direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C15⋊SD16, C30⋊4SD16, C60.41D4, C12.16D20, Dic10⋊17D6, C60.107C23, D60.45C22, C3⋊C8⋊27D10, C15⋊7(C2×SD16), C6⋊2(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), C10⋊1(Q8⋊2S3), (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, C3⋊3(C2×C40⋊C2), C5⋊1(C2×Q8⋊2S3), 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
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, C2, C3, C4, C4, C22, C22, C5, S3, C6, C6, C8, C2×C4, C2×C4, D4, Q8, C23, D5, C10, C10, C12, C12, D6, C2×C6, C15, C2×C8, SD16, C2×D4, C2×Q8, Dic5, C20, D10, C2×C10, C3⋊C8, D12, C2×C12, C2×C12, C3×Q8, C22×S3, D15, C30, C30, C2×SD16, C40, Dic10, Dic10, D20, C2×Dic5, C2×C20, C22×D5, C2×C3⋊C8, Q8⋊2S3, C2×D12, C6×Q8, C3×Dic5, C60, D30, C2×C30, C40⋊C2, C2×C40, C2×Dic10, C2×D20, C2×Q8⋊2S3, C5×C3⋊C8, C3×Dic10, C3×Dic10, C6×Dic5, D60, D60, C2×C60, C22×D15, C2×C40⋊C2, C15⋊SD16, C10×C3⋊C8, C6×Dic10, C2×D60, C2×C15⋊SD16
Quotients: C1, C2, C22, S3, D4, C23, D5, D6, SD16, C2×D4, D10, C3⋊D4, C22×S3, C2×SD16, D20, C22×D5, Q8⋊2S3, C2×C3⋊D4, S3×D5, C40⋊C2, C2×D20, C2×Q8⋊2S3, C3⋊D20, C2×S3×D5, C2×C40⋊C2, C15⋊SD16, C2×C3⋊D20, C2×C15⋊SD16
►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)(31 102)(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)(121 192)(122 193)(123 194)(124 195)(125 181)(126 182)(127 183)(128 184)(129 185)(130 186)(131 187)(132 188)(133 189)(134 190)(135 191)(136 200)(137 201)(138 202)(139 203)(140 204)(141 205)(142 206)(143 207)(144 208)(145 209)(146 210)(147 196)(148 197)(149 198)(150 199)(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)(166 226)(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)
(1 147 44 173 28 134 52 164)(2 143 45 169 29 130 53 160)(3 139 31 180 30 126 54 156)(4 150 32 176 16 122 55 152)(5 146 33 172 17 133 56 163)(6 142 34 168 18 129 57 159)(7 138 35 179 19 125 58 155)(8 149 36 175 20 121 59 151)(9 145 37 171 21 132 60 162)(10 141 38 167 22 128 46 158)(11 137 39 178 23 124 47 154)(12 148 40 174 24 135 48 165)(13 144 41 170 25 131 49 161)(14 140 42 166 26 127 50 157)(15 136 43 177 27 123 51 153)(61 198 92 235 82 192 116 211)(62 209 93 231 83 188 117 222)(63 205 94 227 84 184 118 218)(64 201 95 238 85 195 119 214)(65 197 96 234 86 191 120 225)(66 208 97 230 87 187 106 221)(67 204 98 226 88 183 107 217)(68 200 99 237 89 194 108 213)(69 196 100 233 90 190 109 224)(70 207 101 229 76 186 110 220)(71 203 102 240 77 182 111 216)(72 199 103 236 78 193 112 212)(73 210 104 232 79 189 113 223)(74 206 105 228 80 185 114 219)(75 202 91 239 81 181 115 215)
(1 44)(2 43)(3 42)(4 41)(5 40)(6 39)(7 38)(8 37)(9 36)(10 35)(11 34)(12 33)(13 32)(14 31)(15 45)(16 49)(17 48)(18 47)(19 46)(20 60)(21 59)(22 58)(23 57)(24 56)(25 55)(26 54)(27 53)(28 52)(29 51)(30 50)(61 93)(62 92)(63 91)(64 105)(65 104)(66 103)(67 102)(68 101)(69 100)(70 99)(71 98)(72 97)(73 96)(74 95)(75 94)(76 108)(77 107)(78 106)(79 120)(80 119)(81 118)(82 117)(83 116)(84 115)(85 114)(86 113)(87 112)(88 111)(89 110)(90 109)(121 145)(122 144)(123 143)(124 142)(125 141)(126 140)(127 139)(128 138)(129 137)(130 136)(131 150)(132 149)(133 148)(134 147)(135 146)(151 162)(152 161)(153 160)(154 159)(155 158)(156 157)(163 165)(166 180)(167 179)(168 178)(169 177)(170 176)(171 175)(172 174)(181 205)(182 204)(183 203)(184 202)(185 201)(186 200)(187 199)(188 198)(189 197)(190 196)(191 210)(192 209)(193 208)(194 207)(195 206)(211 222)(212 221)(213 220)(214 219)(215 218)(216 217)(223 225)(226 240)(227 239)(228 238)(229 237)(230 236)(231 235)(232 234)
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)(31,102)(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)(121,192)(122,193)(123,194)(124,195)(125,181)(126,182)(127,183)(128,184)(129,185)(130,186)(131,187)(132,188)(133,189)(134,190)(135,191)(136,200)(137,201)(138,202)(139,203)(140,204)(141,205)(142,206)(143,207)(144,208)(145,209)(146,210)(147,196)(148,197)(149,198)(150,199)(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)(166,226)(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), (1,147,44,173,28,134,52,164)(2,143,45,169,29,130,53,160)(3,139,31,180,30,126,54,156)(4,150,32,176,16,122,55,152)(5,146,33,172,17,133,56,163)(6,142,34,168,18,129,57,159)(7,138,35,179,19,125,58,155)(8,149,36,175,20,121,59,151)(9,145,37,171,21,132,60,162)(10,141,38,167,22,128,46,158)(11,137,39,178,23,124,47,154)(12,148,40,174,24,135,48,165)(13,144,41,170,25,131,49,161)(14,140,42,166,26,127,50,157)(15,136,43,177,27,123,51,153)(61,198,92,235,82,192,116,211)(62,209,93,231,83,188,117,222)(63,205,94,227,84,184,118,218)(64,201,95,238,85,195,119,214)(65,197,96,234,86,191,120,225)(66,208,97,230,87,187,106,221)(67,204,98,226,88,183,107,217)(68,200,99,237,89,194,108,213)(69,196,100,233,90,190,109,224)(70,207,101,229,76,186,110,220)(71,203,102,240,77,182,111,216)(72,199,103,236,78,193,112,212)(73,210,104,232,79,189,113,223)(74,206,105,228,80,185,114,219)(75,202,91,239,81,181,115,215), (1,44)(2,43)(3,42)(4,41)(5,40)(6,39)(7,38)(8,37)(9,36)(10,35)(11,34)(12,33)(13,32)(14,31)(15,45)(16,49)(17,48)(18,47)(19,46)(20,60)(21,59)(22,58)(23,57)(24,56)(25,55)(26,54)(27,53)(28,52)(29,51)(30,50)(61,93)(62,92)(63,91)(64,105)(65,104)(66,103)(67,102)(68,101)(69,100)(70,99)(71,98)(72,97)(73,96)(74,95)(75,94)(76,108)(77,107)(78,106)(79,120)(80,119)(81,118)(82,117)(83,116)(84,115)(85,114)(86,113)(87,112)(88,111)(89,110)(90,109)(121,145)(122,144)(123,143)(124,142)(125,141)(126,140)(127,139)(128,138)(129,137)(130,136)(131,150)(132,149)(133,148)(134,147)(135,146)(151,162)(152,161)(153,160)(154,159)(155,158)(156,157)(163,165)(166,180)(167,179)(168,178)(169,177)(170,176)(171,175)(172,174)(181,205)(182,204)(183,203)(184,202)(185,201)(186,200)(187,199)(188,198)(189,197)(190,196)(191,210)(192,209)(193,208)(194,207)(195,206)(211,222)(212,221)(213,220)(214,219)(215,218)(216,217)(223,225)(226,240)(227,239)(228,238)(229,237)(230,236)(231,235)(232,234)>;
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)(31,102)(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)(121,192)(122,193)(123,194)(124,195)(125,181)(126,182)(127,183)(128,184)(129,185)(130,186)(131,187)(132,188)(133,189)(134,190)(135,191)(136,200)(137,201)(138,202)(139,203)(140,204)(141,205)(142,206)(143,207)(144,208)(145,209)(146,210)(147,196)(148,197)(149,198)(150,199)(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)(166,226)(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), (1,147,44,173,28,134,52,164)(2,143,45,169,29,130,53,160)(3,139,31,180,30,126,54,156)(4,150,32,176,16,122,55,152)(5,146,33,172,17,133,56,163)(6,142,34,168,18,129,57,159)(7,138,35,179,19,125,58,155)(8,149,36,175,20,121,59,151)(9,145,37,171,21,132,60,162)(10,141,38,167,22,128,46,158)(11,137,39,178,23,124,47,154)(12,148,40,174,24,135,48,165)(13,144,41,170,25,131,49,161)(14,140,42,166,26,127,50,157)(15,136,43,177,27,123,51,153)(61,198,92,235,82,192,116,211)(62,209,93,231,83,188,117,222)(63,205,94,227,84,184,118,218)(64,201,95,238,85,195,119,214)(65,197,96,234,86,191,120,225)(66,208,97,230,87,187,106,221)(67,204,98,226,88,183,107,217)(68,200,99,237,89,194,108,213)(69,196,100,233,90,190,109,224)(70,207,101,229,76,186,110,220)(71,203,102,240,77,182,111,216)(72,199,103,236,78,193,112,212)(73,210,104,232,79,189,113,223)(74,206,105,228,80,185,114,219)(75,202,91,239,81,181,115,215), (1,44)(2,43)(3,42)(4,41)(5,40)(6,39)(7,38)(8,37)(9,36)(10,35)(11,34)(12,33)(13,32)(14,31)(15,45)(16,49)(17,48)(18,47)(19,46)(20,60)(21,59)(22,58)(23,57)(24,56)(25,55)(26,54)(27,53)(28,52)(29,51)(30,50)(61,93)(62,92)(63,91)(64,105)(65,104)(66,103)(67,102)(68,101)(69,100)(70,99)(71,98)(72,97)(73,96)(74,95)(75,94)(76,108)(77,107)(78,106)(79,120)(80,119)(81,118)(82,117)(83,116)(84,115)(85,114)(86,113)(87,112)(88,111)(89,110)(90,109)(121,145)(122,144)(123,143)(124,142)(125,141)(126,140)(127,139)(128,138)(129,137)(130,136)(131,150)(132,149)(133,148)(134,147)(135,146)(151,162)(152,161)(153,160)(154,159)(155,158)(156,157)(163,165)(166,180)(167,179)(168,178)(169,177)(170,176)(171,175)(172,174)(181,205)(182,204)(183,203)(184,202)(185,201)(186,200)(187,199)(188,198)(189,197)(190,196)(191,210)(192,209)(193,208)(194,207)(195,206)(211,222)(212,221)(213,220)(214,219)(215,218)(216,217)(223,225)(226,240)(227,239)(228,238)(229,237)(230,236)(231,235)(232,234) );
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),(31,102),(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),(121,192),(122,193),(123,194),(124,195),(125,181),(126,182),(127,183),(128,184),(129,185),(130,186),(131,187),(132,188),(133,189),(134,190),(135,191),(136,200),(137,201),(138,202),(139,203),(140,204),(141,205),(142,206),(143,207),(144,208),(145,209),(146,210),(147,196),(148,197),(149,198),(150,199),(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),(166,226),(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)], [(1,147,44,173,28,134,52,164),(2,143,45,169,29,130,53,160),(3,139,31,180,30,126,54,156),(4,150,32,176,16,122,55,152),(5,146,33,172,17,133,56,163),(6,142,34,168,18,129,57,159),(7,138,35,179,19,125,58,155),(8,149,36,175,20,121,59,151),(9,145,37,171,21,132,60,162),(10,141,38,167,22,128,46,158),(11,137,39,178,23,124,47,154),(12,148,40,174,24,135,48,165),(13,144,41,170,25,131,49,161),(14,140,42,166,26,127,50,157),(15,136,43,177,27,123,51,153),(61,198,92,235,82,192,116,211),(62,209,93,231,83,188,117,222),(63,205,94,227,84,184,118,218),(64,201,95,238,85,195,119,214),(65,197,96,234,86,191,120,225),(66,208,97,230,87,187,106,221),(67,204,98,226,88,183,107,217),(68,200,99,237,89,194,108,213),(69,196,100,233,90,190,109,224),(70,207,101,229,76,186,110,220),(71,203,102,240,77,182,111,216),(72,199,103,236,78,193,112,212),(73,210,104,232,79,189,113,223),(74,206,105,228,80,185,114,219),(75,202,91,239,81,181,115,215)], [(1,44),(2,43),(3,42),(4,41),(5,40),(6,39),(7,38),(8,37),(9,36),(10,35),(11,34),(12,33),(13,32),(14,31),(15,45),(16,49),(17,48),(18,47),(19,46),(20,60),(21,59),(22,58),(23,57),(24,56),(25,55),(26,54),(27,53),(28,52),(29,51),(30,50),(61,93),(62,92),(63,91),(64,105),(65,104),(66,103),(67,102),(68,101),(69,100),(70,99),(71,98),(72,97),(73,96),(74,95),(75,94),(76,108),(77,107),(78,106),(79,120),(80,119),(81,118),(82,117),(83,116),(84,115),(85,114),(86,113),(87,112),(88,111),(89,110),(90,109),(121,145),(122,144),(123,143),(124,142),(125,141),(126,140),(127,139),(128,138),(129,137),(130,136),(131,150),(132,149),(133,148),(134,147),(135,146),(151,162),(152,161),(153,160),(154,159),(155,158),(156,157),(163,165),(166,180),(167,179),(168,178),(169,177),(170,176),(171,175),(172,174),(181,205),(182,204),(183,203),(184,202),(185,201),(186,200),(187,199),(188,198),(189,197),(190,196),(191,210),(192,209),(193,208),(194,207),(195,206),(211,222),(212,221),(213,220),(214,219),(215,218),(216,217),(223,225),(226,240),(227,239),(228,238),(229,237),(230,236),(231,235),(232,234)]])
72 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 3 | 4A | 4B | 4C | 4D | 5A | 5B | 6A | 6B | 6C | 8A | 8B | 8C | 8D | 10A | ··· | 10F | 12A | 12B | 12C | 12D | 12E | 12F | 15A | 15B | 20A | ··· | 20H | 30A | ··· | 30F | 40A | ··· | 40P | 60A | ··· | 60H |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 8 | 8 | 8 | 8 | 10 | ··· | 10 | 12 | 12 | 12 | 12 | 12 | 12 | 15 | 15 | 20 | ··· | 20 | 30 | ··· | 30 | 40 | ··· | 40 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 60 | 60 | 2 | 2 | 2 | 20 | 20 | 2 | 2 | 2 | 2 | 2 | 6 | 6 | 6 | 6 | 2 | ··· | 2 | 4 | 4 | 20 | 20 | 20 | 20 | 4 | 4 | 2 | ··· | 2 | 4 | ··· | 4 | 6 | ··· | 6 | 4 | ··· | 4 |
72 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | S3 | D4 | D4 | D5 | D6 | D6 | SD16 | D10 | D10 | C3⋊D4 | C3⋊D4 | D20 | D20 | C40⋊C2 | Q8⋊2S3 | S3×D5 | C3⋊D20 | C2×S3×D5 | C3⋊D20 | C15⋊SD16 |
| kernel | C2×C15⋊SD16 | C15⋊SD16 | C10×C3⋊C8 | C6×Dic10 | C2×D60 | C2×Dic10 | C60 | C2×C30 | C2×C3⋊C8 | Dic10 | C2×C20 | C30 | C3⋊C8 | C2×C12 | C20 | C2×C10 | C12 | C2×C6 | C6 | C10 | C2×C4 | C4 | C4 | C22 | C2 |
| # reps | 1 | 4 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 1 | 4 | 4 | 2 | 2 | 2 | 4 | 4 | 16 | 2 | 2 | 2 | 2 | 2 | 8 |
Matrix representation of C2×C15⋊SD16 ►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 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 189 | 190 | 0 | 0 | 0 | 0 |
| 52 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 240 | 190 | 0 | 0 |
| 0 | 0 | 51 | 190 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 240 |
| 0 | 0 | 0 | 0 | 1 | 240 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 132 | 184 | 0 | 0 |
| 0 | 0 | 57 | 147 | 0 | 0 |
| 0 | 0 | 0 | 0 | 101 | 70 |
| 0 | 0 | 0 | 0 | 171 | 140 |
| 189 | 190 | 0 | 0 | 0 | 0 |
| 53 | 52 | 0 | 0 | 0 | 0 |
| 0 | 0 | 197 | 163 | 0 | 0 |
| 0 | 0 | 238 | 44 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 240 |
| 0 | 0 | 0 | 0 | 240 | 0 |
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