direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C2×C4×D31, C124⋊3C22, C62.2C23, C22.9D62, D62.4C22, Dic31⋊3C22, C62⋊1(C2×C4), (C2×C124)⋊5C2, C31⋊1(C22×C4), (C2×Dic31)⋊5C2, (C2×C62).9C22, C2.1(C22×D31), (C22×D31).2C2, SmallGroup(496,28)
Series: Derived ►Chief ►Lower central ►Upper central
| C31 — C2×C4×D31 |
Generators and relations for C2×C4×D31
G = < a,b,c,d | a2=b4=c31=d2=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd=c-1 >
Subgroups: 624 in 54 conjugacy classes, 35 normal (11 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C2×C4, C2×C4, C23, C22×C4, C31, D31, C62, C62, Dic31, C124, D62, C2×C62, C4×D31, C2×Dic31, C2×C124, C22×D31, C2×C4×D31
Quotients: C1, C2, C4, C22, C2×C4, C23, C22×C4, D31, D62, C4×D31, C22×D31, C2×C4×D31
►On 248 points
Generators in S248
(1 127)(2 128)(3 129)(4 130)(5 131)(6 132)(7 133)(8 134)(9 135)(10 136)(11 137)(12 138)(13 139)(14 140)(15 141)(16 142)(17 143)(18 144)(19 145)(20 146)(21 147)(22 148)(23 149)(24 150)(25 151)(26 152)(27 153)(28 154)(29 155)(30 125)(31 126)(32 181)(33 182)(34 183)(35 184)(36 185)(37 186)(38 156)(39 157)(40 158)(41 159)(42 160)(43 161)(44 162)(45 163)(46 164)(47 165)(48 166)(49 167)(50 168)(51 169)(52 170)(53 171)(54 172)(55 173)(56 174)(57 175)(58 176)(59 177)(60 178)(61 179)(62 180)(63 215)(64 216)(65 217)(66 187)(67 188)(68 189)(69 190)(70 191)(71 192)(72 193)(73 194)(74 195)(75 196)(76 197)(77 198)(78 199)(79 200)(80 201)(81 202)(82 203)(83 204)(84 205)(85 206)(86 207)(87 208)(88 209)(89 210)(90 211)(91 212)(92 213)(93 214)(94 223)(95 224)(96 225)(97 226)(98 227)(99 228)(100 229)(101 230)(102 231)(103 232)(104 233)(105 234)(106 235)(107 236)(108 237)(109 238)(110 239)(111 240)(112 241)(113 242)(114 243)(115 244)(116 245)(117 246)(118 247)(119 248)(120 218)(121 219)(122 220)(123 221)(124 222)
(1 100 58 89)(2 101 59 90)(3 102 60 91)(4 103 61 92)(5 104 62 93)(6 105 32 63)(7 106 33 64)(8 107 34 65)(9 108 35 66)(10 109 36 67)(11 110 37 68)(12 111 38 69)(13 112 39 70)(14 113 40 71)(15 114 41 72)(16 115 42 73)(17 116 43 74)(18 117 44 75)(19 118 45 76)(20 119 46 77)(21 120 47 78)(22 121 48 79)(23 122 49 80)(24 123 50 81)(25 124 51 82)(26 94 52 83)(27 95 53 84)(28 96 54 85)(29 97 55 86)(30 98 56 87)(31 99 57 88)(125 227 174 208)(126 228 175 209)(127 229 176 210)(128 230 177 211)(129 231 178 212)(130 232 179 213)(131 233 180 214)(132 234 181 215)(133 235 182 216)(134 236 183 217)(135 237 184 187)(136 238 185 188)(137 239 186 189)(138 240 156 190)(139 241 157 191)(140 242 158 192)(141 243 159 193)(142 244 160 194)(143 245 161 195)(144 246 162 196)(145 247 163 197)(146 248 164 198)(147 218 165 199)(148 219 166 200)(149 220 167 201)(150 221 168 202)(151 222 169 203)(152 223 170 204)(153 224 171 205)(154 225 172 206)(155 226 173 207)
(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)
(1 126)(2 125)(3 155)(4 154)(5 153)(6 152)(7 151)(8 150)(9 149)(10 148)(11 147)(12 146)(13 145)(14 144)(15 143)(16 142)(17 141)(18 140)(19 139)(20 138)(21 137)(22 136)(23 135)(24 134)(25 133)(26 132)(27 131)(28 130)(29 129)(30 128)(31 127)(32 170)(33 169)(34 168)(35 167)(36 166)(37 165)(38 164)(39 163)(40 162)(41 161)(42 160)(43 159)(44 158)(45 157)(46 156)(47 186)(48 185)(49 184)(50 183)(51 182)(52 181)(53 180)(54 179)(55 178)(56 177)(57 176)(58 175)(59 174)(60 173)(61 172)(62 171)(63 204)(64 203)(65 202)(66 201)(67 200)(68 199)(69 198)(70 197)(71 196)(72 195)(73 194)(74 193)(75 192)(76 191)(77 190)(78 189)(79 188)(80 187)(81 217)(82 216)(83 215)(84 214)(85 213)(86 212)(87 211)(88 210)(89 209)(90 208)(91 207)(92 206)(93 205)(94 234)(95 233)(96 232)(97 231)(98 230)(99 229)(100 228)(101 227)(102 226)(103 225)(104 224)(105 223)(106 222)(107 221)(108 220)(109 219)(110 218)(111 248)(112 247)(113 246)(114 245)(115 244)(116 243)(117 242)(118 241)(119 240)(120 239)(121 238)(122 237)(123 236)(124 235)
G:=sub<Sym(248)| (1,127)(2,128)(3,129)(4,130)(5,131)(6,132)(7,133)(8,134)(9,135)(10,136)(11,137)(12,138)(13,139)(14,140)(15,141)(16,142)(17,143)(18,144)(19,145)(20,146)(21,147)(22,148)(23,149)(24,150)(25,151)(26,152)(27,153)(28,154)(29,155)(30,125)(31,126)(32,181)(33,182)(34,183)(35,184)(36,185)(37,186)(38,156)(39,157)(40,158)(41,159)(42,160)(43,161)(44,162)(45,163)(46,164)(47,165)(48,166)(49,167)(50,168)(51,169)(52,170)(53,171)(54,172)(55,173)(56,174)(57,175)(58,176)(59,177)(60,178)(61,179)(62,180)(63,215)(64,216)(65,217)(66,187)(67,188)(68,189)(69,190)(70,191)(71,192)(72,193)(73,194)(74,195)(75,196)(76,197)(77,198)(78,199)(79,200)(80,201)(81,202)(82,203)(83,204)(84,205)(85,206)(86,207)(87,208)(88,209)(89,210)(90,211)(91,212)(92,213)(93,214)(94,223)(95,224)(96,225)(97,226)(98,227)(99,228)(100,229)(101,230)(102,231)(103,232)(104,233)(105,234)(106,235)(107,236)(108,237)(109,238)(110,239)(111,240)(112,241)(113,242)(114,243)(115,244)(116,245)(117,246)(118,247)(119,248)(120,218)(121,219)(122,220)(123,221)(124,222), (1,100,58,89)(2,101,59,90)(3,102,60,91)(4,103,61,92)(5,104,62,93)(6,105,32,63)(7,106,33,64)(8,107,34,65)(9,108,35,66)(10,109,36,67)(11,110,37,68)(12,111,38,69)(13,112,39,70)(14,113,40,71)(15,114,41,72)(16,115,42,73)(17,116,43,74)(18,117,44,75)(19,118,45,76)(20,119,46,77)(21,120,47,78)(22,121,48,79)(23,122,49,80)(24,123,50,81)(25,124,51,82)(26,94,52,83)(27,95,53,84)(28,96,54,85)(29,97,55,86)(30,98,56,87)(31,99,57,88)(125,227,174,208)(126,228,175,209)(127,229,176,210)(128,230,177,211)(129,231,178,212)(130,232,179,213)(131,233,180,214)(132,234,181,215)(133,235,182,216)(134,236,183,217)(135,237,184,187)(136,238,185,188)(137,239,186,189)(138,240,156,190)(139,241,157,191)(140,242,158,192)(141,243,159,193)(142,244,160,194)(143,245,161,195)(144,246,162,196)(145,247,163,197)(146,248,164,198)(147,218,165,199)(148,219,166,200)(149,220,167,201)(150,221,168,202)(151,222,169,203)(152,223,170,204)(153,224,171,205)(154,225,172,206)(155,226,173,207), (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), (1,126)(2,125)(3,155)(4,154)(5,153)(6,152)(7,151)(8,150)(9,149)(10,148)(11,147)(12,146)(13,145)(14,144)(15,143)(16,142)(17,141)(18,140)(19,139)(20,138)(21,137)(22,136)(23,135)(24,134)(25,133)(26,132)(27,131)(28,130)(29,129)(30,128)(31,127)(32,170)(33,169)(34,168)(35,167)(36,166)(37,165)(38,164)(39,163)(40,162)(41,161)(42,160)(43,159)(44,158)(45,157)(46,156)(47,186)(48,185)(49,184)(50,183)(51,182)(52,181)(53,180)(54,179)(55,178)(56,177)(57,176)(58,175)(59,174)(60,173)(61,172)(62,171)(63,204)(64,203)(65,202)(66,201)(67,200)(68,199)(69,198)(70,197)(71,196)(72,195)(73,194)(74,193)(75,192)(76,191)(77,190)(78,189)(79,188)(80,187)(81,217)(82,216)(83,215)(84,214)(85,213)(86,212)(87,211)(88,210)(89,209)(90,208)(91,207)(92,206)(93,205)(94,234)(95,233)(96,232)(97,231)(98,230)(99,229)(100,228)(101,227)(102,226)(103,225)(104,224)(105,223)(106,222)(107,221)(108,220)(109,219)(110,218)(111,248)(112,247)(113,246)(114,245)(115,244)(116,243)(117,242)(118,241)(119,240)(120,239)(121,238)(122,237)(123,236)(124,235)>;
G:=Group( (1,127)(2,128)(3,129)(4,130)(5,131)(6,132)(7,133)(8,134)(9,135)(10,136)(11,137)(12,138)(13,139)(14,140)(15,141)(16,142)(17,143)(18,144)(19,145)(20,146)(21,147)(22,148)(23,149)(24,150)(25,151)(26,152)(27,153)(28,154)(29,155)(30,125)(31,126)(32,181)(33,182)(34,183)(35,184)(36,185)(37,186)(38,156)(39,157)(40,158)(41,159)(42,160)(43,161)(44,162)(45,163)(46,164)(47,165)(48,166)(49,167)(50,168)(51,169)(52,170)(53,171)(54,172)(55,173)(56,174)(57,175)(58,176)(59,177)(60,178)(61,179)(62,180)(63,215)(64,216)(65,217)(66,187)(67,188)(68,189)(69,190)(70,191)(71,192)(72,193)(73,194)(74,195)(75,196)(76,197)(77,198)(78,199)(79,200)(80,201)(81,202)(82,203)(83,204)(84,205)(85,206)(86,207)(87,208)(88,209)(89,210)(90,211)(91,212)(92,213)(93,214)(94,223)(95,224)(96,225)(97,226)(98,227)(99,228)(100,229)(101,230)(102,231)(103,232)(104,233)(105,234)(106,235)(107,236)(108,237)(109,238)(110,239)(111,240)(112,241)(113,242)(114,243)(115,244)(116,245)(117,246)(118,247)(119,248)(120,218)(121,219)(122,220)(123,221)(124,222), (1,100,58,89)(2,101,59,90)(3,102,60,91)(4,103,61,92)(5,104,62,93)(6,105,32,63)(7,106,33,64)(8,107,34,65)(9,108,35,66)(10,109,36,67)(11,110,37,68)(12,111,38,69)(13,112,39,70)(14,113,40,71)(15,114,41,72)(16,115,42,73)(17,116,43,74)(18,117,44,75)(19,118,45,76)(20,119,46,77)(21,120,47,78)(22,121,48,79)(23,122,49,80)(24,123,50,81)(25,124,51,82)(26,94,52,83)(27,95,53,84)(28,96,54,85)(29,97,55,86)(30,98,56,87)(31,99,57,88)(125,227,174,208)(126,228,175,209)(127,229,176,210)(128,230,177,211)(129,231,178,212)(130,232,179,213)(131,233,180,214)(132,234,181,215)(133,235,182,216)(134,236,183,217)(135,237,184,187)(136,238,185,188)(137,239,186,189)(138,240,156,190)(139,241,157,191)(140,242,158,192)(141,243,159,193)(142,244,160,194)(143,245,161,195)(144,246,162,196)(145,247,163,197)(146,248,164,198)(147,218,165,199)(148,219,166,200)(149,220,167,201)(150,221,168,202)(151,222,169,203)(152,223,170,204)(153,224,171,205)(154,225,172,206)(155,226,173,207), (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), (1,126)(2,125)(3,155)(4,154)(5,153)(6,152)(7,151)(8,150)(9,149)(10,148)(11,147)(12,146)(13,145)(14,144)(15,143)(16,142)(17,141)(18,140)(19,139)(20,138)(21,137)(22,136)(23,135)(24,134)(25,133)(26,132)(27,131)(28,130)(29,129)(30,128)(31,127)(32,170)(33,169)(34,168)(35,167)(36,166)(37,165)(38,164)(39,163)(40,162)(41,161)(42,160)(43,159)(44,158)(45,157)(46,156)(47,186)(48,185)(49,184)(50,183)(51,182)(52,181)(53,180)(54,179)(55,178)(56,177)(57,176)(58,175)(59,174)(60,173)(61,172)(62,171)(63,204)(64,203)(65,202)(66,201)(67,200)(68,199)(69,198)(70,197)(71,196)(72,195)(73,194)(74,193)(75,192)(76,191)(77,190)(78,189)(79,188)(80,187)(81,217)(82,216)(83,215)(84,214)(85,213)(86,212)(87,211)(88,210)(89,209)(90,208)(91,207)(92,206)(93,205)(94,234)(95,233)(96,232)(97,231)(98,230)(99,229)(100,228)(101,227)(102,226)(103,225)(104,224)(105,223)(106,222)(107,221)(108,220)(109,219)(110,218)(111,248)(112,247)(113,246)(114,245)(115,244)(116,243)(117,242)(118,241)(119,240)(120,239)(121,238)(122,237)(123,236)(124,235) );
G=PermutationGroup([[(1,127),(2,128),(3,129),(4,130),(5,131),(6,132),(7,133),(8,134),(9,135),(10,136),(11,137),(12,138),(13,139),(14,140),(15,141),(16,142),(17,143),(18,144),(19,145),(20,146),(21,147),(22,148),(23,149),(24,150),(25,151),(26,152),(27,153),(28,154),(29,155),(30,125),(31,126),(32,181),(33,182),(34,183),(35,184),(36,185),(37,186),(38,156),(39,157),(40,158),(41,159),(42,160),(43,161),(44,162),(45,163),(46,164),(47,165),(48,166),(49,167),(50,168),(51,169),(52,170),(53,171),(54,172),(55,173),(56,174),(57,175),(58,176),(59,177),(60,178),(61,179),(62,180),(63,215),(64,216),(65,217),(66,187),(67,188),(68,189),(69,190),(70,191),(71,192),(72,193),(73,194),(74,195),(75,196),(76,197),(77,198),(78,199),(79,200),(80,201),(81,202),(82,203),(83,204),(84,205),(85,206),(86,207),(87,208),(88,209),(89,210),(90,211),(91,212),(92,213),(93,214),(94,223),(95,224),(96,225),(97,226),(98,227),(99,228),(100,229),(101,230),(102,231),(103,232),(104,233),(105,234),(106,235),(107,236),(108,237),(109,238),(110,239),(111,240),(112,241),(113,242),(114,243),(115,244),(116,245),(117,246),(118,247),(119,248),(120,218),(121,219),(122,220),(123,221),(124,222)], [(1,100,58,89),(2,101,59,90),(3,102,60,91),(4,103,61,92),(5,104,62,93),(6,105,32,63),(7,106,33,64),(8,107,34,65),(9,108,35,66),(10,109,36,67),(11,110,37,68),(12,111,38,69),(13,112,39,70),(14,113,40,71),(15,114,41,72),(16,115,42,73),(17,116,43,74),(18,117,44,75),(19,118,45,76),(20,119,46,77),(21,120,47,78),(22,121,48,79),(23,122,49,80),(24,123,50,81),(25,124,51,82),(26,94,52,83),(27,95,53,84),(28,96,54,85),(29,97,55,86),(30,98,56,87),(31,99,57,88),(125,227,174,208),(126,228,175,209),(127,229,176,210),(128,230,177,211),(129,231,178,212),(130,232,179,213),(131,233,180,214),(132,234,181,215),(133,235,182,216),(134,236,183,217),(135,237,184,187),(136,238,185,188),(137,239,186,189),(138,240,156,190),(139,241,157,191),(140,242,158,192),(141,243,159,193),(142,244,160,194),(143,245,161,195),(144,246,162,196),(145,247,163,197),(146,248,164,198),(147,218,165,199),(148,219,166,200),(149,220,167,201),(150,221,168,202),(151,222,169,203),(152,223,170,204),(153,224,171,205),(154,225,172,206),(155,226,173,207)], [(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)], [(1,126),(2,125),(3,155),(4,154),(5,153),(6,152),(7,151),(8,150),(9,149),(10,148),(11,147),(12,146),(13,145),(14,144),(15,143),(16,142),(17,141),(18,140),(19,139),(20,138),(21,137),(22,136),(23,135),(24,134),(25,133),(26,132),(27,131),(28,130),(29,129),(30,128),(31,127),(32,170),(33,169),(34,168),(35,167),(36,166),(37,165),(38,164),(39,163),(40,162),(41,161),(42,160),(43,159),(44,158),(45,157),(46,156),(47,186),(48,185),(49,184),(50,183),(51,182),(52,181),(53,180),(54,179),(55,178),(56,177),(57,176),(58,175),(59,174),(60,173),(61,172),(62,171),(63,204),(64,203),(65,202),(66,201),(67,200),(68,199),(69,198),(70,197),(71,196),(72,195),(73,194),(74,193),(75,192),(76,191),(77,190),(78,189),(79,188),(80,187),(81,217),(82,216),(83,215),(84,214),(85,213),(86,212),(87,211),(88,210),(89,209),(90,208),(91,207),(92,206),(93,205),(94,234),(95,233),(96,232),(97,231),(98,230),(99,229),(100,228),(101,227),(102,226),(103,225),(104,224),(105,223),(106,222),(107,221),(108,220),(109,219),(110,218),(111,248),(112,247),(113,246),(114,245),(115,244),(116,243),(117,242),(118,241),(119,240),(120,239),(121,238),(122,237),(123,236),(124,235)]])
136 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 31A | ··· | 31O | 62A | ··· | 62AS | 124A | ··· | 124BH |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 31 | ··· | 31 | 62 | ··· | 62 | 124 | ··· | 124 |
| size | 1 | 1 | 1 | 1 | 31 | 31 | 31 | 31 | 1 | 1 | 1 | 1 | 31 | 31 | 31 | 31 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
136 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C4 | D31 | D62 | D62 | C4×D31 |
| kernel | C2×C4×D31 | C4×D31 | C2×Dic31 | C2×C124 | C22×D31 | D62 | C2×C4 | C4 | C22 | C2 |
| # reps | 1 | 4 | 1 | 1 | 1 | 8 | 15 | 30 | 15 | 60 |
Matrix representation of C2×C4×D31 ►in GL3(𝔽373) generated by
| 372 | 0 | 0 |
| 0 | 372 | 0 |
| 0 | 0 | 372 |
| 372 | 0 | 0 |
| 0 | 269 | 0 |
| 0 | 0 | 269 |
| 1 | 0 | 0 |
| 0 | 61 | 15 |
| 0 | 372 | 12 |
| 1 | 0 | 0 |
| 0 | 196 | 110 |
| 0 | 312 | 177 |
G:=sub<GL(3,GF(373))| [372,0,0,0,372,0,0,0,372],[372,0,0,0,269,0,0,0,269],[1,0,0,0,61,372,0,15,12],[1,0,0,0,196,312,0,110,177] >;
C2×C4×D31 in GAP, Magma, Sage, TeX
C_2\times C_4\times D_{31} % in TeX
G:=Group("C2xC4xD31"); // GroupNames label
G:=SmallGroup(496,28);
// by ID
G=gap.SmallGroup(496,28);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-31,42,12004]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^4=c^31=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