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G = C2×D60⋊11C2order 480 = 25·3·5

Direct product of C2 and D60⋊11C2

Series: Derived Chief Lower central Upper central

 Derived series C1 — C30 — C2×D60⋊11C2
 Chief series C1 — C5 — C15 — C30 — D30 — C22×D15 — C2×C4×D15 — C2×D60⋊11C2
 Lower central C15 — C30 — C2×D60⋊11C2
 Upper central C1 — C2×C4 — C22×C4

Generators and relations for C2×D6011C2
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 [×2], C2 [×6], C3, C4 [×4], C4 [×4], C22, C22 [×2], C22 [×10], C5, S3 [×4], C6, C6 [×2], C6 [×2], C2×C4 [×2], C2×C4 [×4], C2×C4 [×10], D4 [×12], Q8 [×4], C23, C23 [×2], D5 [×4], C10, C10 [×2], C10 [×2], Dic3 [×4], C12 [×4], D6 [×8], C2×C6, C2×C6 [×2], C2×C6 [×2], C15, C22×C4, C22×C4 [×2], C2×D4 [×3], C2×Q8, C4○D4 [×8], Dic5 [×4], C20 [×4], D10 [×8], C2×C10, C2×C10 [×2], C2×C10 [×2], Dic6 [×4], C4×S3 [×8], D12 [×4], C2×Dic3 [×2], C3⋊D4 [×8], C2×C12 [×2], C2×C12 [×4], C22×S3 [×2], C22×C6, D15 [×4], C30, C30 [×2], C30 [×2], C2×C4○D4, Dic10 [×4], C4×D5 [×8], D20 [×4], C2×Dic5 [×2], C5⋊D4 [×8], C2×C20 [×2], C2×C20 [×4], C22×D5 [×2], C22×C10, C2×Dic6, S3×C2×C4 [×2], C2×D12, C4○D12 [×8], C2×C3⋊D4 [×2], C22×C12, Dic15 [×4], C60 [×4], D30 [×4], D30 [×4], C2×C30, C2×C30 [×2], C2×C30 [×2], C2×Dic10, C2×C4×D5 [×2], C2×D20, C4○D20 [×8], C2×C5⋊D4 [×2], C22×C20, C2×C4○D12, Dic30 [×4], C4×D15 [×8], D60 [×4], C2×Dic15 [×2], C157D4 [×8], C2×C60 [×2], C2×C60 [×4], C22×D15 [×2], C22×C30, C2×C4○D20, C2×Dic30, C2×C4×D15 [×2], C2×D60, D6011C2 [×8], C2×C157D4 [×2], C22×C60, C2×D6011C2
Quotients: C1, C2 [×15], C22 [×35], S3, C23 [×15], D5, D6 [×7], C4○D4 [×2], C24, D10 [×7], C22×S3 [×7], D15, C2×C4○D4, C22×D5 [×7], C4○D12 [×2], S3×C23, D30 [×7], C4○D20 [×2], C23×D5, C2×C4○D12, C22×D15 [×7], C2×C4○D20, D6011C2 [×2], C23×D15, C2×D6011C2

Smallest permutation representation of C2×D6011C2
On 240 points
Generators in S240
(1 192)(2 193)(3 194)(4 195)(5 196)(6 197)(7 198)(8 199)(9 200)(10 201)(11 202)(12 203)(13 204)(14 205)(15 206)(16 207)(17 208)(18 209)(19 210)(20 211)(21 212)(22 213)(23 214)(24 215)(25 216)(26 217)(27 218)(28 219)(29 220)(30 221)(31 222)(32 223)(33 224)(34 225)(35 226)(36 227)(37 228)(38 229)(39 230)(40 231)(41 232)(42 233)(43 234)(44 235)(45 236)(46 237)(47 238)(48 239)(49 240)(50 181)(51 182)(52 183)(53 184)(54 185)(55 186)(56 187)(57 188)(58 189)(59 190)(60 191)(61 135)(62 136)(63 137)(64 138)(65 139)(66 140)(67 141)(68 142)(69 143)(70 144)(71 145)(72 146)(73 147)(74 148)(75 149)(76 150)(77 151)(78 152)(79 153)(80 154)(81 155)(82 156)(83 157)(84 158)(85 159)(86 160)(87 161)(88 162)(89 163)(90 164)(91 165)(92 166)(93 167)(94 168)(95 169)(96 170)(97 171)(98 172)(99 173)(100 174)(101 175)(102 176)(103 177)(104 178)(105 179)(106 180)(107 121)(108 122)(109 123)(110 124)(111 125)(112 126)(113 127)(114 128)(115 129)(116 130)(117 131)(118 132)(119 133)(120 134)
(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 70)(62 69)(63 68)(64 67)(65 66)(71 120)(72 119)(73 118)(74 117)(75 116)(76 115)(77 114)(78 113)(79 112)(80 111)(81 110)(82 109)(83 108)(84 107)(85 106)(86 105)(87 104)(88 103)(89 102)(90 101)(91 100)(92 99)(93 98)(94 97)(95 96)(121 158)(122 157)(123 156)(124 155)(125 154)(126 153)(127 152)(128 151)(129 150)(130 149)(131 148)(132 147)(133 146)(134 145)(135 144)(136 143)(137 142)(138 141)(139 140)(159 180)(160 179)(161 178)(162 177)(163 176)(164 175)(165 174)(166 173)(167 172)(168 171)(169 170)(181 202)(182 201)(183 200)(184 199)(185 198)(186 197)(187 196)(188 195)(189 194)(190 193)(191 192)(203 240)(204 239)(205 238)(206 237)(207 236)(208 235)(209 234)(210 233)(211 232)(212 231)(213 230)(214 229)(215 228)(216 227)(217 226)(218 225)(219 224)(220 223)(221 222)
(1 125)(2 126)(3 127)(4 128)(5 129)(6 130)(7 131)(8 132)(9 133)(10 134)(11 135)(12 136)(13 137)(14 138)(15 139)(16 140)(17 141)(18 142)(19 143)(20 144)(21 145)(22 146)(23 147)(24 148)(25 149)(26 150)(27 151)(28 152)(29 153)(30 154)(31 155)(32 156)(33 157)(34 158)(35 159)(36 160)(37 161)(38 162)(39 163)(40 164)(41 165)(42 166)(43 167)(44 168)(45 169)(46 170)(47 171)(48 172)(49 173)(50 174)(51 175)(52 176)(53 177)(54 178)(55 179)(56 180)(57 121)(58 122)(59 123)(60 124)(61 202)(62 203)(63 204)(64 205)(65 206)(66 207)(67 208)(68 209)(69 210)(70 211)(71 212)(72 213)(73 214)(74 215)(75 216)(76 217)(77 218)(78 219)(79 220)(80 221)(81 222)(82 223)(83 224)(84 225)(85 226)(86 227)(87 228)(88 229)(89 230)(90 231)(91 232)(92 233)(93 234)(94 235)(95 236)(96 237)(97 238)(98 239)(99 240)(100 181)(101 182)(102 183)(103 184)(104 185)(105 186)(106 187)(107 188)(108 189)(109 190)(110 191)(111 192)(112 193)(113 194)(114 195)(115 196)(116 197)(117 198)(118 199)(119 200)(120 201)

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

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

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

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×D6011C2 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×D6011C2 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

׿
×
𝔽