41 166 16 125 59 151)(15 149 42 177 17 121 60 162)(61 201 100 229 88 190 119 216)(62 197 101 240 89 186 120 212)(63 208 102 236 90 182 106 223)(64 204 103 232 76 193 107 219)(65 200 104 228 77 189 108 215)(66 196 105 239 78 185 109 211)(67 207 91 235 79 181 110 222)(68 203 92 231 80 192 111 218)(69 199 93 227 81 188 112 214)(70 210 94 238 82 184 113 225)(71 206 95 234 83 195 114 221)(72 202 96 230 84 191 115 217)(73 198 97 226 85 187 116 213)(74 209 98 237 86 183 117 224)(75 205 99 233 87 194 118 220)
(1 43)(2 42)(3 41)(4 40)(5 39)(6 38)(7 37)(8 36)(9 35)(10 34)(11 33)(12 32)(13 31)(14 45)(15 44)(16 48)(17 47)(18 46)(19 60)(20 59)(21 58)(22 57)(23 56)(24 55)(25 54)(26 53)(27 52)(28 51)(29 50)(30 49)(61 98)(62 97)(63 96)(64 95)(65 94)(66 93)(67 92)(68 91)(69 105)(70 104)(71 103)(72 102)(73 101)(74 100)(75 99)(76 114)(77 113)(78 112)(79 111)(80 110)(81 109)(82 108)(83 107)(84 106)(85 120)(86 119)(87 118)(88 117)(89 116)(90 115)(121 141)(122 140)(123 139)(124 138)(125 137)(126 136)(127 150)(128 149)(129 148)(130 147)(131 146)(132 145)(133 144)(134 143)(135 142)(151 165)(152 164)(153 163)(154 162)(155 161)(156 160)(157 159)(166 180)(167 179)(168 178)(169 177)(170 176)(171 175)(172 174)(181 203)(182 202)(183 201)(184 200)(185 199)(186 198)(187 197)(188 196)(189 210)(190 209)(191 208)(192 207)(193 206)(194 205)(195 204)(211 214)(212 213)(215 225)(216 224)(217 223)(218 222)(219 221)(226 240)(227 239)(228 238)(229 237)(230 236)(231 235)(232 234)

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

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

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

72 conjugacy classes

class 1 2A2B2C2D2E 3 4A4B4C4D5A5B6A6B6C8A8B8C8D10A···10F12A12B12C12D12E12F15A15B20A···20H30A···30F40A···40P60A···60H
order1222223444455666888810···10121212121212151520···2030···3040···4060···60
size1111606022220202222266662···24420202020442···24···46···64···4

72 irreducible representations

dim1111122222222222222444444
type+++++++++++++++++++++
imageC1C2C2C2C2S3D4D4D5D6D6SD16D10D10C3⋊D4C3⋊D4D20D20C40⋊C2Q82S3S3×D5C3⋊D20C2×S3×D5C3⋊D20C15⋊SD16
kernelC2×C15⋊SD16C15⋊SD16C10×C3⋊C8C6×Dic10C2×D60C2×Dic10C60C2×C30C2×C3⋊C8Dic10C2×C20C30C3⋊C8C2×C12C20C2×C10C12C2×C6C6C10C2×C4C4C4C22C2
# reps14111111221442224416222228

Matrix representation of C2×C15⋊SD16 in GL6(𝔽241)

24000000
02400000
00240000
00024000
000010
000001
,
1891900000
5200000
0024019000
005119000
00000240
00001240
,
100000
010000
0013218400
005714700
000010170
0000171140
,
1891900000
53520000
0019716300
002384400
00000240
00002400

G:=sub<GL(6,GF(241))| [240,0,0,0,0,0,0,240,0,0,0,0,0,0,240,0,0,0,0,0,0,240,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[189,52,0,0,0,0,190,0,0,0,0,0,0,0,240,51,0,0,0,0,190,190,0,0,0,0,0,0,0,1,0,0,0,0,240,240],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,132,57,0,0,0,0,184,147,0,0,0,0,0,0,101,171,0,0,0,0,70,140],[189,53,0,0,0,0,190,52,0,0,0,0,0,0,197,238,0,0,0,0,163,44,0,0,0,0,0,0,0,240,0,0,0,0,240,0] >;

C2×C15⋊SD16 in GAP, Magma, Sage, TeX

C_2\times C_{15}\rtimes {\rm SD}_{16}
% in TeX

G:=Group("C2xC15:SD16");
// GroupNames label

G:=SmallGroup(480,390);
// by ID

G=gap.SmallGroup(480,390);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,112,141,64,675,80,1356,18822]);
// 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^11,d*b*d=b^-1,d*c*d=c^3>;
// generators/relations

׿
×
𝔽