direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×D60⋊11C2, D60⋊42C22, C30.57C24, C23.32D30, C60.251C23, D30.24C23, Dic30⋊38C22, Dic15.27C23, (C2×C4)⋊10D30, (C2×C20)⋊34D6, (C2×D60)⋊30C2, C6⋊5(C4○D20), (C2×C12)⋊34D10, (C22×C4)⋊8D15, (C22×C12)⋊8D5, C30⋊11(C4○D4), C10⋊5(C4○D12), (C2×C60)⋊45C22, (C22×C60)⋊12C2, (C22×C20)⋊12S3, C2.5(C23×D15), C6.57(C23×D5), (C2×Dic30)⋊31C2, (C4×D15)⋊20C22, C15⋊7D4⋊22C22, C10.57(S3×C23), C4.42(C22×D15), (C2×C30).321C23, C20.230(C22×S3), (C22×C10).145D6, C12.232(C22×D5), (C22×C6).127D10, C22.5(C22×D15), (C22×C30).150C22, (C22×D15).90C22, (C2×Dic15).177C22, C3⋊6(C2×C4○D20), C5⋊6(C2×C4○D12), (C2×C4×D15)⋊21C2, C15⋊20(C2×C4○D4), (C2×C15⋊7D4)⋊27C2, (C2×C6).317(C22×D5), (C2×C10).316(C22×S3), SmallGroup(480,1168)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×D60⋊11C2
G = < a,b,c,d | a2=b60=c2=d2=1, ab=ba, ac=ca, ad=da, cbc=b-1, bd=db, dcd=b30c >
Subgroups: 1716 in 328 conjugacy classes, 127 normal (31 characteristic)
C1, C2, C2, C2, C3, C4, C4, C22, C22, C22, C5, S3, C6, C6, C6, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D5, C10, C10, C10, Dic3, C12, D6, C2×C6, C2×C6, C2×C6, C15, C22×C4, C22×C4, C2×D4, C2×Q8, C4○D4, Dic5, C20, D10, C2×C10, C2×C10, C2×C10, Dic6, C4×S3, D12, C2×Dic3, C3⋊D4, C2×C12, C2×C12, C22×S3, C22×C6, D15, C30, C30, C30, C2×C4○D4, Dic10, C4×D5, D20, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C22×D5, C22×C10, C2×Dic6, S3×C2×C4, C2×D12, C4○D12, C2×C3⋊D4, C22×C12, Dic15, C60, D30, D30, C2×C30, C2×C30, C2×C30, C2×Dic10, C2×C4×D5, C2×D20, C4○D20, C2×C5⋊D4, C22×C20, C2×C4○D12, Dic30, C4×D15, D60, C2×Dic15, C15⋊7D4, C2×C60, C2×C60, C22×D15, C22×C30, C2×C4○D20, C2×Dic30, C2×C4×D15, C2×D60, D60⋊11C2, C2×C15⋊7D4, C22×C60, C2×D60⋊11C2
Quotients: C1, C2, C22, S3, C23, D5, D6, C4○D4, C24, D10, C22×S3, D15, C2×C4○D4, C22×D5, C4○D12, S3×C23, D30, C4○D20, C23×D5, C2×C4○D12, C22×D15, C2×C4○D20, D60⋊11C2, C23×D15, C2×D60⋊11C2
►On 240 points
Generators in S240
(1 61)(2 62)(3 63)(4 64)(5 65)(6 66)(7 67)(8 68)(9 69)(10 70)(11 71)(12 72)(13 73)(14 74)(15 75)(16 76)(17 77)(18 78)(19 79)(20 80)(21 81)(22 82)(23 83)(24 84)(25 85)(26 86)(27 87)(28 88)(29 89)(30 90)(31 91)(32 92)(33 93)(34 94)(35 95)(36 96)(37 97)(38 98)(39 99)(40 100)(41 101)(42 102)(43 103)(44 104)(45 105)(46 106)(47 107)(48 108)(49 109)(50 110)(51 111)(52 112)(53 113)(54 114)(55 115)(56 116)(57 117)(58 118)(59 119)(60 120)(121 240)(122 181)(123 182)(124 183)(125 184)(126 185)(127 186)(128 187)(129 188)(130 189)(131 190)(132 191)(133 192)(134 193)(135 194)(136 195)(137 196)(138 197)(139 198)(140 199)(141 200)(142 201)(143 202)(144 203)(145 204)(146 205)(147 206)(148 207)(149 208)(150 209)(151 210)(152 211)(153 212)(154 213)(155 214)(156 215)(157 216)(158 217)(159 218)(160 219)(161 220)(162 221)(163 222)(164 223)(165 224)(166 225)(167 226)(168 227)(169 228)(170 229)(171 230)(172 231)(173 232)(174 233)(175 234)(176 235)(177 236)(178 237)(179 238)(180 239)
(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 60)(2 59)(3 58)(4 57)(5 56)(6 55)(7 54)(8 53)(9 52)(10 51)(11 50)(12 49)(13 48)(14 47)(15 46)(16 45)(17 44)(18 43)(19 42)(20 41)(21 40)(22 39)(23 38)(24 37)(25 36)(26 35)(27 34)(28 33)(29 32)(30 31)(61 120)(62 119)(63 118)(64 117)(65 116)(66 115)(67 114)(68 113)(69 112)(70 111)(71 110)(72 109)(73 108)(74 107)(75 106)(76 105)(77 104)(78 103)(79 102)(80 101)(81 100)(82 99)(83 98)(84 97)(85 96)(86 95)(87 94)(88 93)(89 92)(90 91)(121 154)(122 153)(123 152)(124 151)(125 150)(126 149)(127 148)(128 147)(129 146)(130 145)(131 144)(132 143)(133 142)(134 141)(135 140)(136 139)(137 138)(155 180)(156 179)(157 178)(158 177)(159 176)(160 175)(161 174)(162 173)(163 172)(164 171)(165 170)(166 169)(167 168)(181 212)(182 211)(183 210)(184 209)(185 208)(186 207)(187 206)(188 205)(189 204)(190 203)(191 202)(192 201)(193 200)(194 199)(195 198)(196 197)(213 240)(214 239)(215 238)(216 237)(217 236)(218 235)(219 234)(220 233)(221 232)(222 231)(223 230)(224 229)(225 228)(226 227)
(1 182)(2 183)(3 184)(4 185)(5 186)(6 187)(7 188)(8 189)(9 190)(10 191)(11 192)(12 193)(13 194)(14 195)(15 196)(16 197)(17 198)(18 199)(19 200)(20 201)(21 202)(22 203)(23 204)(24 205)(25 206)(26 207)(27 208)(28 209)(29 210)(30 211)(31 212)(32 213)(33 214)(34 215)(35 216)(36 217)(37 218)(38 219)(39 220)(40 221)(41 222)(42 223)(43 224)(44 225)(45 226)(46 227)(47 228)(48 229)(49 230)(50 231)(51 232)(52 233)(53 234)(54 235)(55 236)(56 237)(57 238)(58 239)(59 240)(60 181)(61 123)(62 124)(63 125)(64 126)(65 127)(66 128)(67 129)(68 130)(69 131)(70 132)(71 133)(72 134)(73 135)(74 136)(75 137)(76 138)(77 139)(78 140)(79 141)(80 142)(81 143)(82 144)(83 145)(84 146)(85 147)(86 148)(87 149)(88 150)(89 151)(90 152)(91 153)(92 154)(93 155)(94 156)(95 157)(96 158)(97 159)(98 160)(99 161)(100 162)(101 163)(102 164)(103 165)(104 166)(105 167)(106 168)(107 169)(108 170)(109 171)(110 172)(111 173)(112 174)(113 175)(114 176)(115 177)(116 178)(117 179)(118 180)(119 121)(120 122)
G:=sub<Sym(240)| (1,61)(2,62)(3,63)(4,64)(5,65)(6,66)(7,67)(8,68)(9,69)(10,70)(11,71)(12,72)(13,73)(14,74)(15,75)(16,76)(17,77)(18,78)(19,79)(20,80)(21,81)(22,82)(23,83)(24,84)(25,85)(26,86)(27,87)(28,88)(29,89)(30,90)(31,91)(32,92)(33,93)(34,94)(35,95)(36,96)(37,97)(38,98)(39,99)(40,100)(41,101)(42,102)(43,103)(44,104)(45,105)(46,106)(47,107)(48,108)(49,109)(50,110)(51,111)(52,112)(53,113)(54,114)(55,115)(56,116)(57,117)(58,118)(59,119)(60,120)(121,240)(122,181)(123,182)(124,183)(125,184)(126,185)(127,186)(128,187)(129,188)(130,189)(131,190)(132,191)(133,192)(134,193)(135,194)(136,195)(137,196)(138,197)(139,198)(140,199)(141,200)(142,201)(143,202)(144,203)(145,204)(146,205)(147,206)(148,207)(149,208)(150,209)(151,210)(152,211)(153,212)(154,213)(155,214)(156,215)(157,216)(158,217)(159,218)(160,219)(161,220)(162,221)(163,222)(164,223)(165,224)(166,225)(167,226)(168,227)(169,228)(170,229)(171,230)(172,231)(173,232)(174,233)(175,234)(176,235)(177,236)(178,237)(179,238)(180,239), (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), (1,60)(2,59)(3,58)(4,57)(5,56)(6,55)(7,54)(8,53)(9,52)(10,51)(11,50)(12,49)(13,48)(14,47)(15,46)(16,45)(17,44)(18,43)(19,42)(20,41)(21,40)(22,39)(23,38)(24,37)(25,36)(26,35)(27,34)(28,33)(29,32)(30,31)(61,120)(62,119)(63,118)(64,117)(65,116)(66,115)(67,114)(68,113)(69,112)(70,111)(71,110)(72,109)(73,108)(74,107)(75,106)(76,105)(77,104)(78,103)(79,102)(80,101)(81,100)(82,99)(83,98)(84,97)(85,96)(86,95)(87,94)(88,93)(89,92)(90,91)(121,154)(122,153)(123,152)(124,151)(125,150)(126,149)(127,148)(128,147)(129,146)(130,145)(131,144)(132,143)(133,142)(134,141)(135,140)(136,139)(137,138)(155,180)(156,179)(157,178)(158,177)(159,176)(160,175)(161,174)(162,173)(163,172)(164,171)(165,170)(166,169)(167,168)(181,212)(182,211)(183,210)(184,209)(185,208)(186,207)(187,206)(188,205)(189,204)(190,203)(191,202)(192,201)(193,200)(194,199)(195,198)(196,197)(213,240)(214,239)(215,238)(216,237)(217,236)(218,235)(219,234)(220,233)(221,232)(222,231)(223,230)(224,229)(225,228)(226,227), (1,182)(2,183)(3,184)(4,185)(5,186)(6,187)(7,188)(8,189)(9,190)(10,191)(11,192)(12,193)(13,194)(14,195)(15,196)(16,197)(17,198)(18,199)(19,200)(20,201)(21,202)(22,203)(23,204)(24,205)(25,206)(26,207)(27,208)(28,209)(29,210)(30,211)(31,212)(32,213)(33,214)(34,215)(35,216)(36,217)(37,218)(38,219)(39,220)(40,221)(41,222)(42,223)(43,224)(44,225)(45,226)(46,227)(47,228)(48,229)(49,230)(50,231)(51,232)(52,233)(53,234)(54,235)(55,236)(56,237)(57,238)(58,239)(59,240)(60,181)(61,123)(62,124)(63,125)(64,126)(65,127)(66,128)(67,129)(68,130)(69,131)(70,132)(71,133)(72,134)(73,135)(74,136)(75,137)(76,138)(77,139)(78,140)(79,141)(80,142)(81,143)(82,144)(83,145)(84,146)(85,147)(86,148)(87,149)(88,150)(89,151)(90,152)(91,153)(92,154)(93,155)(94,156)(95,157)(96,158)(97,159)(98,160)(99,161)(100,162)(101,163)(102,164)(103,165)(104,166)(105,167)(106,168)(107,169)(108,170)(109,171)(110,172)(111,173)(112,174)(113,175)(114,176)(115,177)(116,178)(117,179)(118,180)(119,121)(120,122)>;
G:=Group( (1,61)(2,62)(3,63)(4,64)(5,65)(6,66)(7,67)(8,68)(9,69)(10,70)(11,71)(12,72)(13,73)(14,74)(15,75)(16,76)(17,77)(18,78)(19,79)(20,80)(21,81)(22,82)(23,83)(24,84)(25,85)(26,86)(27,87)(28,88)(29,89)(30,90)(31,91)(32,92)(33,93)(34,94)(35,95)(36,96)(37,97)(38,98)(39,99)(40,100)(41,101)(42,102)(43,103)(44,104)(45,105)(46,106)(47,107)(48,108)(49,109)(50,110)(51,111)(52,112)(53,113)(54,114)(55,115)(56,116)(57,117)(58,118)(59,119)(60,120)(121,240)(122,181)(123,182)(124,183)(125,184)(126,185)(127,186)(128,187)(129,188)(130,189)(131,190)(132,191)(133,192)(134,193)(135,194)(136,195)(137,196)(138,197)(139,198)(140,199)(141,200)(142,201)(143,202)(144,203)(145,204)(146,205)(147,206)(148,207)(149,208)(150,209)(151,210)(152,211)(153,212)(154,213)(155,214)(156,215)(157,216)(158,217)(159,218)(160,219)(161,220)(162,221)(163,222)(164,223)(165,224)(166,225)(167,226)(168,227)(169,228)(170,229)(171,230)(172,231)(173,232)(174,233)(175,234)(176,235)(177,236)(178,237)(179,238)(180,239), (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), (1,60)(2,59)(3,58)(4,57)(5,56)(6,55)(7,54)(8,53)(9,52)(10,51)(11,50)(12,49)(13,48)(14,47)(15,46)(16,45)(17,44)(18,43)(19,42)(20,41)(21,40)(22,39)(23,38)(24,37)(25,36)(26,35)(27,34)(28,33)(29,32)(30,31)(61,120)(62,119)(63,118)(64,117)(65,116)(66,115)(67,114)(68,113)(69,112)(70,111)(71,110)(72,109)(73,108)(74,107)(75,106)(76,105)(77,104)(78,103)(79,102)(80,101)(81,100)(82,99)(83,98)(84,97)(85,96)(86,95)(87,94)(88,93)(89,92)(90,91)(121,154)(122,153)(123,152)(124,151)(125,150)(126,149)(127,148)(128,147)(129,146)(130,145)(131,144)(132,143)(133,142)(134,141)(135,140)(136,139)(137,138)(155,180)(156,179)(157,178)(158,177)(159,176)(160,175)(161,174)(162,173)(163,172)(164,171)(165,170)(166,169)(167,168)(181,212)(182,211)(183,210)(184,209)(185,208)(186,207)(187,206)(188,205)(189,204)(190,203)(191,202)(192,201)(193,200)(194,199)(195,198)(196,197)(213,240)(214,239)(215,238)(216,237)(217,236)(218,235)(219,234)(220,233)(221,232)(222,231)(223,230)(224,229)(225,228)(226,227), (1,182)(2,183)(3,184)(4,185)(5,186)(6,187)(7,188)(8,189)(9,190)(10,191)(11,192)(12,193)(13,194)(14,195)(15,196)(16,197)(17,198)(18,199)(19,200)(20,201)(21,202)(22,203)(23,204)(24,205)(25,206)(26,207)(27,208)(28,209)(29,210)(30,211)(31,212)(32,213)(33,214)(34,215)(35,216)(36,217)(37,218)(38,219)(39,220)(40,221)(41,222)(42,223)(43,224)(44,225)(45,226)(46,227)(47,228)(48,229)(49,230)(50,231)(51,232)(52,233)(53,234)(54,235)(55,236)(56,237)(57,238)(58,239)(59,240)(60,181)(61,123)(62,124)(63,125)(64,126)(65,127)(66,128)(67,129)(68,130)(69,131)(70,132)(71,133)(72,134)(73,135)(74,136)(75,137)(76,138)(77,139)(78,140)(79,141)(80,142)(81,143)(82,144)(83,145)(84,146)(85,147)(86,148)(87,149)(88,150)(89,151)(90,152)(91,153)(92,154)(93,155)(94,156)(95,157)(96,158)(97,159)(98,160)(99,161)(100,162)(101,163)(102,164)(103,165)(104,166)(105,167)(106,168)(107,169)(108,170)(109,171)(110,172)(111,173)(112,174)(113,175)(114,176)(115,177)(116,178)(117,179)(118,180)(119,121)(120,122) );
G=PermutationGroup([[(1,61),(2,62),(3,63),(4,64),(5,65),(6,66),(7,67),(8,68),(9,69),(10,70),(11,71),(12,72),(13,73),(14,74),(15,75),(16,76),(17,77),(18,78),(19,79),(20,80),(21,81),(22,82),(23,83),(24,84),(25,85),(26,86),(27,87),(28,88),(29,89),(30,90),(31,91),(32,92),(33,93),(34,94),(35,95),(36,96),(37,97),(38,98),(39,99),(40,100),(41,101),(42,102),(43,103),(44,104),(45,105),(46,106),(47,107),(48,108),(49,109),(50,110),(51,111),(52,112),(53,113),(54,114),(55,115),(56,116),(57,117),(58,118),(59,119),(60,120),(121,240),(122,181),(123,182),(124,183),(125,184),(126,185),(127,186),(128,187),(129,188),(130,189),(131,190),(132,191),(133,192),(134,193),(135,194),(136,195),(137,196),(138,197),(139,198),(140,199),(141,200),(142,201),(143,202),(144,203),(145,204),(146,205),(147,206),(148,207),(149,208),(150,209),(151,210),(152,211),(153,212),(154,213),(155,214),(156,215),(157,216),(158,217),(159,218),(160,219),(161,220),(162,221),(163,222),(164,223),(165,224),(166,225),(167,226),(168,227),(169,228),(170,229),(171,230),(172,231),(173,232),(174,233),(175,234),(176,235),(177,236),(178,237),(179,238),(180,239)], [(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)], [(1,60),(2,59),(3,58),(4,57),(5,56),(6,55),(7,54),(8,53),(9,52),(10,51),(11,50),(12,49),(13,48),(14,47),(15,46),(16,45),(17,44),(18,43),(19,42),(20,41),(21,40),(22,39),(23,38),(24,37),(25,36),(26,35),(27,34),(28,33),(29,32),(30,31),(61,120),(62,119),(63,118),(64,117),(65,116),(66,115),(67,114),(68,113),(69,112),(70,111),(71,110),(72,109),(73,108),(74,107),(75,106),(76,105),(77,104),(78,103),(79,102),(80,101),(81,100),(82,99),(83,98),(84,97),(85,96),(86,95),(87,94),(88,93),(89,92),(90,91),(121,154),(122,153),(123,152),(124,151),(125,150),(126,149),(127,148),(128,147),(129,146),(130,145),(131,144),(132,143),(133,142),(134,141),(135,140),(136,139),(137,138),(155,180),(156,179),(157,178),(158,177),(159,176),(160,175),(161,174),(162,173),(163,172),(164,171),(165,170),(166,169),(167,168),(181,212),(182,211),(183,210),(184,209),(185,208),(186,207),(187,206),(188,205),(189,204),(190,203),(191,202),(192,201),(193,200),(194,199),(195,198),(196,197),(213,240),(214,239),(215,238),(216,237),(217,236),(218,235),(219,234),(220,233),(221,232),(222,231),(223,230),(224,229),(225,228),(226,227)], [(1,182),(2,183),(3,184),(4,185),(5,186),(6,187),(7,188),(8,189),(9,190),(10,191),(11,192),(12,193),(13,194),(14,195),(15,196),(16,197),(17,198),(18,199),(19,200),(20,201),(21,202),(22,203),(23,204),(24,205),(25,206),(26,207),(27,208),(28,209),(29,210),(30,211),(31,212),(32,213),(33,214),(34,215),(35,216),(36,217),(37,218),(38,219),(39,220),(40,221),(41,222),(42,223),(43,224),(44,225),(45,226),(46,227),(47,228),(48,229),(49,230),(50,231),(51,232),(52,233),(53,234),(54,235),(55,236),(56,237),(57,238),(58,239),(59,240),(60,181),(61,123),(62,124),(63,125),(64,126),(65,127),(66,128),(67,129),(68,130),(69,131),(70,132),(71,133),(72,134),(73,135),(74,136),(75,137),(76,138),(77,139),(78,140),(79,141),(80,142),(81,143),(82,144),(83,145),(84,146),(85,147),(86,148),(87,149),(88,150),(89,151),(90,152),(91,153),(92,154),(93,155),(94,156),(95,157),(96,158),(97,159),(98,160),(99,161),(100,162),(101,163),(102,164),(103,165),(104,166),(105,167),(106,168),(107,169),(108,170),(109,171),(110,172),(111,173),(112,174),(113,175),(114,176),(115,177),(116,178),(117,179),(118,180),(119,121),(120,122)]])
132 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 5A | 5B | 6A | ··· | 6G | 10A | ··· | 10N | 12A | ··· | 12H | 15A | 15B | 15C | 15D | 20A | ··· | 20P | 30A | ··· | 30AB | 60A | ··· | 60AF |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | ··· | 6 | 10 | ··· | 10 | 12 | ··· | 12 | 15 | 15 | 15 | 15 | 20 | ··· | 20 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 30 | 30 | 30 | 30 | 2 | 1 | 1 | 1 | 1 | 2 | 2 | 30 | 30 | 30 | 30 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
132 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | S3 | D5 | D6 | D6 | C4○D4 | D10 | D10 | D15 | C4○D12 | D30 | D30 | C4○D20 | D60⋊11C2 |
| kernel | C2×D60⋊11C2 | C2×Dic30 | C2×C4×D15 | C2×D60 | D60⋊11C2 | C2×C15⋊7D4 | C22×C60 | C22×C20 | C22×C12 | C2×C20 | C22×C10 | C30 | C2×C12 | C22×C6 | C22×C4 | C10 | C2×C4 | C23 | C6 | C2 |
| # reps | 1 | 1 | 2 | 1 | 8 | 2 | 1 | 1 | 2 | 6 | 1 | 4 | 12 | 2 | 4 | 8 | 24 | 4 | 16 | 32 |
Matrix representation of C2×D60⋊11C2 ►in GL4(𝔽61) generated by
| 60 | 0 | 0 | 0 |
| 0 | 60 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 37 | 47 | 0 | 0 |
| 14 | 31 | 0 | 0 |
| 0 | 0 | 53 | 28 |
| 0 | 0 | 37 | 0 |
| 25 | 28 | 0 | 0 |
| 30 | 36 | 0 | 0 |
| 0 | 0 | 8 | 33 |
| 0 | 0 | 48 | 53 |
| 60 | 0 | 0 | 0 |
| 0 | 60 | 0 | 0 |
| 0 | 0 | 34 | 6 |
| 0 | 0 | 21 | 27 |
G:=sub<GL(4,GF(61))| [60,0,0,0,0,60,0,0,0,0,1,0,0,0,0,1],[37,14,0,0,47,31,0,0,0,0,53,37,0,0,28,0],[25,30,0,0,28,36,0,0,0,0,8,48,0,0,33,53],[60,0,0,0,0,60,0,0,0,0,34,21,0,0,6,27] >;
C2×D60⋊11C2 in GAP, Magma, Sage, TeX
C_2\times D_{60}\rtimes_{11}C_2 % in TeX
G:=Group("C2xD60:11C2"); // GroupNames label
G:=SmallGroup(480,1168);
// by ID
G=gap.SmallGroup(480,1168);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,100,675,2693,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^60=c^2=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c=b^-1,b*d=d*b,d*c*d=b^30*c>;
// generators/relations