metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C23.D31, C62.11D4, C22⋊Dic31, C22.7D62, (C2×C62)⋊2C4, C62.9(C2×C4), C31⋊2(C22⋊C4), (C2×Dic31)⋊2C2, C2.3(C31⋊D4), (C22×C62).2C2, (C2×C62).7C22, C2.5(C2×Dic31), SmallGroup(496,18)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C23.D31
G = < a,b,c,d,e | a2=b2=c2=d31=1, e2=b, ab=ba, eae-1=ac=ca, ad=da, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >
Smallest permutation representation of C23.D31
►On 248 points
Generators in S248
(125 156)(126 157)(127 158)(128 159)(129 160)(130 161)(131 162)(132 163)(133 164)(134 165)(135 166)(136 167)(137 168)(138 169)(139 170)(140 171)(141 172)(142 173)(143 174)(144 175)(145 176)(146 177)(147 178)(148 179)(149 180)(150 181)(151 182)(152 183)(153 184)(154 185)(155 186)(187 218)(188 219)(189 220)(190 221)(191 222)(192 223)(193 224)(194 225)(195 226)(196 227)(197 228)(198 229)(199 230)(200 231)(201 232)(202 233)(203 234)(204 235)(205 236)(206 237)(207 238)(208 239)(209 240)(210 241)(211 242)(212 243)(213 244)(214 245)(215 246)(216 247)(217 248)
(1 70)(2 71)(3 72)(4 73)(5 74)(6 75)(7 76)(8 77)(9 78)(10 79)(11 80)(12 81)(13 82)(14 83)(15 84)(16 85)(17 86)(18 87)(19 88)(20 89)(21 90)(22 91)(23 92)(24 93)(25 63)(26 64)(27 65)(28 66)(29 67)(30 68)(31 69)(32 98)(33 99)(34 100)(35 101)(36 102)(37 103)(38 104)(39 105)(40 106)(41 107)(42 108)(43 109)(44 110)(45 111)(46 112)(47 113)(48 114)(49 115)(50 116)(51 117)(52 118)(53 119)(54 120)(55 121)(56 122)(57 123)(58 124)(59 94)(60 95)(61 96)(62 97)(125 187)(126 188)(127 189)(128 190)(129 191)(130 192)(131 193)(132 194)(133 195)(134 196)(135 197)(136 198)(137 199)(138 200)(139 201)(140 202)(141 203)(142 204)(143 205)(144 206)(145 207)(146 208)(147 209)(148 210)(149 211)(150 212)(151 213)(152 214)(153 215)(154 216)(155 217)(156 218)(157 219)(158 220)(159 221)(160 222)(161 223)(162 224)(163 225)(164 226)(165 227)(166 228)(167 229)(168 230)(169 231)(170 232)(171 233)(172 234)(173 235)(174 236)(175 237)(176 238)(177 239)(178 240)(179 241)(180 242)(181 243)(182 244)(183 245)(184 246)(185 247)(186 248)
(1 62)(2 32)(3 33)(4 34)(5 35)(6 36)(7 37)(8 38)(9 39)(10 40)(11 41)(12 42)(13 43)(14 44)(15 45)(16 46)(17 47)(18 48)(19 49)(20 50)(21 51)(22 52)(23 53)(24 54)(25 55)(26 56)(27 57)(28 58)(29 59)(30 60)(31 61)(63 121)(64 122)(65 123)(66 124)(67 94)(68 95)(69 96)(70 97)(71 98)(72 99)(73 100)(74 101)(75 102)(76 103)(77 104)(78 105)(79 106)(80 107)(81 108)(82 109)(83 110)(84 111)(85 112)(86 113)(87 114)(88 115)(89 116)(90 117)(91 118)(92 119)(93 120)(125 156)(126 157)(127 158)(128 159)(129 160)(130 161)(131 162)(132 163)(133 164)(134 165)(135 166)(136 167)(137 168)(138 169)(139 170)(140 171)(141 172)(142 173)(143 174)(144 175)(145 176)(146 177)(147 178)(148 179)(149 180)(150 181)(151 182)(152 183)(153 184)(154 185)(155 186)(187 218)(188 219)(189 220)(190 221)(191 222)(192 223)(193 224)(194 225)(195 226)(196 227)(197 228)(198 229)(199 230)(200 231)(201 232)(202 233)(203 234)(204 235)(205 236)(206 237)(207 238)(208 239)(209 240)(210 241)(211 242)(212 243)(213 244)(214 245)(215 246)(216 247)(217 248)
(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)
(1 217 70 155)(2 216 71 154)(3 215 72 153)(4 214 73 152)(5 213 74 151)(6 212 75 150)(7 211 76 149)(8 210 77 148)(9 209 78 147)(10 208 79 146)(11 207 80 145)(12 206 81 144)(13 205 82 143)(14 204 83 142)(15 203 84 141)(16 202 85 140)(17 201 86 139)(18 200 87 138)(19 199 88 137)(20 198 89 136)(21 197 90 135)(22 196 91 134)(23 195 92 133)(24 194 93 132)(25 193 63 131)(26 192 64 130)(27 191 65 129)(28 190 66 128)(29 189 67 127)(30 188 68 126)(31 187 69 125)(32 247 98 185)(33 246 99 184)(34 245 100 183)(35 244 101 182)(36 243 102 181)(37 242 103 180)(38 241 104 179)(39 240 105 178)(40 239 106 177)(41 238 107 176)(42 237 108 175)(43 236 109 174)(44 235 110 173)(45 234 111 172)(46 233 112 171)(47 232 113 170)(48 231 114 169)(49 230 115 168)(50 229 116 167)(51 228 117 166)(52 227 118 165)(53 226 119 164)(54 225 120 163)(55 224 121 162)(56 223 122 161)(57 222 123 160)(58 221 124 159)(59 220 94 158)(60 219 95 157)(61 218 96 156)(62 248 97 186)
G:=sub<Sym(248)| (125,156)(126,157)(127,158)(128,159)(129,160)(130,161)(131,162)(132,163)(133,164)(134,165)(135,166)(136,167)(137,168)(138,169)(139,170)(140,171)(141,172)(142,173)(143,174)(144,175)(145,176)(146,177)(147,178)(148,179)(149,180)(150,181)(151,182)(152,183)(153,184)(154,185)(155,186)(187,218)(188,219)(189,220)(190,221)(191,222)(192,223)(193,224)(194,225)(195,226)(196,227)(197,228)(198,229)(199,230)(200,231)(201,232)(202,233)(203,234)(204,235)(205,236)(206,237)(207,238)(208,239)(209,240)(210,241)(211,242)(212,243)(213,244)(214,245)(215,246)(216,247)(217,248), (1,70)(2,71)(3,72)(4,73)(5,74)(6,75)(7,76)(8,77)(9,78)(10,79)(11,80)(12,81)(13,82)(14,83)(15,84)(16,85)(17,86)(18,87)(19,88)(20,89)(21,90)(22,91)(23,92)(24,93)(25,63)(26,64)(27,65)(28,66)(29,67)(30,68)(31,69)(32,98)(33,99)(34,100)(35,101)(36,102)(37,103)(38,104)(39,105)(40,106)(41,107)(42,108)(43,109)(44,110)(45,111)(46,112)(47,113)(48,114)(49,115)(50,116)(51,117)(52,118)(53,119)(54,120)(55,121)(56,122)(57,123)(58,124)(59,94)(60,95)(61,96)(62,97)(125,187)(126,188)(127,189)(128,190)(129,191)(130,192)(131,193)(132,194)(133,195)(134,196)(135,197)(136,198)(137,199)(138,200)(139,201)(140,202)(141,203)(142,204)(143,205)(144,206)(145,207)(146,208)(147,209)(148,210)(149,211)(150,212)(151,213)(152,214)(153,215)(154,216)(155,217)(156,218)(157,219)(158,220)(159,221)(160,222)(161,223)(162,224)(163,225)(164,226)(165,227)(166,228)(167,229)(168,230)(169,231)(170,232)(171,233)(172,234)(173,235)(174,236)(175,237)(176,238)(177,239)(178,240)(179,241)(180,242)(181,243)(182,244)(183,245)(184,246)(185,247)(186,248), (1,62)(2,32)(3,33)(4,34)(5,35)(6,36)(7,37)(8,38)(9,39)(10,40)(11,41)(12,42)(13,43)(14,44)(15,45)(16,46)(17,47)(18,48)(19,49)(20,50)(21,51)(22,52)(23,53)(24,54)(25,55)(26,56)(27,57)(28,58)(29,59)(30,60)(31,61)(63,121)(64,122)(65,123)(66,124)(67,94)(68,95)(69,96)(70,97)(71,98)(72,99)(73,100)(74,101)(75,102)(76,103)(77,104)(78,105)(79,106)(80,107)(81,108)(82,109)(83,110)(84,111)(85,112)(86,113)(87,114)(88,115)(89,116)(90,117)(91,118)(92,119)(93,120)(125,156)(126,157)(127,158)(128,159)(129,160)(130,161)(131,162)(132,163)(133,164)(134,165)(135,166)(136,167)(137,168)(138,169)(139,170)(140,171)(141,172)(142,173)(143,174)(144,175)(145,176)(146,177)(147,178)(148,179)(149,180)(150,181)(151,182)(152,183)(153,184)(154,185)(155,186)(187,218)(188,219)(189,220)(190,221)(191,222)(192,223)(193,224)(194,225)(195,226)(196,227)(197,228)(198,229)(199,230)(200,231)(201,232)(202,233)(203,234)(204,235)(205,236)(206,237)(207,238)(208,239)(209,240)(210,241)(211,242)(212,243)(213,244)(214,245)(215,246)(216,247)(217,248), (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), (1,217,70,155)(2,216,71,154)(3,215,72,153)(4,214,73,152)(5,213,74,151)(6,212,75,150)(7,211,76,149)(8,210,77,148)(9,209,78,147)(10,208,79,146)(11,207,80,145)(12,206,81,144)(13,205,82,143)(14,204,83,142)(15,203,84,141)(16,202,85,140)(17,201,86,139)(18,200,87,138)(19,199,88,137)(20,198,89,136)(21,197,90,135)(22,196,91,134)(23,195,92,133)(24,194,93,132)(25,193,63,131)(26,192,64,130)(27,191,65,129)(28,190,66,128)(29,189,67,127)(30,188,68,126)(31,187,69,125)(32,247,98,185)(33,246,99,184)(34,245,100,183)(35,244,101,182)(36,243,102,181)(37,242,103,180)(38,241,104,179)(39,240,105,178)(40,239,106,177)(41,238,107,176)(42,237,108,175)(43,236,109,174)(44,235,110,173)(45,234,111,172)(46,233,112,171)(47,232,113,170)(48,231,114,169)(49,230,115,168)(50,229,116,167)(51,228,117,166)(52,227,118,165)(53,226,119,164)(54,225,120,163)(55,224,121,162)(56,223,122,161)(57,222,123,160)(58,221,124,159)(59,220,94,158)(60,219,95,157)(61,218,96,156)(62,248,97,186)>;
G:=Group( (125,156)(126,157)(127,158)(128,159)(129,160)(130,161)(131,162)(132,163)(133,164)(134,165)(135,166)(136,167)(137,168)(138,169)(139,170)(140,171)(141,172)(142,173)(143,174)(144,175)(145,176)(146,177)(147,178)(148,179)(149,180)(150,181)(151,182)(152,183)(153,184)(154,185)(155,186)(187,218)(188,219)(189,220)(190,221)(191,222)(192,223)(193,224)(194,225)(195,226)(196,227)(197,228)(198,229)(199,230)(200,231)(201,232)(202,233)(203,234)(204,235)(205,236)(206,237)(207,238)(208,239)(209,240)(210,241)(211,242)(212,243)(213,244)(214,245)(215,246)(216,247)(217,248), (1,70)(2,71)(3,72)(4,73)(5,74)(6,75)(7,76)(8,77)(9,78)(10,79)(11,80)(12,81)(13,82)(14,83)(15,84)(16,85)(17,86)(18,87)(19,88)(20,89)(21,90)(22,91)(23,92)(24,93)(25,63)(26,64)(27,65)(28,66)(29,67)(30,68)(31,69)(32,98)(33,99)(34,100)(35,101)(36,102)(37,103)(38,104)(39,105)(40,106)(41,107)(42,108)(43,109)(44,110)(45,111)(46,112)(47,113)(48,114)(49,115)(50,116)(51,117)(52,118)(53,119)(54,120)(55,121)(56,122)(57,123)(58,124)(59,94)(60,95)(61,96)(62,97)(125,187)(126,188)(127,189)(128,190)(129,191)(130,192)(131,193)(132,194)(133,195)(134,196)(135,197)(136,198)(137,199)(138,200)(139,201)(140,202)(141,203)(142,204)(143,205)(144,206)(145,207)(146,208)(147,209)(148,210)(149,211)(150,212)(151,213)(152,214)(153,215)(154,216)(155,217)(156,218)(157,219)(158,220)(159,221)(160,222)(161,223)(162,224)(163,225)(164,226)(165,227)(166,228)(167,229)(168,230)(169,231)(170,232)(171,233)(172,234)(173,235)(174,236)(175,237)(176,238)(177,239)(178,240)(179,241)(180,242)(181,243)(182,244)(183,245)(184,246)(185,247)(186,248), (1,62)(2,32)(3,33)(4,34)(5,35)(6,36)(7,37)(8,38)(9,39)(10,40)(11,41)(12,42)(13,43)(14,44)(15,45)(16,46)(17,47)(18,48)(19,49)(20,50)(21,51)(22,52)(23,53)(24,54)(25,55)(26,56)(27,57)(28,58)(29,59)(30,60)(31,61)(63,121)(64,122)(65,123)(66,124)(67,94)(68,95)(69,96)(70,97)(71,98)(72,99)(73,100)(74,101)(75,102)(76,103)(77,104)(78,105)(79,106)(80,107)(81,108)(82,109)(83,110)(84,111)(85,112)(86,113)(87,114)(88,115)(89,116)(90,117)(91,118)(92,119)(93,120)(125,156)(126,157)(127,158)(128,159)(129,160)(130,161)(131,162)(132,163)(133,164)(134,165)(135,166)(136,167)(137,168)(138,169)(139,170)(140,171)(141,172)(142,173)(143,174)(144,175)(145,176)(146,177)(147,178)(148,179)(149,180)(150,181)(151,182)(152,183)(153,184)(154,185)(155,186)(187,218)(188,219)(189,220)(190,221)(191,222)(192,223)(193,224)(194,225)(195,226)(196,227)(197,228)(198,229)(199,230)(200,231)(201,232)(202,233)(203,234)(204,235)(205,236)(206,237)(207,238)(208,239)(209,240)(210,241)(211,242)(212,243)(213,244)(214,245)(215,246)(216,247)(217,248), (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), (1,217,70,155)(2,216,71,154)(3,215,72,153)(4,214,73,152)(5,213,74,151)(6,212,75,150)(7,211,76,149)(8,210,77,148)(9,209,78,147)(10,208,79,146)(11,207,80,145)(12,206,81,144)(13,205,82,143)(14,204,83,142)(15,203,84,141)(16,202,85,140)(17,201,86,139)(18,200,87,138)(19,199,88,137)(20,198,89,136)(21,197,90,135)(22,196,91,134)(23,195,92,133)(24,194,93,132)(25,193,63,131)(26,192,64,130)(27,191,65,129)(28,190,66,128)(29,189,67,127)(30,188,68,126)(31,187,69,125)(32,247,98,185)(33,246,99,184)(34,245,100,183)(35,244,101,182)(36,243,102,181)(37,242,103,180)(38,241,104,179)(39,240,105,178)(40,239,106,177)(41,238,107,176)(42,237,108,175)(43,236,109,174)(44,235,110,173)(45,234,111,172)(46,233,112,171)(47,232,113,170)(48,231,114,169)(49,230,115,168)(50,229,116,167)(51,228,117,166)(52,227,118,165)(53,226,119,164)(54,225,120,163)(55,224,121,162)(56,223,122,161)(57,222,123,160)(58,221,124,159)(59,220,94,158)(60,219,95,157)(61,218,96,156)(62,248,97,186) );
G=PermutationGroup([[(125,156),(126,157),(127,158),(128,159),(129,160),(130,161),(131,162),(132,163),(133,164),(134,165),(135,166),(136,167),(137,168),(138,169),(139,170),(140,171),(141,172),(142,173),(143,174),(144,175),(145,176),(146,177),(147,178),(148,179),(149,180),(150,181),(151,182),(152,183),(153,184),(154,185),(155,186),(187,218),(188,219),(189,220),(190,221),(191,222),(192,223),(193,224),(194,225),(195,226),(196,227),(197,228),(198,229),(199,230),(200,231),(201,232),(202,233),(203,234),(204,235),(205,236),(206,237),(207,238),(208,239),(209,240),(210,241),(211,242),(212,243),(213,244),(214,245),(215,246),(216,247),(217,248)], [(1,70),(2,71),(3,72),(4,73),(5,74),(6,75),(7,76),(8,77),(9,78),(10,79),(11,80),(12,81),(13,82),(14,83),(15,84),(16,85),(17,86),(18,87),(19,88),(20,89),(21,90),(22,91),(23,92),(24,93),(25,63),(26,64),(27,65),(28,66),(29,67),(30,68),(31,69),(32,98),(33,99),(34,100),(35,101),(36,102),(37,103),(38,104),(39,105),(40,106),(41,107),(42,108),(43,109),(44,110),(45,111),(46,112),(47,113),(48,114),(49,115),(50,116),(51,117),(52,118),(53,119),(54,120),(55,121),(56,122),(57,123),(58,124),(59,94),(60,95),(61,96),(62,97),(125,187),(126,188),(127,189),(128,190),(129,191),(130,192),(131,193),(132,194),(133,195),(134,196),(135,197),(136,198),(137,199),(138,200),(139,201),(140,202),(141,203),(142,204),(143,205),(144,206),(145,207),(146,208),(147,209),(148,210),(149,211),(150,212),(151,213),(152,214),(153,215),(154,216),(155,217),(156,218),(157,219),(158,220),(159,221),(160,222),(161,223),(162,224),(163,225),(164,226),(165,227),(166,228),(167,229),(168,230),(169,231),(170,232),(171,233),(172,234),(173,235),(174,236),(175,237),(176,238),(177,239),(178,240),(179,241),(180,242),(181,243),(182,244),(183,245),(184,246),(185,247),(186,248)], [(1,62),(2,32),(3,33),(4,34),(5,35),(6,36),(7,37),(8,38),(9,39),(10,40),(11,41),(12,42),(13,43),(14,44),(15,45),(16,46),(17,47),(18,48),(19,49),(20,50),(21,51),(22,52),(23,53),(24,54),(25,55),(26,56),(27,57),(28,58),(29,59),(30,60),(31,61),(63,121),(64,122),(65,123),(66,124),(67,94),(68,95),(69,96),(70,97),(71,98),(72,99),(73,100),(74,101),(75,102),(76,103),(77,104),(78,105),(79,106),(80,107),(81,108),(82,109),(83,110),(84,111),(85,112),(86,113),(87,114),(88,115),(89,116),(90,117),(91,118),(92,119),(93,120),(125,156),(126,157),(127,158),(128,159),(129,160),(130,161),(131,162),(132,163),(133,164),(134,165),(135,166),(136,167),(137,168),(138,169),(139,170),(140,171),(141,172),(142,173),(143,174),(144,175),(145,176),(146,177),(147,178),(148,179),(149,180),(150,181),(151,182),(152,183),(153,184),(154,185),(155,186),(187,218),(188,219),(189,220),(190,221),(191,222),(192,223),(193,224),(194,225),(195,226),(196,227),(197,228),(198,229),(199,230),(200,231),(201,232),(202,233),(203,234),(204,235),(205,236),(206,237),(207,238),(208,239),(209,240),(210,241),(211,242),(212,243),(213,244),(214,245),(215,246),(216,247),(217,248)], [(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)], [(1,217,70,155),(2,216,71,154),(3,215,72,153),(4,214,73,152),(5,213,74,151),(6,212,75,150),(7,211,76,149),(8,210,77,148),(9,209,78,147),(10,208,79,146),(11,207,80,145),(12,206,81,144),(13,205,82,143),(14,204,83,142),(15,203,84,141),(16,202,85,140),(17,201,86,139),(18,200,87,138),(19,199,88,137),(20,198,89,136),(21,197,90,135),(22,196,91,134),(23,195,92,133),(24,194,93,132),(25,193,63,131),(26,192,64,130),(27,191,65,129),(28,190,66,128),(29,189,67,127),(30,188,68,126),(31,187,69,125),(32,247,98,185),(33,246,99,184),(34,245,100,183),(35,244,101,182),(36,243,102,181),(37,242,103,180),(38,241,104,179),(39,240,105,178),(40,239,106,177),(41,238,107,176),(42,237,108,175),(43,236,109,174),(44,235,110,173),(45,234,111,172),(46,233,112,171),(47,232,113,170),(48,231,114,169),(49,230,115,168),(50,229,116,167),(51,228,117,166),(52,227,118,165),(53,226,119,164),(54,225,120,163),(55,224,121,162),(56,223,122,161),(57,222,123,160),(58,221,124,159),(59,220,94,158),(60,219,95,157),(61,218,96,156),(62,248,97,186)]])
130 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 31A | ··· | 31O | 62A | ··· | 62DA |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 31 | ··· | 31 | 62 | ··· | 62 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 62 | 62 | 62 | 62 | 2 | ··· | 2 | 2 | ··· | 2 |
130 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | - | + | ||
| image | C1 | C2 | C2 | C4 | D4 | D31 | Dic31 | D62 | C31⋊D4 |
| kernel | C23.D31 | C2×Dic31 | C22×C62 | C2×C62 | C62 | C23 | C22 | C22 | C2 |
| # reps | 1 | 2 | 1 | 4 | 2 | 15 | 30 | 15 | 60 |
Matrix representation of C23.D31 ►in GL4(𝔽373) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 239 | 372 |
| 372 | 0 | 0 | 0 |
| 0 | 372 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 372 | 0 |
| 0 | 0 | 0 | 372 |
| 8 | 1 | 0 | 0 |
| 326 | 274 | 0 | 0 |
| 0 | 0 | 91 | 0 |
| 0 | 0 | 7 | 41 |
| 198 | 229 | 0 | 0 |
| 21 | 175 | 0 | 0 |
| 0 | 0 | 116 | 24 |
| 0 | 0 | 232 | 257 |
G:=sub<GL(4,GF(373))| [1,0,0,0,0,1,0,0,0,0,1,239,0,0,0,372],[372,0,0,0,0,372,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,372,0,0,0,0,372],[8,326,0,0,1,274,0,0,0,0,91,7,0,0,0,41],[198,21,0,0,229,175,0,0,0,0,116,232,0,0,24,257] >;
C23.D31 in GAP, Magma, Sage, TeX
C_2^3.D_{31} % in TeX
G:=Group("C2^3.D31"); // GroupNames label
G:=SmallGroup(496,18);
// by ID
G=gap.SmallGroup(496,18);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-31,20,101,12004]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^2=d^31=1,e^2=b,a*b=b*a,e*a*e^-1=a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations
Export