Copied to
clipboard

## G = C2×C31⋊D4order 496 = 24·31

### Direct product of C2 and C31⋊D4

Aliases: C2×C31⋊D4, C622D4, C23⋊D31, C222D62, D623C22, C62.10C23, Dic312C22, C313(C2×D4), (C2×C62)⋊3C22, (C22×C62)⋊2C2, (C2×Dic31)⋊4C2, (C22×D31)⋊3C2, C2.10(C22×D31), SmallGroup(496,36)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C62 — C2×C31⋊D4
 Chief series C1 — C31 — C62 — D62 — C22×D31 — C2×C31⋊D4
 Lower central C31 — C62 — C2×C31⋊D4
 Upper central C1 — C22 — C23

Generators and relations for C2×C31⋊D4
G = < a,b,c,d | a2=b31=c4=d2=1, ab=ba, ac=ca, ad=da, cbc-1=dbd=b-1, dcd=c-1 >

Subgroups: 640 in 54 conjugacy classes, 27 normal (11 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C2×C4, D4, C23, C23, C2×D4, C31, D31, C62, C62, C62, Dic31, D62, D62, C2×C62, C2×C62, C2×C62, C2×Dic31, C31⋊D4, C22×D31, C22×C62, C2×C31⋊D4
Quotients: C1, C2, C22, D4, C23, C2×D4, D31, D62, C31⋊D4, C22×D31, C2×C31⋊D4

Smallest permutation representation of C2×C31⋊D4
On 248 points
Generators in S248
(1 156)(2 157)(3 158)(4 159)(5 160)(6 161)(7 162)(8 163)(9 164)(10 165)(11 166)(12 167)(13 168)(14 169)(15 170)(16 171)(17 172)(18 173)(19 174)(20 175)(21 176)(22 177)(23 178)(24 179)(25 180)(26 181)(27 182)(28 183)(29 184)(30 185)(31 186)(32 125)(33 126)(34 127)(35 128)(36 129)(37 130)(38 131)(39 132)(40 133)(41 134)(42 135)(43 136)(44 137)(45 138)(46 139)(47 140)(48 141)(49 142)(50 143)(51 144)(52 145)(53 146)(54 147)(55 148)(56 149)(57 150)(58 151)(59 152)(60 153)(61 154)(62 155)(63 218)(64 219)(65 220)(66 221)(67 222)(68 223)(69 224)(70 225)(71 226)(72 227)(73 228)(74 229)(75 230)(76 231)(77 232)(78 233)(79 234)(80 235)(81 236)(82 237)(83 238)(84 239)(85 240)(86 241)(87 242)(88 243)(89 244)(90 245)(91 246)(92 247)(93 248)(94 187)(95 188)(96 189)(97 190)(98 191)(99 192)(100 193)(101 194)(102 195)(103 196)(104 197)(105 198)(106 199)(107 200)(108 201)(109 202)(110 203)(111 204)(112 205)(113 206)(114 207)(115 208)(116 209)(117 210)(118 211)(119 212)(120 213)(121 214)(122 215)(123 216)(124 217)
(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 63 32 94)(2 93 33 124)(3 92 34 123)(4 91 35 122)(5 90 36 121)(6 89 37 120)(7 88 38 119)(8 87 39 118)(9 86 40 117)(10 85 41 116)(11 84 42 115)(12 83 43 114)(13 82 44 113)(14 81 45 112)(15 80 46 111)(16 79 47 110)(17 78 48 109)(18 77 49 108)(19 76 50 107)(20 75 51 106)(21 74 52 105)(22 73 53 104)(23 72 54 103)(24 71 55 102)(25 70 56 101)(26 69 57 100)(27 68 58 99)(28 67 59 98)(29 66 60 97)(30 65 61 96)(31 64 62 95)(125 187 156 218)(126 217 157 248)(127 216 158 247)(128 215 159 246)(129 214 160 245)(130 213 161 244)(131 212 162 243)(132 211 163 242)(133 210 164 241)(134 209 165 240)(135 208 166 239)(136 207 167 238)(137 206 168 237)(138 205 169 236)(139 204 170 235)(140 203 171 234)(141 202 172 233)(142 201 173 232)(143 200 174 231)(144 199 175 230)(145 198 176 229)(146 197 177 228)(147 196 178 227)(148 195 179 226)(149 194 180 225)(150 193 181 224)(151 192 182 223)(152 191 183 222)(153 190 184 221)(154 189 185 220)(155 188 186 219)
(2 31)(3 30)(4 29)(5 28)(6 27)(7 26)(8 25)(9 24)(10 23)(11 22)(12 21)(13 20)(14 19)(15 18)(16 17)(33 62)(34 61)(35 60)(36 59)(37 58)(38 57)(39 56)(40 55)(41 54)(42 53)(43 52)(44 51)(45 50)(46 49)(47 48)(63 94)(64 124)(65 123)(66 122)(67 121)(68 120)(69 119)(70 118)(71 117)(72 116)(73 115)(74 114)(75 113)(76 112)(77 111)(78 110)(79 109)(80 108)(81 107)(82 106)(83 105)(84 104)(85 103)(86 102)(87 101)(88 100)(89 99)(90 98)(91 97)(92 96)(93 95)(126 155)(127 154)(128 153)(129 152)(130 151)(131 150)(132 149)(133 148)(134 147)(135 146)(136 145)(137 144)(138 143)(139 142)(140 141)(157 186)(158 185)(159 184)(160 183)(161 182)(162 181)(163 180)(164 179)(165 178)(166 177)(167 176)(168 175)(169 174)(170 173)(171 172)(187 218)(188 248)(189 247)(190 246)(191 245)(192 244)(193 243)(194 242)(195 241)(196 240)(197 239)(198 238)(199 237)(200 236)(201 235)(202 234)(203 233)(204 232)(205 231)(206 230)(207 229)(208 228)(209 227)(210 226)(211 225)(212 224)(213 223)(214 222)(215 221)(216 220)(217 219)

G:=sub<Sym(248)| (1,156)(2,157)(3,158)(4,159)(5,160)(6,161)(7,162)(8,163)(9,164)(10,165)(11,166)(12,167)(13,168)(14,169)(15,170)(16,171)(17,172)(18,173)(19,174)(20,175)(21,176)(22,177)(23,178)(24,179)(25,180)(26,181)(27,182)(28,183)(29,184)(30,185)(31,186)(32,125)(33,126)(34,127)(35,128)(36,129)(37,130)(38,131)(39,132)(40,133)(41,134)(42,135)(43,136)(44,137)(45,138)(46,139)(47,140)(48,141)(49,142)(50,143)(51,144)(52,145)(53,146)(54,147)(55,148)(56,149)(57,150)(58,151)(59,152)(60,153)(61,154)(62,155)(63,218)(64,219)(65,220)(66,221)(67,222)(68,223)(69,224)(70,225)(71,226)(72,227)(73,228)(74,229)(75,230)(76,231)(77,232)(78,233)(79,234)(80,235)(81,236)(82,237)(83,238)(84,239)(85,240)(86,241)(87,242)(88,243)(89,244)(90,245)(91,246)(92,247)(93,248)(94,187)(95,188)(96,189)(97,190)(98,191)(99,192)(100,193)(101,194)(102,195)(103,196)(104,197)(105,198)(106,199)(107,200)(108,201)(109,202)(110,203)(111,204)(112,205)(113,206)(114,207)(115,208)(116,209)(117,210)(118,211)(119,212)(120,213)(121,214)(122,215)(123,216)(124,217), (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), (1,63,32,94)(2,93,33,124)(3,92,34,123)(4,91,35,122)(5,90,36,121)(6,89,37,120)(7,88,38,119)(8,87,39,118)(9,86,40,117)(10,85,41,116)(11,84,42,115)(12,83,43,114)(13,82,44,113)(14,81,45,112)(15,80,46,111)(16,79,47,110)(17,78,48,109)(18,77,49,108)(19,76,50,107)(20,75,51,106)(21,74,52,105)(22,73,53,104)(23,72,54,103)(24,71,55,102)(25,70,56,101)(26,69,57,100)(27,68,58,99)(28,67,59,98)(29,66,60,97)(30,65,61,96)(31,64,62,95)(125,187,156,218)(126,217,157,248)(127,216,158,247)(128,215,159,246)(129,214,160,245)(130,213,161,244)(131,212,162,243)(132,211,163,242)(133,210,164,241)(134,209,165,240)(135,208,166,239)(136,207,167,238)(137,206,168,237)(138,205,169,236)(139,204,170,235)(140,203,171,234)(141,202,172,233)(142,201,173,232)(143,200,174,231)(144,199,175,230)(145,198,176,229)(146,197,177,228)(147,196,178,227)(148,195,179,226)(149,194,180,225)(150,193,181,224)(151,192,182,223)(152,191,183,222)(153,190,184,221)(154,189,185,220)(155,188,186,219), (2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(33,62)(34,61)(35,60)(36,59)(37,58)(38,57)(39,56)(40,55)(41,54)(42,53)(43,52)(44,51)(45,50)(46,49)(47,48)(63,94)(64,124)(65,123)(66,122)(67,121)(68,120)(69,119)(70,118)(71,117)(72,116)(73,115)(74,114)(75,113)(76,112)(77,111)(78,110)(79,109)(80,108)(81,107)(82,106)(83,105)(84,104)(85,103)(86,102)(87,101)(88,100)(89,99)(90,98)(91,97)(92,96)(93,95)(126,155)(127,154)(128,153)(129,152)(130,151)(131,150)(132,149)(133,148)(134,147)(135,146)(136,145)(137,144)(138,143)(139,142)(140,141)(157,186)(158,185)(159,184)(160,183)(161,182)(162,181)(163,180)(164,179)(165,178)(166,177)(167,176)(168,175)(169,174)(170,173)(171,172)(187,218)(188,248)(189,247)(190,246)(191,245)(192,244)(193,243)(194,242)(195,241)(196,240)(197,239)(198,238)(199,237)(200,236)(201,235)(202,234)(203,233)(204,232)(205,231)(206,230)(207,229)(208,228)(209,227)(210,226)(211,225)(212,224)(213,223)(214,222)(215,221)(216,220)(217,219)>;

G:=Group( (1,156)(2,157)(3,158)(4,159)(5,160)(6,161)(7,162)(8,163)(9,164)(10,165)(11,166)(12,167)(13,168)(14,169)(15,170)(16,171)(17,172)(18,173)(19,174)(20,175)(21,176)(22,177)(23,178)(24,179)(25,180)(26,181)(27,182)(28,183)(29,184)(30,185)(31,186)(32,125)(33,126)(34,127)(35,128)(36,129)(37,130)(38,131)(39,132)(40,133)(41,134)(42,135)(43,136)(44,137)(45,138)(46,139)(47,140)(48,141)(49,142)(50,143)(51,144)(52,145)(53,146)(54,147)(55,148)(56,149)(57,150)(58,151)(59,152)(60,153)(61,154)(62,155)(63,218)(64,219)(65,220)(66,221)(67,222)(68,223)(69,224)(70,225)(71,226)(72,227)(73,228)(74,229)(75,230)(76,231)(77,232)(78,233)(79,234)(80,235)(81,236)(82,237)(83,238)(84,239)(85,240)(86,241)(87,242)(88,243)(89,244)(90,245)(91,246)(92,247)(93,248)(94,187)(95,188)(96,189)(97,190)(98,191)(99,192)(100,193)(101,194)(102,195)(103,196)(104,197)(105,198)(106,199)(107,200)(108,201)(109,202)(110,203)(111,204)(112,205)(113,206)(114,207)(115,208)(116,209)(117,210)(118,211)(119,212)(120,213)(121,214)(122,215)(123,216)(124,217), (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), (1,63,32,94)(2,93,33,124)(3,92,34,123)(4,91,35,122)(5,90,36,121)(6,89,37,120)(7,88,38,119)(8,87,39,118)(9,86,40,117)(10,85,41,116)(11,84,42,115)(12,83,43,114)(13,82,44,113)(14,81,45,112)(15,80,46,111)(16,79,47,110)(17,78,48,109)(18,77,49,108)(19,76,50,107)(20,75,51,106)(21,74,52,105)(22,73,53,104)(23,72,54,103)(24,71,55,102)(25,70,56,101)(26,69,57,100)(27,68,58,99)(28,67,59,98)(29,66,60,97)(30,65,61,96)(31,64,62,95)(125,187,156,218)(126,217,157,248)(127,216,158,247)(128,215,159,246)(129,214,160,245)(130,213,161,244)(131,212,162,243)(132,211,163,242)(133,210,164,241)(134,209,165,240)(135,208,166,239)(136,207,167,238)(137,206,168,237)(138,205,169,236)(139,204,170,235)(140,203,171,234)(141,202,172,233)(142,201,173,232)(143,200,174,231)(144,199,175,230)(145,198,176,229)(146,197,177,228)(147,196,178,227)(148,195,179,226)(149,194,180,225)(150,193,181,224)(151,192,182,223)(152,191,183,222)(153,190,184,221)(154,189,185,220)(155,188,186,219), (2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(33,62)(34,61)(35,60)(36,59)(37,58)(38,57)(39,56)(40,55)(41,54)(42,53)(43,52)(44,51)(45,50)(46,49)(47,48)(63,94)(64,124)(65,123)(66,122)(67,121)(68,120)(69,119)(70,118)(71,117)(72,116)(73,115)(74,114)(75,113)(76,112)(77,111)(78,110)(79,109)(80,108)(81,107)(82,106)(83,105)(84,104)(85,103)(86,102)(87,101)(88,100)(89,99)(90,98)(91,97)(92,96)(93,95)(126,155)(127,154)(128,153)(129,152)(130,151)(131,150)(132,149)(133,148)(134,147)(135,146)(136,145)(137,144)(138,143)(139,142)(140,141)(157,186)(158,185)(159,184)(160,183)(161,182)(162,181)(163,180)(164,179)(165,178)(166,177)(167,176)(168,175)(169,174)(170,173)(171,172)(187,218)(188,248)(189,247)(190,246)(191,245)(192,244)(193,243)(194,242)(195,241)(196,240)(197,239)(198,238)(199,237)(200,236)(201,235)(202,234)(203,233)(204,232)(205,231)(206,230)(207,229)(208,228)(209,227)(210,226)(211,225)(212,224)(213,223)(214,222)(215,221)(216,220)(217,219) );

G=PermutationGroup([[(1,156),(2,157),(3,158),(4,159),(5,160),(6,161),(7,162),(8,163),(9,164),(10,165),(11,166),(12,167),(13,168),(14,169),(15,170),(16,171),(17,172),(18,173),(19,174),(20,175),(21,176),(22,177),(23,178),(24,179),(25,180),(26,181),(27,182),(28,183),(29,184),(30,185),(31,186),(32,125),(33,126),(34,127),(35,128),(36,129),(37,130),(38,131),(39,132),(40,133),(41,134),(42,135),(43,136),(44,137),(45,138),(46,139),(47,140),(48,141),(49,142),(50,143),(51,144),(52,145),(53,146),(54,147),(55,148),(56,149),(57,150),(58,151),(59,152),(60,153),(61,154),(62,155),(63,218),(64,219),(65,220),(66,221),(67,222),(68,223),(69,224),(70,225),(71,226),(72,227),(73,228),(74,229),(75,230),(76,231),(77,232),(78,233),(79,234),(80,235),(81,236),(82,237),(83,238),(84,239),(85,240),(86,241),(87,242),(88,243),(89,244),(90,245),(91,246),(92,247),(93,248),(94,187),(95,188),(96,189),(97,190),(98,191),(99,192),(100,193),(101,194),(102,195),(103,196),(104,197),(105,198),(106,199),(107,200),(108,201),(109,202),(110,203),(111,204),(112,205),(113,206),(114,207),(115,208),(116,209),(117,210),(118,211),(119,212),(120,213),(121,214),(122,215),(123,216),(124,217)], [(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)], [(1,63,32,94),(2,93,33,124),(3,92,34,123),(4,91,35,122),(5,90,36,121),(6,89,37,120),(7,88,38,119),(8,87,39,118),(9,86,40,117),(10,85,41,116),(11,84,42,115),(12,83,43,114),(13,82,44,113),(14,81,45,112),(15,80,46,111),(16,79,47,110),(17,78,48,109),(18,77,49,108),(19,76,50,107),(20,75,51,106),(21,74,52,105),(22,73,53,104),(23,72,54,103),(24,71,55,102),(25,70,56,101),(26,69,57,100),(27,68,58,99),(28,67,59,98),(29,66,60,97),(30,65,61,96),(31,64,62,95),(125,187,156,218),(126,217,157,248),(127,216,158,247),(128,215,159,246),(129,214,160,245),(130,213,161,244),(131,212,162,243),(132,211,163,242),(133,210,164,241),(134,209,165,240),(135,208,166,239),(136,207,167,238),(137,206,168,237),(138,205,169,236),(139,204,170,235),(140,203,171,234),(141,202,172,233),(142,201,173,232),(143,200,174,231),(144,199,175,230),(145,198,176,229),(146,197,177,228),(147,196,178,227),(148,195,179,226),(149,194,180,225),(150,193,181,224),(151,192,182,223),(152,191,183,222),(153,190,184,221),(154,189,185,220),(155,188,186,219)], [(2,31),(3,30),(4,29),(5,28),(6,27),(7,26),(8,25),(9,24),(10,23),(11,22),(12,21),(13,20),(14,19),(15,18),(16,17),(33,62),(34,61),(35,60),(36,59),(37,58),(38,57),(39,56),(40,55),(41,54),(42,53),(43,52),(44,51),(45,50),(46,49),(47,48),(63,94),(64,124),(65,123),(66,122),(67,121),(68,120),(69,119),(70,118),(71,117),(72,116),(73,115),(74,114),(75,113),(76,112),(77,111),(78,110),(79,109),(80,108),(81,107),(82,106),(83,105),(84,104),(85,103),(86,102),(87,101),(88,100),(89,99),(90,98),(91,97),(92,96),(93,95),(126,155),(127,154),(128,153),(129,152),(130,151),(131,150),(132,149),(133,148),(134,147),(135,146),(136,145),(137,144),(138,143),(139,142),(140,141),(157,186),(158,185),(159,184),(160,183),(161,182),(162,181),(163,180),(164,179),(165,178),(166,177),(167,176),(168,175),(169,174),(170,173),(171,172),(187,218),(188,248),(189,247),(190,246),(191,245),(192,244),(193,243),(194,242),(195,241),(196,240),(197,239),(198,238),(199,237),(200,236),(201,235),(202,234),(203,233),(204,232),(205,231),(206,230),(207,229),(208,228),(209,227),(210,226),(211,225),(212,224),(213,223),(214,222),(215,221),(216,220),(217,219)]])

130 conjugacy classes

 class 1 2A 2B 2C 2D 2E 2F 2G 4A 4B 31A ··· 31O 62A ··· 62DA order 1 2 2 2 2 2 2 2 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 1 2 2 2 2 type + + + + + + + + image C1 C2 C2 C2 C2 D4 D31 D62 C31⋊D4 kernel C2×C31⋊D4 C2×Dic31 C31⋊D4 C22×D31 C22×C62 C62 C23 C22 C2 # reps 1 1 4 1 1 2 15 45 60

Matrix representation of C2×C31⋊D4 in GL3(𝔽373) generated by

 372 0 0 0 1 0 0 0 1
,
 1 0 0 0 271 372 0 25 88
,
 1 0 0 0 268 29 0 160 105
,
 372 0 0 0 308 14 0 18 65
G:=sub<GL(3,GF(373))| [372,0,0,0,1,0,0,0,1],[1,0,0,0,271,25,0,372,88],[1,0,0,0,268,160,0,29,105],[372,0,0,0,308,18,0,14,65] >;

C2×C31⋊D4 in GAP, Magma, Sage, TeX

C_2\times C_{31}\rtimes D_4
% in TeX

G:=Group("C2xC31:D4");
// GroupNames label

G:=SmallGroup(496,36);
// by ID

G=gap.SmallGroup(496,36);
# by ID

G:=PCGroup([5,-2,-2,-2,-2,-31,182,12004]);
// Polycyclic

G:=Group<a,b,c,d|a^2=b^31=c^4=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d=b^-1,d*c*d=c^-1>;
// generators/relations

׿
×
𝔽