metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D4⋊D31, C31⋊2D8, C62.7D4, C4.1D62, D124⋊2C2, C124.1C22, C31⋊C8⋊1C2, (D4×C31)⋊1C2, C2.4(C31⋊D4), SmallGroup(496,14)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D4⋊D31
G = < a,b,c,d | a4=b2=c31=d2=1, bab=dad=a-1, ac=ca, bc=cb, dbd=ab, dcd=c-1 >
Smallest permutation representation of D4⋊D31
►On 248 points
Generators in S248
(1 96 45 90)(2 97 46 91)(3 98 47 92)(4 99 48 93)(5 100 49 63)(6 101 50 64)(7 102 51 65)(8 103 52 66)(9 104 53 67)(10 105 54 68)(11 106 55 69)(12 107 56 70)(13 108 57 71)(14 109 58 72)(15 110 59 73)(16 111 60 74)(17 112 61 75)(18 113 62 76)(19 114 32 77)(20 115 33 78)(21 116 34 79)(22 117 35 80)(23 118 36 81)(24 119 37 82)(25 120 38 83)(26 121 39 84)(27 122 40 85)(28 123 41 86)(29 124 42 87)(30 94 43 88)(31 95 44 89)(125 198 159 235)(126 199 160 236)(127 200 161 237)(128 201 162 238)(129 202 163 239)(130 203 164 240)(131 204 165 241)(132 205 166 242)(133 206 167 243)(134 207 168 244)(135 208 169 245)(136 209 170 246)(137 210 171 247)(138 211 172 248)(139 212 173 218)(140 213 174 219)(141 214 175 220)(142 215 176 221)(143 216 177 222)(144 217 178 223)(145 187 179 224)(146 188 180 225)(147 189 181 226)(148 190 182 227)(149 191 183 228)(150 192 184 229)(151 193 185 230)(152 194 186 231)(153 195 156 232)(154 196 157 233)(155 197 158 234)
(1 226)(2 227)(3 228)(4 229)(5 230)(6 231)(7 232)(8 233)(9 234)(10 235)(11 236)(12 237)(13 238)(14 239)(15 240)(16 241)(17 242)(18 243)(19 244)(20 245)(21 246)(22 247)(23 248)(24 218)(25 219)(26 220)(27 221)(28 222)(29 223)(30 224)(31 225)(32 207)(33 208)(34 209)(35 210)(36 211)(37 212)(38 213)(39 214)(40 215)(41 216)(42 217)(43 187)(44 188)(45 189)(46 190)(47 191)(48 192)(49 193)(50 194)(51 195)(52 196)(53 197)(54 198)(55 199)(56 200)(57 201)(58 202)(59 203)(60 204)(61 205)(62 206)(63 151)(64 152)(65 153)(66 154)(67 155)(68 125)(69 126)(70 127)(71 128)(72 129)(73 130)(74 131)(75 132)(76 133)(77 134)(78 135)(79 136)(80 137)(81 138)(82 139)(83 140)(84 141)(85 142)(86 143)(87 144)(88 145)(89 146)(90 147)(91 148)(92 149)(93 150)(94 179)(95 180)(96 181)(97 182)(98 183)(99 184)(100 185)(101 186)(102 156)(103 157)(104 158)(105 159)(106 160)(107 161)(108 162)(109 163)(110 164)(111 165)(112 166)(113 167)(114 168)(115 169)(116 170)(117 171)(118 172)(119 173)(120 174)(121 175)(122 176)(123 177)(124 178)
(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 31)(2 30)(3 29)(4 28)(5 27)(6 26)(7 25)(8 24)(9 23)(10 22)(11 21)(12 20)(13 19)(14 18)(15 17)(32 57)(33 56)(34 55)(35 54)(36 53)(37 52)(38 51)(39 50)(40 49)(41 48)(42 47)(43 46)(44 45)(58 62)(59 61)(63 122)(64 121)(65 120)(66 119)(67 118)(68 117)(69 116)(70 115)(71 114)(72 113)(73 112)(74 111)(75 110)(76 109)(77 108)(78 107)(79 106)(80 105)(81 104)(82 103)(83 102)(84 101)(85 100)(86 99)(87 98)(88 97)(89 96)(90 95)(91 94)(92 124)(93 123)(125 210)(126 209)(127 208)(128 207)(129 206)(130 205)(131 204)(132 203)(133 202)(134 201)(135 200)(136 199)(137 198)(138 197)(139 196)(140 195)(141 194)(142 193)(143 192)(144 191)(145 190)(146 189)(147 188)(148 187)(149 217)(150 216)(151 215)(152 214)(153 213)(154 212)(155 211)(156 219)(157 218)(158 248)(159 247)(160 246)(161 245)(162 244)(163 243)(164 242)(165 241)(166 240)(167 239)(168 238)(169 237)(170 236)(171 235)(172 234)(173 233)(174 232)(175 231)(176 230)(177 229)(178 228)(179 227)(180 226)(181 225)(182 224)(183 223)(184 222)(185 221)(186 220)
G:=sub<Sym(248)| (1,96,45,90)(2,97,46,91)(3,98,47,92)(4,99,48,93)(5,100,49,63)(6,101,50,64)(7,102,51,65)(8,103,52,66)(9,104,53,67)(10,105,54,68)(11,106,55,69)(12,107,56,70)(13,108,57,71)(14,109,58,72)(15,110,59,73)(16,111,60,74)(17,112,61,75)(18,113,62,76)(19,114,32,77)(20,115,33,78)(21,116,34,79)(22,117,35,80)(23,118,36,81)(24,119,37,82)(25,120,38,83)(26,121,39,84)(27,122,40,85)(28,123,41,86)(29,124,42,87)(30,94,43,88)(31,95,44,89)(125,198,159,235)(126,199,160,236)(127,200,161,237)(128,201,162,238)(129,202,163,239)(130,203,164,240)(131,204,165,241)(132,205,166,242)(133,206,167,243)(134,207,168,244)(135,208,169,245)(136,209,170,246)(137,210,171,247)(138,211,172,248)(139,212,173,218)(140,213,174,219)(141,214,175,220)(142,215,176,221)(143,216,177,222)(144,217,178,223)(145,187,179,224)(146,188,180,225)(147,189,181,226)(148,190,182,227)(149,191,183,228)(150,192,184,229)(151,193,185,230)(152,194,186,231)(153,195,156,232)(154,196,157,233)(155,197,158,234), (1,226)(2,227)(3,228)(4,229)(5,230)(6,231)(7,232)(8,233)(9,234)(10,235)(11,236)(12,237)(13,238)(14,239)(15,240)(16,241)(17,242)(18,243)(19,244)(20,245)(21,246)(22,247)(23,248)(24,218)(25,219)(26,220)(27,221)(28,222)(29,223)(30,224)(31,225)(32,207)(33,208)(34,209)(35,210)(36,211)(37,212)(38,213)(39,214)(40,215)(41,216)(42,217)(43,187)(44,188)(45,189)(46,190)(47,191)(48,192)(49,193)(50,194)(51,195)(52,196)(53,197)(54,198)(55,199)(56,200)(57,201)(58,202)(59,203)(60,204)(61,205)(62,206)(63,151)(64,152)(65,153)(66,154)(67,155)(68,125)(69,126)(70,127)(71,128)(72,129)(73,130)(74,131)(75,132)(76,133)(77,134)(78,135)(79,136)(80,137)(81,138)(82,139)(83,140)(84,141)(85,142)(86,143)(87,144)(88,145)(89,146)(90,147)(91,148)(92,149)(93,150)(94,179)(95,180)(96,181)(97,182)(98,183)(99,184)(100,185)(101,186)(102,156)(103,157)(104,158)(105,159)(106,160)(107,161)(108,162)(109,163)(110,164)(111,165)(112,166)(113,167)(114,168)(115,169)(116,170)(117,171)(118,172)(119,173)(120,174)(121,175)(122,176)(123,177)(124,178), (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), (1,31)(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)(32,57)(33,56)(34,55)(35,54)(36,53)(37,52)(38,51)(39,50)(40,49)(41,48)(42,47)(43,46)(44,45)(58,62)(59,61)(63,122)(64,121)(65,120)(66,119)(67,118)(68,117)(69,116)(70,115)(71,114)(72,113)(73,112)(74,111)(75,110)(76,109)(77,108)(78,107)(79,106)(80,105)(81,104)(82,103)(83,102)(84,101)(85,100)(86,99)(87,98)(88,97)(89,96)(90,95)(91,94)(92,124)(93,123)(125,210)(126,209)(127,208)(128,207)(129,206)(130,205)(131,204)(132,203)(133,202)(134,201)(135,200)(136,199)(137,198)(138,197)(139,196)(140,195)(141,194)(142,193)(143,192)(144,191)(145,190)(146,189)(147,188)(148,187)(149,217)(150,216)(151,215)(152,214)(153,213)(154,212)(155,211)(156,219)(157,218)(158,248)(159,247)(160,246)(161,245)(162,244)(163,243)(164,242)(165,241)(166,240)(167,239)(168,238)(169,237)(170,236)(171,235)(172,234)(173,233)(174,232)(175,231)(176,230)(177,229)(178,228)(179,227)(180,226)(181,225)(182,224)(183,223)(184,222)(185,221)(186,220)>;
G:=Group( (1,96,45,90)(2,97,46,91)(3,98,47,92)(4,99,48,93)(5,100,49,63)(6,101,50,64)(7,102,51,65)(8,103,52,66)(9,104,53,67)(10,105,54,68)(11,106,55,69)(12,107,56,70)(13,108,57,71)(14,109,58,72)(15,110,59,73)(16,111,60,74)(17,112,61,75)(18,113,62,76)(19,114,32,77)(20,115,33,78)(21,116,34,79)(22,117,35,80)(23,118,36,81)(24,119,37,82)(25,120,38,83)(26,121,39,84)(27,122,40,85)(28,123,41,86)(29,124,42,87)(30,94,43,88)(31,95,44,89)(125,198,159,235)(126,199,160,236)(127,200,161,237)(128,201,162,238)(129,202,163,239)(130,203,164,240)(131,204,165,241)(132,205,166,242)(133,206,167,243)(134,207,168,244)(135,208,169,245)(136,209,170,246)(137,210,171,247)(138,211,172,248)(139,212,173,218)(140,213,174,219)(141,214,175,220)(142,215,176,221)(143,216,177,222)(144,217,178,223)(145,187,179,224)(146,188,180,225)(147,189,181,226)(148,190,182,227)(149,191,183,228)(150,192,184,229)(151,193,185,230)(152,194,186,231)(153,195,156,232)(154,196,157,233)(155,197,158,234), (1,226)(2,227)(3,228)(4,229)(5,230)(6,231)(7,232)(8,233)(9,234)(10,235)(11,236)(12,237)(13,238)(14,239)(15,240)(16,241)(17,242)(18,243)(19,244)(20,245)(21,246)(22,247)(23,248)(24,218)(25,219)(26,220)(27,221)(28,222)(29,223)(30,224)(31,225)(32,207)(33,208)(34,209)(35,210)(36,211)(37,212)(38,213)(39,214)(40,215)(41,216)(42,217)(43,187)(44,188)(45,189)(46,190)(47,191)(48,192)(49,193)(50,194)(51,195)(52,196)(53,197)(54,198)(55,199)(56,200)(57,201)(58,202)(59,203)(60,204)(61,205)(62,206)(63,151)(64,152)(65,153)(66,154)(67,155)(68,125)(69,126)(70,127)(71,128)(72,129)(73,130)(74,131)(75,132)(76,133)(77,134)(78,135)(79,136)(80,137)(81,138)(82,139)(83,140)(84,141)(85,142)(86,143)(87,144)(88,145)(89,146)(90,147)(91,148)(92,149)(93,150)(94,179)(95,180)(96,181)(97,182)(98,183)(99,184)(100,185)(101,186)(102,156)(103,157)(104,158)(105,159)(106,160)(107,161)(108,162)(109,163)(110,164)(111,165)(112,166)(113,167)(114,168)(115,169)(116,170)(117,171)(118,172)(119,173)(120,174)(121,175)(122,176)(123,177)(124,178), (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), (1,31)(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)(32,57)(33,56)(34,55)(35,54)(36,53)(37,52)(38,51)(39,50)(40,49)(41,48)(42,47)(43,46)(44,45)(58,62)(59,61)(63,122)(64,121)(65,120)(66,119)(67,118)(68,117)(69,116)(70,115)(71,114)(72,113)(73,112)(74,111)(75,110)(76,109)(77,108)(78,107)(79,106)(80,105)(81,104)(82,103)(83,102)(84,101)(85,100)(86,99)(87,98)(88,97)(89,96)(90,95)(91,94)(92,124)(93,123)(125,210)(126,209)(127,208)(128,207)(129,206)(130,205)(131,204)(132,203)(133,202)(134,201)(135,200)(136,199)(137,198)(138,197)(139,196)(140,195)(141,194)(142,193)(143,192)(144,191)(145,190)(146,189)(147,188)(148,187)(149,217)(150,216)(151,215)(152,214)(153,213)(154,212)(155,211)(156,219)(157,218)(158,248)(159,247)(160,246)(161,245)(162,244)(163,243)(164,242)(165,241)(166,240)(167,239)(168,238)(169,237)(170,236)(171,235)(172,234)(173,233)(174,232)(175,231)(176,230)(177,229)(178,228)(179,227)(180,226)(181,225)(182,224)(183,223)(184,222)(185,221)(186,220) );
G=PermutationGroup([[(1,96,45,90),(2,97,46,91),(3,98,47,92),(4,99,48,93),(5,100,49,63),(6,101,50,64),(7,102,51,65),(8,103,52,66),(9,104,53,67),(10,105,54,68),(11,106,55,69),(12,107,56,70),(13,108,57,71),(14,109,58,72),(15,110,59,73),(16,111,60,74),(17,112,61,75),(18,113,62,76),(19,114,32,77),(20,115,33,78),(21,116,34,79),(22,117,35,80),(23,118,36,81),(24,119,37,82),(25,120,38,83),(26,121,39,84),(27,122,40,85),(28,123,41,86),(29,124,42,87),(30,94,43,88),(31,95,44,89),(125,198,159,235),(126,199,160,236),(127,200,161,237),(128,201,162,238),(129,202,163,239),(130,203,164,240),(131,204,165,241),(132,205,166,242),(133,206,167,243),(134,207,168,244),(135,208,169,245),(136,209,170,246),(137,210,171,247),(138,211,172,248),(139,212,173,218),(140,213,174,219),(141,214,175,220),(142,215,176,221),(143,216,177,222),(144,217,178,223),(145,187,179,224),(146,188,180,225),(147,189,181,226),(148,190,182,227),(149,191,183,228),(150,192,184,229),(151,193,185,230),(152,194,186,231),(153,195,156,232),(154,196,157,233),(155,197,158,234)], [(1,226),(2,227),(3,228),(4,229),(5,230),(6,231),(7,232),(8,233),(9,234),(10,235),(11,236),(12,237),(13,238),(14,239),(15,240),(16,241),(17,242),(18,243),(19,244),(20,245),(21,246),(22,247),(23,248),(24,218),(25,219),(26,220),(27,221),(28,222),(29,223),(30,224),(31,225),(32,207),(33,208),(34,209),(35,210),(36,211),(37,212),(38,213),(39,214),(40,215),(41,216),(42,217),(43,187),(44,188),(45,189),(46,190),(47,191),(48,192),(49,193),(50,194),(51,195),(52,196),(53,197),(54,198),(55,199),(56,200),(57,201),(58,202),(59,203),(60,204),(61,205),(62,206),(63,151),(64,152),(65,153),(66,154),(67,155),(68,125),(69,126),(70,127),(71,128),(72,129),(73,130),(74,131),(75,132),(76,133),(77,134),(78,135),(79,136),(80,137),(81,138),(82,139),(83,140),(84,141),(85,142),(86,143),(87,144),(88,145),(89,146),(90,147),(91,148),(92,149),(93,150),(94,179),(95,180),(96,181),(97,182),(98,183),(99,184),(100,185),(101,186),(102,156),(103,157),(104,158),(105,159),(106,160),(107,161),(108,162),(109,163),(110,164),(111,165),(112,166),(113,167),(114,168),(115,169),(116,170),(117,171),(118,172),(119,173),(120,174),(121,175),(122,176),(123,177),(124,178)], [(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)], [(1,31),(2,30),(3,29),(4,28),(5,27),(6,26),(7,25),(8,24),(9,23),(10,22),(11,21),(12,20),(13,19),(14,18),(15,17),(32,57),(33,56),(34,55),(35,54),(36,53),(37,52),(38,51),(39,50),(40,49),(41,48),(42,47),(43,46),(44,45),(58,62),(59,61),(63,122),(64,121),(65,120),(66,119),(67,118),(68,117),(69,116),(70,115),(71,114),(72,113),(73,112),(74,111),(75,110),(76,109),(77,108),(78,107),(79,106),(80,105),(81,104),(82,103),(83,102),(84,101),(85,100),(86,99),(87,98),(88,97),(89,96),(90,95),(91,94),(92,124),(93,123),(125,210),(126,209),(127,208),(128,207),(129,206),(130,205),(131,204),(132,203),(133,202),(134,201),(135,200),(136,199),(137,198),(138,197),(139,196),(140,195),(141,194),(142,193),(143,192),(144,191),(145,190),(146,189),(147,188),(148,187),(149,217),(150,216),(151,215),(152,214),(153,213),(154,212),(155,211),(156,219),(157,218),(158,248),(159,247),(160,246),(161,245),(162,244),(163,243),(164,242),(165,241),(166,240),(167,239),(168,238),(169,237),(170,236),(171,235),(172,234),(173,233),(174,232),(175,231),(176,230),(177,229),(178,228),(179,227),(180,226),(181,225),(182,224),(183,223),(184,222),(185,221),(186,220)]])
82 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4 | 8A | 8B | 31A | ··· | 31O | 62A | ··· | 62O | 62P | ··· | 62AS | 124A | ··· | 124O |
| order | 1 | 2 | 2 | 2 | 4 | 8 | 8 | 31 | ··· | 31 | 62 | ··· | 62 | 62 | ··· | 62 | 124 | ··· | 124 |
| size | 1 | 1 | 4 | 124 | 2 | 62 | 62 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | + | + | + | |
| image | C1 | C2 | C2 | C2 | D4 | D8 | D31 | D62 | C31⋊D4 | D4⋊D31 |
| kernel | D4⋊D31 | C31⋊C8 | D124 | D4×C31 | C62 | C31 | D4 | C4 | C2 | C1 |
| # reps | 1 | 1 | 1 | 1 | 1 | 2 | 15 | 15 | 30 | 15 |
Matrix representation of D4⋊D31 ►in GL4(𝔽1489) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 476 |
| 0 | 0 | 1245 | 1488 |
| 1488 | 0 | 0 | 0 |
| 0 | 1488 | 0 | 0 |
| 0 | 0 | 0 | 87 |
| 0 | 0 | 445 | 0 |
| 0 | 1 | 0 | 0 |
| 1488 | 246 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 1245 | 1488 |
G:=sub<GL(4,GF(1489))| [1,0,0,0,0,1,0,0,0,0,1,1245,0,0,476,1488],[1488,0,0,0,0,1488,0,0,0,0,0,445,0,0,87,0],[0,1488,0,0,1,246,0,0,0,0,1,0,0,0,0,1],[0,1,0,0,1,0,0,0,0,0,1,1245,0,0,0,1488] >;
D4⋊D31 in GAP, Magma, Sage, TeX
D_4\rtimes D_{31} % in TeX
G:=Group("D4:D31"); // GroupNames label
G:=SmallGroup(496,14);
// by ID
G=gap.SmallGroup(496,14);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-31,61,182,97,42,12004]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^2=c^31=d^2=1,b*a*b=d*a*d=a^-1,a*c=c*a,b*c=c*b,d*b*d=a*b,d*c*d=c^-1>;
// generators/relations
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