direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C22⋊C4×C31, C22⋊C124, C23.C62, C62.12D4, (C2×C62)⋊1C4, (C2×C4)⋊1C62, (C2×C124)⋊2C2, C2.1(D4×C31), C62.10(C2×C4), C2.1(C2×C124), C22.2(C2×C62), (C22×C62).1C2, (C2×C62).13C22, SmallGroup(496,20)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C22⋊C4×C31
G = < a,b,c,d | a31=b2=c2=d4=1, ab=ba, ac=ca, ad=da, dbd-1=bc=cb, cd=dc >
Smallest permutation representation of C22⋊C4×C31
►On 248 points
Generators in S248
(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)(218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248)
(1 41)(2 42)(3 43)(4 44)(5 45)(6 46)(7 47)(8 48)(9 49)(10 50)(11 51)(12 52)(13 53)(14 54)(15 55)(16 56)(17 57)(18 58)(19 59)(20 60)(21 61)(22 62)(23 32)(24 33)(25 34)(26 35)(27 36)(28 37)(29 38)(30 39)(31 40)(63 199)(64 200)(65 201)(66 202)(67 203)(68 204)(69 205)(70 206)(71 207)(72 208)(73 209)(74 210)(75 211)(76 212)(77 213)(78 214)(79 215)(80 216)(81 217)(82 187)(83 188)(84 189)(85 190)(86 191)(87 192)(88 193)(89 194)(90 195)(91 196)(92 197)(93 198)(94 163)(95 164)(96 165)(97 166)(98 167)(99 168)(100 169)(101 170)(102 171)(103 172)(104 173)(105 174)(106 175)(107 176)(108 177)(109 178)(110 179)(111 180)(112 181)(113 182)(114 183)(115 184)(116 185)(117 186)(118 156)(119 157)(120 158)(121 159)(122 160)(123 161)(124 162)(125 223)(126 224)(127 225)(128 226)(129 227)(130 228)(131 229)(132 230)(133 231)(134 232)(135 233)(136 234)(137 235)(138 236)(139 237)(140 238)(141 239)(142 240)(143 241)(144 242)(145 243)(146 244)(147 245)(148 246)(149 247)(150 248)(151 218)(152 219)(153 220)(154 221)(155 222)
(1 188)(2 189)(3 190)(4 191)(5 192)(6 193)(7 194)(8 195)(9 196)(10 197)(11 198)(12 199)(13 200)(14 201)(15 202)(16 203)(17 204)(18 205)(19 206)(20 207)(21 208)(22 209)(23 210)(24 211)(25 212)(26 213)(27 214)(28 215)(29 216)(30 217)(31 187)(32 74)(33 75)(34 76)(35 77)(36 78)(37 79)(38 80)(39 81)(40 82)(41 83)(42 84)(43 85)(44 86)(45 87)(46 88)(47 89)(48 90)(49 91)(50 92)(51 93)(52 63)(53 64)(54 65)(55 66)(56 67)(57 68)(58 69)(59 70)(60 71)(61 72)(62 73)(94 144)(95 145)(96 146)(97 147)(98 148)(99 149)(100 150)(101 151)(102 152)(103 153)(104 154)(105 155)(106 125)(107 126)(108 127)(109 128)(110 129)(111 130)(112 131)(113 132)(114 133)(115 134)(116 135)(117 136)(118 137)(119 138)(120 139)(121 140)(122 141)(123 142)(124 143)(156 235)(157 236)(158 237)(159 238)(160 239)(161 240)(162 241)(163 242)(164 243)(165 244)(166 245)(167 246)(168 247)(169 248)(170 218)(171 219)(172 220)(173 221)(174 222)(175 223)(176 224)(177 225)(178 226)(179 227)(180 228)(181 229)(182 230)(183 231)(184 232)(185 233)(186 234)
(1 248 41 100)(2 218 42 101)(3 219 43 102)(4 220 44 103)(5 221 45 104)(6 222 46 105)(7 223 47 106)(8 224 48 107)(9 225 49 108)(10 226 50 109)(11 227 51 110)(12 228 52 111)(13 229 53 112)(14 230 54 113)(15 231 55 114)(16 232 56 115)(17 233 57 116)(18 234 58 117)(19 235 59 118)(20 236 60 119)(21 237 61 120)(22 238 62 121)(23 239 32 122)(24 240 33 123)(25 241 34 124)(26 242 35 94)(27 243 36 95)(28 244 37 96)(29 245 38 97)(30 246 39 98)(31 247 40 99)(63 130 199 180)(64 131 200 181)(65 132 201 182)(66 133 202 183)(67 134 203 184)(68 135 204 185)(69 136 205 186)(70 137 206 156)(71 138 207 157)(72 139 208 158)(73 140 209 159)(74 141 210 160)(75 142 211 161)(76 143 212 162)(77 144 213 163)(78 145 214 164)(79 146 215 165)(80 147 216 166)(81 148 217 167)(82 149 187 168)(83 150 188 169)(84 151 189 170)(85 152 190 171)(86 153 191 172)(87 154 192 173)(88 155 193 174)(89 125 194 175)(90 126 195 176)(91 127 196 177)(92 128 197 178)(93 129 198 179)
G:=sub<Sym(248)| (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)(218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248), (1,41)(2,42)(3,43)(4,44)(5,45)(6,46)(7,47)(8,48)(9,49)(10,50)(11,51)(12,52)(13,53)(14,54)(15,55)(16,56)(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)(23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38)(30,39)(31,40)(63,199)(64,200)(65,201)(66,202)(67,203)(68,204)(69,205)(70,206)(71,207)(72,208)(73,209)(74,210)(75,211)(76,212)(77,213)(78,214)(79,215)(80,216)(81,217)(82,187)(83,188)(84,189)(85,190)(86,191)(87,192)(88,193)(89,194)(90,195)(91,196)(92,197)(93,198)(94,163)(95,164)(96,165)(97,166)(98,167)(99,168)(100,169)(101,170)(102,171)(103,172)(104,173)(105,174)(106,175)(107,176)(108,177)(109,178)(110,179)(111,180)(112,181)(113,182)(114,183)(115,184)(116,185)(117,186)(118,156)(119,157)(120,158)(121,159)(122,160)(123,161)(124,162)(125,223)(126,224)(127,225)(128,226)(129,227)(130,228)(131,229)(132,230)(133,231)(134,232)(135,233)(136,234)(137,235)(138,236)(139,237)(140,238)(141,239)(142,240)(143,241)(144,242)(145,243)(146,244)(147,245)(148,246)(149,247)(150,248)(151,218)(152,219)(153,220)(154,221)(155,222), (1,188)(2,189)(3,190)(4,191)(5,192)(6,193)(7,194)(8,195)(9,196)(10,197)(11,198)(12,199)(13,200)(14,201)(15,202)(16,203)(17,204)(18,205)(19,206)(20,207)(21,208)(22,209)(23,210)(24,211)(25,212)(26,213)(27,214)(28,215)(29,216)(30,217)(31,187)(32,74)(33,75)(34,76)(35,77)(36,78)(37,79)(38,80)(39,81)(40,82)(41,83)(42,84)(43,85)(44,86)(45,87)(46,88)(47,89)(48,90)(49,91)(50,92)(51,93)(52,63)(53,64)(54,65)(55,66)(56,67)(57,68)(58,69)(59,70)(60,71)(61,72)(62,73)(94,144)(95,145)(96,146)(97,147)(98,148)(99,149)(100,150)(101,151)(102,152)(103,153)(104,154)(105,155)(106,125)(107,126)(108,127)(109,128)(110,129)(111,130)(112,131)(113,132)(114,133)(115,134)(116,135)(117,136)(118,137)(119,138)(120,139)(121,140)(122,141)(123,142)(124,143)(156,235)(157,236)(158,237)(159,238)(160,239)(161,240)(162,241)(163,242)(164,243)(165,244)(166,245)(167,246)(168,247)(169,248)(170,218)(171,219)(172,220)(173,221)(174,222)(175,223)(176,224)(177,225)(178,226)(179,227)(180,228)(181,229)(182,230)(183,231)(184,232)(185,233)(186,234), (1,248,41,100)(2,218,42,101)(3,219,43,102)(4,220,44,103)(5,221,45,104)(6,222,46,105)(7,223,47,106)(8,224,48,107)(9,225,49,108)(10,226,50,109)(11,227,51,110)(12,228,52,111)(13,229,53,112)(14,230,54,113)(15,231,55,114)(16,232,56,115)(17,233,57,116)(18,234,58,117)(19,235,59,118)(20,236,60,119)(21,237,61,120)(22,238,62,121)(23,239,32,122)(24,240,33,123)(25,241,34,124)(26,242,35,94)(27,243,36,95)(28,244,37,96)(29,245,38,97)(30,246,39,98)(31,247,40,99)(63,130,199,180)(64,131,200,181)(65,132,201,182)(66,133,202,183)(67,134,203,184)(68,135,204,185)(69,136,205,186)(70,137,206,156)(71,138,207,157)(72,139,208,158)(73,140,209,159)(74,141,210,160)(75,142,211,161)(76,143,212,162)(77,144,213,163)(78,145,214,164)(79,146,215,165)(80,147,216,166)(81,148,217,167)(82,149,187,168)(83,150,188,169)(84,151,189,170)(85,152,190,171)(86,153,191,172)(87,154,192,173)(88,155,193,174)(89,125,194,175)(90,126,195,176)(91,127,196,177)(92,128,197,178)(93,129,198,179)>;
G:=Group( (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)(218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248), (1,41)(2,42)(3,43)(4,44)(5,45)(6,46)(7,47)(8,48)(9,49)(10,50)(11,51)(12,52)(13,53)(14,54)(15,55)(16,56)(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)(23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38)(30,39)(31,40)(63,199)(64,200)(65,201)(66,202)(67,203)(68,204)(69,205)(70,206)(71,207)(72,208)(73,209)(74,210)(75,211)(76,212)(77,213)(78,214)(79,215)(80,216)(81,217)(82,187)(83,188)(84,189)(85,190)(86,191)(87,192)(88,193)(89,194)(90,195)(91,196)(92,197)(93,198)(94,163)(95,164)(96,165)(97,166)(98,167)(99,168)(100,169)(101,170)(102,171)(103,172)(104,173)(105,174)(106,175)(107,176)(108,177)(109,178)(110,179)(111,180)(112,181)(113,182)(114,183)(115,184)(116,185)(117,186)(118,156)(119,157)(120,158)(121,159)(122,160)(123,161)(124,162)(125,223)(126,224)(127,225)(128,226)(129,227)(130,228)(131,229)(132,230)(133,231)(134,232)(135,233)(136,234)(137,235)(138,236)(139,237)(140,238)(141,239)(142,240)(143,241)(144,242)(145,243)(146,244)(147,245)(148,246)(149,247)(150,248)(151,218)(152,219)(153,220)(154,221)(155,222), (1,188)(2,189)(3,190)(4,191)(5,192)(6,193)(7,194)(8,195)(9,196)(10,197)(11,198)(12,199)(13,200)(14,201)(15,202)(16,203)(17,204)(18,205)(19,206)(20,207)(21,208)(22,209)(23,210)(24,211)(25,212)(26,213)(27,214)(28,215)(29,216)(30,217)(31,187)(32,74)(33,75)(34,76)(35,77)(36,78)(37,79)(38,80)(39,81)(40,82)(41,83)(42,84)(43,85)(44,86)(45,87)(46,88)(47,89)(48,90)(49,91)(50,92)(51,93)(52,63)(53,64)(54,65)(55,66)(56,67)(57,68)(58,69)(59,70)(60,71)(61,72)(62,73)(94,144)(95,145)(96,146)(97,147)(98,148)(99,149)(100,150)(101,151)(102,152)(103,153)(104,154)(105,155)(106,125)(107,126)(108,127)(109,128)(110,129)(111,130)(112,131)(113,132)(114,133)(115,134)(116,135)(117,136)(118,137)(119,138)(120,139)(121,140)(122,141)(123,142)(124,143)(156,235)(157,236)(158,237)(159,238)(160,239)(161,240)(162,241)(163,242)(164,243)(165,244)(166,245)(167,246)(168,247)(169,248)(170,218)(171,219)(172,220)(173,221)(174,222)(175,223)(176,224)(177,225)(178,226)(179,227)(180,228)(181,229)(182,230)(183,231)(184,232)(185,233)(186,234), (1,248,41,100)(2,218,42,101)(3,219,43,102)(4,220,44,103)(5,221,45,104)(6,222,46,105)(7,223,47,106)(8,224,48,107)(9,225,49,108)(10,226,50,109)(11,227,51,110)(12,228,52,111)(13,229,53,112)(14,230,54,113)(15,231,55,114)(16,232,56,115)(17,233,57,116)(18,234,58,117)(19,235,59,118)(20,236,60,119)(21,237,61,120)(22,238,62,121)(23,239,32,122)(24,240,33,123)(25,241,34,124)(26,242,35,94)(27,243,36,95)(28,244,37,96)(29,245,38,97)(30,246,39,98)(31,247,40,99)(63,130,199,180)(64,131,200,181)(65,132,201,182)(66,133,202,183)(67,134,203,184)(68,135,204,185)(69,136,205,186)(70,137,206,156)(71,138,207,157)(72,139,208,158)(73,140,209,159)(74,141,210,160)(75,142,211,161)(76,143,212,162)(77,144,213,163)(78,145,214,164)(79,146,215,165)(80,147,216,166)(81,148,217,167)(82,149,187,168)(83,150,188,169)(84,151,189,170)(85,152,190,171)(86,153,191,172)(87,154,192,173)(88,155,193,174)(89,125,194,175)(90,126,195,176)(91,127,196,177)(92,128,197,178)(93,129,198,179) );
G=PermutationGroup([[(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),(218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248)], [(1,41),(2,42),(3,43),(4,44),(5,45),(6,46),(7,47),(8,48),(9,49),(10,50),(11,51),(12,52),(13,53),(14,54),(15,55),(16,56),(17,57),(18,58),(19,59),(20,60),(21,61),(22,62),(23,32),(24,33),(25,34),(26,35),(27,36),(28,37),(29,38),(30,39),(31,40),(63,199),(64,200),(65,201),(66,202),(67,203),(68,204),(69,205),(70,206),(71,207),(72,208),(73,209),(74,210),(75,211),(76,212),(77,213),(78,214),(79,215),(80,216),(81,217),(82,187),(83,188),(84,189),(85,190),(86,191),(87,192),(88,193),(89,194),(90,195),(91,196),(92,197),(93,198),(94,163),(95,164),(96,165),(97,166),(98,167),(99,168),(100,169),(101,170),(102,171),(103,172),(104,173),(105,174),(106,175),(107,176),(108,177),(109,178),(110,179),(111,180),(112,181),(113,182),(114,183),(115,184),(116,185),(117,186),(118,156),(119,157),(120,158),(121,159),(122,160),(123,161),(124,162),(125,223),(126,224),(127,225),(128,226),(129,227),(130,228),(131,229),(132,230),(133,231),(134,232),(135,233),(136,234),(137,235),(138,236),(139,237),(140,238),(141,239),(142,240),(143,241),(144,242),(145,243),(146,244),(147,245),(148,246),(149,247),(150,248),(151,218),(152,219),(153,220),(154,221),(155,222)], [(1,188),(2,189),(3,190),(4,191),(5,192),(6,193),(7,194),(8,195),(9,196),(10,197),(11,198),(12,199),(13,200),(14,201),(15,202),(16,203),(17,204),(18,205),(19,206),(20,207),(21,208),(22,209),(23,210),(24,211),(25,212),(26,213),(27,214),(28,215),(29,216),(30,217),(31,187),(32,74),(33,75),(34,76),(35,77),(36,78),(37,79),(38,80),(39,81),(40,82),(41,83),(42,84),(43,85),(44,86),(45,87),(46,88),(47,89),(48,90),(49,91),(50,92),(51,93),(52,63),(53,64),(54,65),(55,66),(56,67),(57,68),(58,69),(59,70),(60,71),(61,72),(62,73),(94,144),(95,145),(96,146),(97,147),(98,148),(99,149),(100,150),(101,151),(102,152),(103,153),(104,154),(105,155),(106,125),(107,126),(108,127),(109,128),(110,129),(111,130),(112,131),(113,132),(114,133),(115,134),(116,135),(117,136),(118,137),(119,138),(120,139),(121,140),(122,141),(123,142),(124,143),(156,235),(157,236),(158,237),(159,238),(160,239),(161,240),(162,241),(163,242),(164,243),(165,244),(166,245),(167,246),(168,247),(169,248),(170,218),(171,219),(172,220),(173,221),(174,222),(175,223),(176,224),(177,225),(178,226),(179,227),(180,228),(181,229),(182,230),(183,231),(184,232),(185,233),(186,234)], [(1,248,41,100),(2,218,42,101),(3,219,43,102),(4,220,44,103),(5,221,45,104),(6,222,46,105),(7,223,47,106),(8,224,48,107),(9,225,49,108),(10,226,50,109),(11,227,51,110),(12,228,52,111),(13,229,53,112),(14,230,54,113),(15,231,55,114),(16,232,56,115),(17,233,57,116),(18,234,58,117),(19,235,59,118),(20,236,60,119),(21,237,61,120),(22,238,62,121),(23,239,32,122),(24,240,33,123),(25,241,34,124),(26,242,35,94),(27,243,36,95),(28,244,37,96),(29,245,38,97),(30,246,39,98),(31,247,40,99),(63,130,199,180),(64,131,200,181),(65,132,201,182),(66,133,202,183),(67,134,203,184),(68,135,204,185),(69,136,205,186),(70,137,206,156),(71,138,207,157),(72,139,208,158),(73,140,209,159),(74,141,210,160),(75,142,211,161),(76,143,212,162),(77,144,213,163),(78,145,214,164),(79,146,215,165),(80,147,216,166),(81,148,217,167),(82,149,187,168),(83,150,188,169),(84,151,189,170),(85,152,190,171),(86,153,191,172),(87,154,192,173),(88,155,193,174),(89,125,194,175),(90,126,195,176),(91,127,196,177),(92,128,197,178),(93,129,198,179)]])
310 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 31A | ··· | 31AD | 62A | ··· | 62CL | 62CM | ··· | 62ET | 124A | ··· | 124DP |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 31 | ··· | 31 | 62 | ··· | 62 | 62 | ··· | 62 | 124 | ··· | 124 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | ··· | 2 |
310 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 |
| type | + | + | + | + | ||||||
| image | C1 | C2 | C2 | C4 | C31 | C62 | C62 | C124 | D4 | D4×C31 |
| kernel | C22⋊C4×C31 | C2×C124 | C22×C62 | C2×C62 | C22⋊C4 | C2×C4 | C23 | C22 | C62 | C2 |
| # reps | 1 | 2 | 1 | 4 | 30 | 60 | 30 | 120 | 2 | 60 |
Matrix representation of C22⋊C4×C31 ►in GL3(𝔽373) generated by
| 1 | 0 | 0 |
| 0 | 215 | 0 |
| 0 | 0 | 215 |
| 1 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 372 |
| 1 | 0 | 0 |
| 0 | 372 | 0 |
| 0 | 0 | 372 |
| 269 | 0 | 0 |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
G:=sub<GL(3,GF(373))| [1,0,0,0,215,0,0,0,215],[1,0,0,0,1,0,0,0,372],[1,0,0,0,372,0,0,0,372],[269,0,0,0,0,1,0,1,0] >;
C22⋊C4×C31 in GAP, Magma, Sage, TeX
C_2^2\rtimes C_4\times C_{31} % in TeX
G:=Group("C2^2:C4xC31"); // GroupNames label
G:=SmallGroup(496,20);
// by ID
G=gap.SmallGroup(496,20);
# by ID
G:=PCGroup([5,-2,-2,-31,-2,-2,1240,1261]);
// Polycyclic
G:=Group<a,b,c,d|a^31=b^2=c^2=d^4=1,a*b=b*a,a*c=c*a,a*d=d*a,d*b*d^-1=b*c=c*b,c*d=d*c>;
// generators/relations
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