direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C22×D61, C61⋊C23, C122⋊C22, (C2×C122)⋊3C2, SmallGroup(488,13)
Series: Derived ►Chief ►Lower central ►Upper central
| C61 — C22×D61 |
Generators and relations for C22×D61
G = < a,b,c,d | a2=b2=c61=d2=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd=c-1 >
Smallest permutation representation of C22×D61
►On 244 points
Generators in S244
(1 227)(2 228)(3 229)(4 230)(5 231)(6 232)(7 233)(8 234)(9 235)(10 236)(11 237)(12 238)(13 239)(14 240)(15 241)(16 242)(17 243)(18 244)(19 184)(20 185)(21 186)(22 187)(23 188)(24 189)(25 190)(26 191)(27 192)(28 193)(29 194)(30 195)(31 196)(32 197)(33 198)(34 199)(35 200)(36 201)(37 202)(38 203)(39 204)(40 205)(41 206)(42 207)(43 208)(44 209)(45 210)(46 211)(47 212)(48 213)(49 214)(50 215)(51 216)(52 217)(53 218)(54 219)(55 220)(56 221)(57 222)(58 223)(59 224)(60 225)(61 226)(62 165)(63 166)(64 167)(65 168)(66 169)(67 170)(68 171)(69 172)(70 173)(71 174)(72 175)(73 176)(74 177)(75 178)(76 179)(77 180)(78 181)(79 182)(80 183)(81 123)(82 124)(83 125)(84 126)(85 127)(86 128)(87 129)(88 130)(89 131)(90 132)(91 133)(92 134)(93 135)(94 136)(95 137)(96 138)(97 139)(98 140)(99 141)(100 142)(101 143)(102 144)(103 145)(104 146)(105 147)(106 148)(107 149)(108 150)(109 151)(110 152)(111 153)(112 154)(113 155)(114 156)(115 157)(116 158)(117 159)(118 160)(119 161)(120 162)(121 163)(122 164)
(1 89)(2 90)(3 91)(4 92)(5 93)(6 94)(7 95)(8 96)(9 97)(10 98)(11 99)(12 100)(13 101)(14 102)(15 103)(16 104)(17 105)(18 106)(19 107)(20 108)(21 109)(22 110)(23 111)(24 112)(25 113)(26 114)(27 115)(28 116)(29 117)(30 118)(31 119)(32 120)(33 121)(34 122)(35 62)(36 63)(37 64)(38 65)(39 66)(40 67)(41 68)(42 69)(43 70)(44 71)(45 72)(46 73)(47 74)(48 75)(49 76)(50 77)(51 78)(52 79)(53 80)(54 81)(55 82)(56 83)(57 84)(58 85)(59 86)(60 87)(61 88)(123 219)(124 220)(125 221)(126 222)(127 223)(128 224)(129 225)(130 226)(131 227)(132 228)(133 229)(134 230)(135 231)(136 232)(137 233)(138 234)(139 235)(140 236)(141 237)(142 238)(143 239)(144 240)(145 241)(146 242)(147 243)(148 244)(149 184)(150 185)(151 186)(152 187)(153 188)(154 189)(155 190)(156 191)(157 192)(158 193)(159 194)(160 195)(161 196)(162 197)(163 198)(164 199)(165 200)(166 201)(167 202)(168 203)(169 204)(170 205)(171 206)(172 207)(173 208)(174 209)(175 210)(176 211)(177 212)(178 213)(179 214)(180 215)(181 216)(182 217)(183 218)
(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)(184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244)
(1 130)(2 129)(3 128)(4 127)(5 126)(6 125)(7 124)(8 123)(9 183)(10 182)(11 181)(12 180)(13 179)(14 178)(15 177)(16 176)(17 175)(18 174)(19 173)(20 172)(21 171)(22 170)(23 169)(24 168)(25 167)(26 166)(27 165)(28 164)(29 163)(30 162)(31 161)(32 160)(33 159)(34 158)(35 157)(36 156)(37 155)(38 154)(39 153)(40 152)(41 151)(42 150)(43 149)(44 148)(45 147)(46 146)(47 145)(48 144)(49 143)(50 142)(51 141)(52 140)(53 139)(54 138)(55 137)(56 136)(57 135)(58 134)(59 133)(60 132)(61 131)(62 192)(63 191)(64 190)(65 189)(66 188)(67 187)(68 186)(69 185)(70 184)(71 244)(72 243)(73 242)(74 241)(75 240)(76 239)(77 238)(78 237)(79 236)(80 235)(81 234)(82 233)(83 232)(84 231)(85 230)(86 229)(87 228)(88 227)(89 226)(90 225)(91 224)(92 223)(93 222)(94 221)(95 220)(96 219)(97 218)(98 217)(99 216)(100 215)(101 214)(102 213)(103 212)(104 211)(105 210)(106 209)(107 208)(108 207)(109 206)(110 205)(111 204)(112 203)(113 202)(114 201)(115 200)(116 199)(117 198)(118 197)(119 196)(120 195)(121 194)(122 193)
G:=sub<Sym(244)| (1,227)(2,228)(3,229)(4,230)(5,231)(6,232)(7,233)(8,234)(9,235)(10,236)(11,237)(12,238)(13,239)(14,240)(15,241)(16,242)(17,243)(18,244)(19,184)(20,185)(21,186)(22,187)(23,188)(24,189)(25,190)(26,191)(27,192)(28,193)(29,194)(30,195)(31,196)(32,197)(33,198)(34,199)(35,200)(36,201)(37,202)(38,203)(39,204)(40,205)(41,206)(42,207)(43,208)(44,209)(45,210)(46,211)(47,212)(48,213)(49,214)(50,215)(51,216)(52,217)(53,218)(54,219)(55,220)(56,221)(57,222)(58,223)(59,224)(60,225)(61,226)(62,165)(63,166)(64,167)(65,168)(66,169)(67,170)(68,171)(69,172)(70,173)(71,174)(72,175)(73,176)(74,177)(75,178)(76,179)(77,180)(78,181)(79,182)(80,183)(81,123)(82,124)(83,125)(84,126)(85,127)(86,128)(87,129)(88,130)(89,131)(90,132)(91,133)(92,134)(93,135)(94,136)(95,137)(96,138)(97,139)(98,140)(99,141)(100,142)(101,143)(102,144)(103,145)(104,146)(105,147)(106,148)(107,149)(108,150)(109,151)(110,152)(111,153)(112,154)(113,155)(114,156)(115,157)(116,158)(117,159)(118,160)(119,161)(120,162)(121,163)(122,164), (1,89)(2,90)(3,91)(4,92)(5,93)(6,94)(7,95)(8,96)(9,97)(10,98)(11,99)(12,100)(13,101)(14,102)(15,103)(16,104)(17,105)(18,106)(19,107)(20,108)(21,109)(22,110)(23,111)(24,112)(25,113)(26,114)(27,115)(28,116)(29,117)(30,118)(31,119)(32,120)(33,121)(34,122)(35,62)(36,63)(37,64)(38,65)(39,66)(40,67)(41,68)(42,69)(43,70)(44,71)(45,72)(46,73)(47,74)(48,75)(49,76)(50,77)(51,78)(52,79)(53,80)(54,81)(55,82)(56,83)(57,84)(58,85)(59,86)(60,87)(61,88)(123,219)(124,220)(125,221)(126,222)(127,223)(128,224)(129,225)(130,226)(131,227)(132,228)(133,229)(134,230)(135,231)(136,232)(137,233)(138,234)(139,235)(140,236)(141,237)(142,238)(143,239)(144,240)(145,241)(146,242)(147,243)(148,244)(149,184)(150,185)(151,186)(152,187)(153,188)(154,189)(155,190)(156,191)(157,192)(158,193)(159,194)(160,195)(161,196)(162,197)(163,198)(164,199)(165,200)(166,201)(167,202)(168,203)(169,204)(170,205)(171,206)(172,207)(173,208)(174,209)(175,210)(176,211)(177,212)(178,213)(179,214)(180,215)(181,216)(182,217)(183,218), (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)(184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244), (1,130)(2,129)(3,128)(4,127)(5,126)(6,125)(7,124)(8,123)(9,183)(10,182)(11,181)(12,180)(13,179)(14,178)(15,177)(16,176)(17,175)(18,174)(19,173)(20,172)(21,171)(22,170)(23,169)(24,168)(25,167)(26,166)(27,165)(28,164)(29,163)(30,162)(31,161)(32,160)(33,159)(34,158)(35,157)(36,156)(37,155)(38,154)(39,153)(40,152)(41,151)(42,150)(43,149)(44,148)(45,147)(46,146)(47,145)(48,144)(49,143)(50,142)(51,141)(52,140)(53,139)(54,138)(55,137)(56,136)(57,135)(58,134)(59,133)(60,132)(61,131)(62,192)(63,191)(64,190)(65,189)(66,188)(67,187)(68,186)(69,185)(70,184)(71,244)(72,243)(73,242)(74,241)(75,240)(76,239)(77,238)(78,237)(79,236)(80,235)(81,234)(82,233)(83,232)(84,231)(85,230)(86,229)(87,228)(88,227)(89,226)(90,225)(91,224)(92,223)(93,222)(94,221)(95,220)(96,219)(97,218)(98,217)(99,216)(100,215)(101,214)(102,213)(103,212)(104,211)(105,210)(106,209)(107,208)(108,207)(109,206)(110,205)(111,204)(112,203)(113,202)(114,201)(115,200)(116,199)(117,198)(118,197)(119,196)(120,195)(121,194)(122,193)>;
G:=Group( (1,227)(2,228)(3,229)(4,230)(5,231)(6,232)(7,233)(8,234)(9,235)(10,236)(11,237)(12,238)(13,239)(14,240)(15,241)(16,242)(17,243)(18,244)(19,184)(20,185)(21,186)(22,187)(23,188)(24,189)(25,190)(26,191)(27,192)(28,193)(29,194)(30,195)(31,196)(32,197)(33,198)(34,199)(35,200)(36,201)(37,202)(38,203)(39,204)(40,205)(41,206)(42,207)(43,208)(44,209)(45,210)(46,211)(47,212)(48,213)(49,214)(50,215)(51,216)(52,217)(53,218)(54,219)(55,220)(56,221)(57,222)(58,223)(59,224)(60,225)(61,226)(62,165)(63,166)(64,167)(65,168)(66,169)(67,170)(68,171)(69,172)(70,173)(71,174)(72,175)(73,176)(74,177)(75,178)(76,179)(77,180)(78,181)(79,182)(80,183)(81,123)(82,124)(83,125)(84,126)(85,127)(86,128)(87,129)(88,130)(89,131)(90,132)(91,133)(92,134)(93,135)(94,136)(95,137)(96,138)(97,139)(98,140)(99,141)(100,142)(101,143)(102,144)(103,145)(104,146)(105,147)(106,148)(107,149)(108,150)(109,151)(110,152)(111,153)(112,154)(113,155)(114,156)(115,157)(116,158)(117,159)(118,160)(119,161)(120,162)(121,163)(122,164), (1,89)(2,90)(3,91)(4,92)(5,93)(6,94)(7,95)(8,96)(9,97)(10,98)(11,99)(12,100)(13,101)(14,102)(15,103)(16,104)(17,105)(18,106)(19,107)(20,108)(21,109)(22,110)(23,111)(24,112)(25,113)(26,114)(27,115)(28,116)(29,117)(30,118)(31,119)(32,120)(33,121)(34,122)(35,62)(36,63)(37,64)(38,65)(39,66)(40,67)(41,68)(42,69)(43,70)(44,71)(45,72)(46,73)(47,74)(48,75)(49,76)(50,77)(51,78)(52,79)(53,80)(54,81)(55,82)(56,83)(57,84)(58,85)(59,86)(60,87)(61,88)(123,219)(124,220)(125,221)(126,222)(127,223)(128,224)(129,225)(130,226)(131,227)(132,228)(133,229)(134,230)(135,231)(136,232)(137,233)(138,234)(139,235)(140,236)(141,237)(142,238)(143,239)(144,240)(145,241)(146,242)(147,243)(148,244)(149,184)(150,185)(151,186)(152,187)(153,188)(154,189)(155,190)(156,191)(157,192)(158,193)(159,194)(160,195)(161,196)(162,197)(163,198)(164,199)(165,200)(166,201)(167,202)(168,203)(169,204)(170,205)(171,206)(172,207)(173,208)(174,209)(175,210)(176,211)(177,212)(178,213)(179,214)(180,215)(181,216)(182,217)(183,218), (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)(184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244), (1,130)(2,129)(3,128)(4,127)(5,126)(6,125)(7,124)(8,123)(9,183)(10,182)(11,181)(12,180)(13,179)(14,178)(15,177)(16,176)(17,175)(18,174)(19,173)(20,172)(21,171)(22,170)(23,169)(24,168)(25,167)(26,166)(27,165)(28,164)(29,163)(30,162)(31,161)(32,160)(33,159)(34,158)(35,157)(36,156)(37,155)(38,154)(39,153)(40,152)(41,151)(42,150)(43,149)(44,148)(45,147)(46,146)(47,145)(48,144)(49,143)(50,142)(51,141)(52,140)(53,139)(54,138)(55,137)(56,136)(57,135)(58,134)(59,133)(60,132)(61,131)(62,192)(63,191)(64,190)(65,189)(66,188)(67,187)(68,186)(69,185)(70,184)(71,244)(72,243)(73,242)(74,241)(75,240)(76,239)(77,238)(78,237)(79,236)(80,235)(81,234)(82,233)(83,232)(84,231)(85,230)(86,229)(87,228)(88,227)(89,226)(90,225)(91,224)(92,223)(93,222)(94,221)(95,220)(96,219)(97,218)(98,217)(99,216)(100,215)(101,214)(102,213)(103,212)(104,211)(105,210)(106,209)(107,208)(108,207)(109,206)(110,205)(111,204)(112,203)(113,202)(114,201)(115,200)(116,199)(117,198)(118,197)(119,196)(120,195)(121,194)(122,193) );
G=PermutationGroup([[(1,227),(2,228),(3,229),(4,230),(5,231),(6,232),(7,233),(8,234),(9,235),(10,236),(11,237),(12,238),(13,239),(14,240),(15,241),(16,242),(17,243),(18,244),(19,184),(20,185),(21,186),(22,187),(23,188),(24,189),(25,190),(26,191),(27,192),(28,193),(29,194),(30,195),(31,196),(32,197),(33,198),(34,199),(35,200),(36,201),(37,202),(38,203),(39,204),(40,205),(41,206),(42,207),(43,208),(44,209),(45,210),(46,211),(47,212),(48,213),(49,214),(50,215),(51,216),(52,217),(53,218),(54,219),(55,220),(56,221),(57,222),(58,223),(59,224),(60,225),(61,226),(62,165),(63,166),(64,167),(65,168),(66,169),(67,170),(68,171),(69,172),(70,173),(71,174),(72,175),(73,176),(74,177),(75,178),(76,179),(77,180),(78,181),(79,182),(80,183),(81,123),(82,124),(83,125),(84,126),(85,127),(86,128),(87,129),(88,130),(89,131),(90,132),(91,133),(92,134),(93,135),(94,136),(95,137),(96,138),(97,139),(98,140),(99,141),(100,142),(101,143),(102,144),(103,145),(104,146),(105,147),(106,148),(107,149),(108,150),(109,151),(110,152),(111,153),(112,154),(113,155),(114,156),(115,157),(116,158),(117,159),(118,160),(119,161),(120,162),(121,163),(122,164)], [(1,89),(2,90),(3,91),(4,92),(5,93),(6,94),(7,95),(8,96),(9,97),(10,98),(11,99),(12,100),(13,101),(14,102),(15,103),(16,104),(17,105),(18,106),(19,107),(20,108),(21,109),(22,110),(23,111),(24,112),(25,113),(26,114),(27,115),(28,116),(29,117),(30,118),(31,119),(32,120),(33,121),(34,122),(35,62),(36,63),(37,64),(38,65),(39,66),(40,67),(41,68),(42,69),(43,70),(44,71),(45,72),(46,73),(47,74),(48,75),(49,76),(50,77),(51,78),(52,79),(53,80),(54,81),(55,82),(56,83),(57,84),(58,85),(59,86),(60,87),(61,88),(123,219),(124,220),(125,221),(126,222),(127,223),(128,224),(129,225),(130,226),(131,227),(132,228),(133,229),(134,230),(135,231),(136,232),(137,233),(138,234),(139,235),(140,236),(141,237),(142,238),(143,239),(144,240),(145,241),(146,242),(147,243),(148,244),(149,184),(150,185),(151,186),(152,187),(153,188),(154,189),(155,190),(156,191),(157,192),(158,193),(159,194),(160,195),(161,196),(162,197),(163,198),(164,199),(165,200),(166,201),(167,202),(168,203),(169,204),(170,205),(171,206),(172,207),(173,208),(174,209),(175,210),(176,211),(177,212),(178,213),(179,214),(180,215),(181,216),(182,217),(183,218)], [(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),(184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244)], [(1,130),(2,129),(3,128),(4,127),(5,126),(6,125),(7,124),(8,123),(9,183),(10,182),(11,181),(12,180),(13,179),(14,178),(15,177),(16,176),(17,175),(18,174),(19,173),(20,172),(21,171),(22,170),(23,169),(24,168),(25,167),(26,166),(27,165),(28,164),(29,163),(30,162),(31,161),(32,160),(33,159),(34,158),(35,157),(36,156),(37,155),(38,154),(39,153),(40,152),(41,151),(42,150),(43,149),(44,148),(45,147),(46,146),(47,145),(48,144),(49,143),(50,142),(51,141),(52,140),(53,139),(54,138),(55,137),(56,136),(57,135),(58,134),(59,133),(60,132),(61,131),(62,192),(63,191),(64,190),(65,189),(66,188),(67,187),(68,186),(69,185),(70,184),(71,244),(72,243),(73,242),(74,241),(75,240),(76,239),(77,238),(78,237),(79,236),(80,235),(81,234),(82,233),(83,232),(84,231),(85,230),(86,229),(87,228),(88,227),(89,226),(90,225),(91,224),(92,223),(93,222),(94,221),(95,220),(96,219),(97,218),(98,217),(99,216),(100,215),(101,214),(102,213),(103,212),(104,211),(105,210),(106,209),(107,208),(108,207),(109,206),(110,205),(111,204),(112,203),(113,202),(114,201),(115,200),(116,199),(117,198),(118,197),(119,196),(120,195),(121,194),(122,193)]])
128 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 61A | ··· | 61AD | 122A | ··· | 122CL |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 61 | ··· | 61 | 122 | ··· | 122 |
| size | 1 | 1 | 1 | 1 | 61 | 61 | 61 | 61 | 2 | ··· | 2 | 2 | ··· | 2 |
128 irreducible representations
| dim | 1 | 1 | 1 | 2 | 2 |
| type | + | + | + | + | + |
| image | C1 | C2 | C2 | D61 | D122 |
| kernel | C22×D61 | D122 | C2×C122 | C22 | C2 |
| # reps | 1 | 6 | 1 | 30 | 90 |
Matrix representation of C22×D61 ►in GL3(𝔽367) generated by
| 366 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 1 |
| 366 | 0 | 0 |
| 0 | 366 | 0 |
| 0 | 0 | 366 |
| 1 | 0 | 0 |
| 0 | 317 | 1 |
| 0 | 115 | 350 |
| 366 | 0 | 0 |
| 0 | 277 | 365 |
| 0 | 196 | 90 |
G:=sub<GL(3,GF(367))| [366,0,0,0,1,0,0,0,1],[366,0,0,0,366,0,0,0,366],[1,0,0,0,317,115,0,1,350],[366,0,0,0,277,196,0,365,90] >;
C22×D61 in GAP, Magma, Sage, TeX
C_2^2\times D_{61} % in TeX
G:=Group("C2^2xD61"); // GroupNames label
G:=SmallGroup(488,13);
// by ID
G=gap.SmallGroup(488,13);
# by ID
G:=PCGroup([4,-2,-2,-2,-61,7683]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^2=c^61=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d=c^-1>;
// generators/relations
Export