direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C2×Dic43, C86⋊C4, C2.2D86, C22.D43, C86.4C22, C43⋊2(C2×C4), (C2×C86).C2, SmallGroup(344,6)
Series: Derived ►Chief ►Lower central ►Upper central
| C43 — C2×Dic43 |
Generators and relations for C2×Dic43
G = < a,b,c | a2=b86=1, c2=b43, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C2×Dic43
►Regular action on 344 points
Generators in S344
(1 139)(2 140)(3 141)(4 142)(5 143)(6 144)(7 145)(8 146)(9 147)(10 148)(11 149)(12 150)(13 151)(14 152)(15 153)(16 154)(17 155)(18 156)(19 157)(20 158)(21 159)(22 160)(23 161)(24 162)(25 163)(26 164)(27 165)(28 166)(29 167)(30 168)(31 169)(32 170)(33 171)(34 172)(35 87)(36 88)(37 89)(38 90)(39 91)(40 92)(41 93)(42 94)(43 95)(44 96)(45 97)(46 98)(47 99)(48 100)(49 101)(50 102)(51 103)(52 104)(53 105)(54 106)(55 107)(56 108)(57 109)(58 110)(59 111)(60 112)(61 113)(62 114)(63 115)(64 116)(65 117)(66 118)(67 119)(68 120)(69 121)(70 122)(71 123)(72 124)(73 125)(74 126)(75 127)(76 128)(77 129)(78 130)(79 131)(80 132)(81 133)(82 134)(83 135)(84 136)(85 137)(86 138)(173 302)(174 303)(175 304)(176 305)(177 306)(178 307)(179 308)(180 309)(181 310)(182 311)(183 312)(184 313)(185 314)(186 315)(187 316)(188 317)(189 318)(190 319)(191 320)(192 321)(193 322)(194 323)(195 324)(196 325)(197 326)(198 327)(199 328)(200 329)(201 330)(202 331)(203 332)(204 333)(205 334)(206 335)(207 336)(208 337)(209 338)(210 339)(211 340)(212 341)(213 342)(214 343)(215 344)(216 259)(217 260)(218 261)(219 262)(220 263)(221 264)(222 265)(223 266)(224 267)(225 268)(226 269)(227 270)(228 271)(229 272)(230 273)(231 274)(232 275)(233 276)(234 277)(235 278)(236 279)(237 280)(238 281)(239 282)(240 283)(241 284)(242 285)(243 286)(244 287)(245 288)(246 289)(247 290)(248 291)(249 292)(250 293)(251 294)(252 295)(253 296)(254 297)(255 298)(256 299)(257 300)(258 301)
(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)(173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258)(259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344)
(1 216 44 173)(2 215 45 258)(3 214 46 257)(4 213 47 256)(5 212 48 255)(6 211 49 254)(7 210 50 253)(8 209 51 252)(9 208 52 251)(10 207 53 250)(11 206 54 249)(12 205 55 248)(13 204 56 247)(14 203 57 246)(15 202 58 245)(16 201 59 244)(17 200 60 243)(18 199 61 242)(19 198 62 241)(20 197 63 240)(21 196 64 239)(22 195 65 238)(23 194 66 237)(24 193 67 236)(25 192 68 235)(26 191 69 234)(27 190 70 233)(28 189 71 232)(29 188 72 231)(30 187 73 230)(31 186 74 229)(32 185 75 228)(33 184 76 227)(34 183 77 226)(35 182 78 225)(36 181 79 224)(37 180 80 223)(38 179 81 222)(39 178 82 221)(40 177 83 220)(41 176 84 219)(42 175 85 218)(43 174 86 217)(87 311 130 268)(88 310 131 267)(89 309 132 266)(90 308 133 265)(91 307 134 264)(92 306 135 263)(93 305 136 262)(94 304 137 261)(95 303 138 260)(96 302 139 259)(97 301 140 344)(98 300 141 343)(99 299 142 342)(100 298 143 341)(101 297 144 340)(102 296 145 339)(103 295 146 338)(104 294 147 337)(105 293 148 336)(106 292 149 335)(107 291 150 334)(108 290 151 333)(109 289 152 332)(110 288 153 331)(111 287 154 330)(112 286 155 329)(113 285 156 328)(114 284 157 327)(115 283 158 326)(116 282 159 325)(117 281 160 324)(118 280 161 323)(119 279 162 322)(120 278 163 321)(121 277 164 320)(122 276 165 319)(123 275 166 318)(124 274 167 317)(125 273 168 316)(126 272 169 315)(127 271 170 314)(128 270 171 313)(129 269 172 312)
G:=sub<Sym(344)| (1,139)(2,140)(3,141)(4,142)(5,143)(6,144)(7,145)(8,146)(9,147)(10,148)(11,149)(12,150)(13,151)(14,152)(15,153)(16,154)(17,155)(18,156)(19,157)(20,158)(21,159)(22,160)(23,161)(24,162)(25,163)(26,164)(27,165)(28,166)(29,167)(30,168)(31,169)(32,170)(33,171)(34,172)(35,87)(36,88)(37,89)(38,90)(39,91)(40,92)(41,93)(42,94)(43,95)(44,96)(45,97)(46,98)(47,99)(48,100)(49,101)(50,102)(51,103)(52,104)(53,105)(54,106)(55,107)(56,108)(57,109)(58,110)(59,111)(60,112)(61,113)(62,114)(63,115)(64,116)(65,117)(66,118)(67,119)(68,120)(69,121)(70,122)(71,123)(72,124)(73,125)(74,126)(75,127)(76,128)(77,129)(78,130)(79,131)(80,132)(81,133)(82,134)(83,135)(84,136)(85,137)(86,138)(173,302)(174,303)(175,304)(176,305)(177,306)(178,307)(179,308)(180,309)(181,310)(182,311)(183,312)(184,313)(185,314)(186,315)(187,316)(188,317)(189,318)(190,319)(191,320)(192,321)(193,322)(194,323)(195,324)(196,325)(197,326)(198,327)(199,328)(200,329)(201,330)(202,331)(203,332)(204,333)(205,334)(206,335)(207,336)(208,337)(209,338)(210,339)(211,340)(212,341)(213,342)(214,343)(215,344)(216,259)(217,260)(218,261)(219,262)(220,263)(221,264)(222,265)(223,266)(224,267)(225,268)(226,269)(227,270)(228,271)(229,272)(230,273)(231,274)(232,275)(233,276)(234,277)(235,278)(236,279)(237,280)(238,281)(239,282)(240,283)(241,284)(242,285)(243,286)(244,287)(245,288)(246,289)(247,290)(248,291)(249,292)(250,293)(251,294)(252,295)(253,296)(254,297)(255,298)(256,299)(257,300)(258,301), (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)(173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258)(259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344), (1,216,44,173)(2,215,45,258)(3,214,46,257)(4,213,47,256)(5,212,48,255)(6,211,49,254)(7,210,50,253)(8,209,51,252)(9,208,52,251)(10,207,53,250)(11,206,54,249)(12,205,55,248)(13,204,56,247)(14,203,57,246)(15,202,58,245)(16,201,59,244)(17,200,60,243)(18,199,61,242)(19,198,62,241)(20,197,63,240)(21,196,64,239)(22,195,65,238)(23,194,66,237)(24,193,67,236)(25,192,68,235)(26,191,69,234)(27,190,70,233)(28,189,71,232)(29,188,72,231)(30,187,73,230)(31,186,74,229)(32,185,75,228)(33,184,76,227)(34,183,77,226)(35,182,78,225)(36,181,79,224)(37,180,80,223)(38,179,81,222)(39,178,82,221)(40,177,83,220)(41,176,84,219)(42,175,85,218)(43,174,86,217)(87,311,130,268)(88,310,131,267)(89,309,132,266)(90,308,133,265)(91,307,134,264)(92,306,135,263)(93,305,136,262)(94,304,137,261)(95,303,138,260)(96,302,139,259)(97,301,140,344)(98,300,141,343)(99,299,142,342)(100,298,143,341)(101,297,144,340)(102,296,145,339)(103,295,146,338)(104,294,147,337)(105,293,148,336)(106,292,149,335)(107,291,150,334)(108,290,151,333)(109,289,152,332)(110,288,153,331)(111,287,154,330)(112,286,155,329)(113,285,156,328)(114,284,157,327)(115,283,158,326)(116,282,159,325)(117,281,160,324)(118,280,161,323)(119,279,162,322)(120,278,163,321)(121,277,164,320)(122,276,165,319)(123,275,166,318)(124,274,167,317)(125,273,168,316)(126,272,169,315)(127,271,170,314)(128,270,171,313)(129,269,172,312)>;
G:=Group( (1,139)(2,140)(3,141)(4,142)(5,143)(6,144)(7,145)(8,146)(9,147)(10,148)(11,149)(12,150)(13,151)(14,152)(15,153)(16,154)(17,155)(18,156)(19,157)(20,158)(21,159)(22,160)(23,161)(24,162)(25,163)(26,164)(27,165)(28,166)(29,167)(30,168)(31,169)(32,170)(33,171)(34,172)(35,87)(36,88)(37,89)(38,90)(39,91)(40,92)(41,93)(42,94)(43,95)(44,96)(45,97)(46,98)(47,99)(48,100)(49,101)(50,102)(51,103)(52,104)(53,105)(54,106)(55,107)(56,108)(57,109)(58,110)(59,111)(60,112)(61,113)(62,114)(63,115)(64,116)(65,117)(66,118)(67,119)(68,120)(69,121)(70,122)(71,123)(72,124)(73,125)(74,126)(75,127)(76,128)(77,129)(78,130)(79,131)(80,132)(81,133)(82,134)(83,135)(84,136)(85,137)(86,138)(173,302)(174,303)(175,304)(176,305)(177,306)(178,307)(179,308)(180,309)(181,310)(182,311)(183,312)(184,313)(185,314)(186,315)(187,316)(188,317)(189,318)(190,319)(191,320)(192,321)(193,322)(194,323)(195,324)(196,325)(197,326)(198,327)(199,328)(200,329)(201,330)(202,331)(203,332)(204,333)(205,334)(206,335)(207,336)(208,337)(209,338)(210,339)(211,340)(212,341)(213,342)(214,343)(215,344)(216,259)(217,260)(218,261)(219,262)(220,263)(221,264)(222,265)(223,266)(224,267)(225,268)(226,269)(227,270)(228,271)(229,272)(230,273)(231,274)(232,275)(233,276)(234,277)(235,278)(236,279)(237,280)(238,281)(239,282)(240,283)(241,284)(242,285)(243,286)(244,287)(245,288)(246,289)(247,290)(248,291)(249,292)(250,293)(251,294)(252,295)(253,296)(254,297)(255,298)(256,299)(257,300)(258,301), (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)(173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258)(259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344), (1,216,44,173)(2,215,45,258)(3,214,46,257)(4,213,47,256)(5,212,48,255)(6,211,49,254)(7,210,50,253)(8,209,51,252)(9,208,52,251)(10,207,53,250)(11,206,54,249)(12,205,55,248)(13,204,56,247)(14,203,57,246)(15,202,58,245)(16,201,59,244)(17,200,60,243)(18,199,61,242)(19,198,62,241)(20,197,63,240)(21,196,64,239)(22,195,65,238)(23,194,66,237)(24,193,67,236)(25,192,68,235)(26,191,69,234)(27,190,70,233)(28,189,71,232)(29,188,72,231)(30,187,73,230)(31,186,74,229)(32,185,75,228)(33,184,76,227)(34,183,77,226)(35,182,78,225)(36,181,79,224)(37,180,80,223)(38,179,81,222)(39,178,82,221)(40,177,83,220)(41,176,84,219)(42,175,85,218)(43,174,86,217)(87,311,130,268)(88,310,131,267)(89,309,132,266)(90,308,133,265)(91,307,134,264)(92,306,135,263)(93,305,136,262)(94,304,137,261)(95,303,138,260)(96,302,139,259)(97,301,140,344)(98,300,141,343)(99,299,142,342)(100,298,143,341)(101,297,144,340)(102,296,145,339)(103,295,146,338)(104,294,147,337)(105,293,148,336)(106,292,149,335)(107,291,150,334)(108,290,151,333)(109,289,152,332)(110,288,153,331)(111,287,154,330)(112,286,155,329)(113,285,156,328)(114,284,157,327)(115,283,158,326)(116,282,159,325)(117,281,160,324)(118,280,161,323)(119,279,162,322)(120,278,163,321)(121,277,164,320)(122,276,165,319)(123,275,166,318)(124,274,167,317)(125,273,168,316)(126,272,169,315)(127,271,170,314)(128,270,171,313)(129,269,172,312) );
G=PermutationGroup([[(1,139),(2,140),(3,141),(4,142),(5,143),(6,144),(7,145),(8,146),(9,147),(10,148),(11,149),(12,150),(13,151),(14,152),(15,153),(16,154),(17,155),(18,156),(19,157),(20,158),(21,159),(22,160),(23,161),(24,162),(25,163),(26,164),(27,165),(28,166),(29,167),(30,168),(31,169),(32,170),(33,171),(34,172),(35,87),(36,88),(37,89),(38,90),(39,91),(40,92),(41,93),(42,94),(43,95),(44,96),(45,97),(46,98),(47,99),(48,100),(49,101),(50,102),(51,103),(52,104),(53,105),(54,106),(55,107),(56,108),(57,109),(58,110),(59,111),(60,112),(61,113),(62,114),(63,115),(64,116),(65,117),(66,118),(67,119),(68,120),(69,121),(70,122),(71,123),(72,124),(73,125),(74,126),(75,127),(76,128),(77,129),(78,130),(79,131),(80,132),(81,133),(82,134),(83,135),(84,136),(85,137),(86,138),(173,302),(174,303),(175,304),(176,305),(177,306),(178,307),(179,308),(180,309),(181,310),(182,311),(183,312),(184,313),(185,314),(186,315),(187,316),(188,317),(189,318),(190,319),(191,320),(192,321),(193,322),(194,323),(195,324),(196,325),(197,326),(198,327),(199,328),(200,329),(201,330),(202,331),(203,332),(204,333),(205,334),(206,335),(207,336),(208,337),(209,338),(210,339),(211,340),(212,341),(213,342),(214,343),(215,344),(216,259),(217,260),(218,261),(219,262),(220,263),(221,264),(222,265),(223,266),(224,267),(225,268),(226,269),(227,270),(228,271),(229,272),(230,273),(231,274),(232,275),(233,276),(234,277),(235,278),(236,279),(237,280),(238,281),(239,282),(240,283),(241,284),(242,285),(243,286),(244,287),(245,288),(246,289),(247,290),(248,291),(249,292),(250,293),(251,294),(252,295),(253,296),(254,297),(255,298),(256,299),(257,300),(258,301)], [(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),(173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258),(259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344)], [(1,216,44,173),(2,215,45,258),(3,214,46,257),(4,213,47,256),(5,212,48,255),(6,211,49,254),(7,210,50,253),(8,209,51,252),(9,208,52,251),(10,207,53,250),(11,206,54,249),(12,205,55,248),(13,204,56,247),(14,203,57,246),(15,202,58,245),(16,201,59,244),(17,200,60,243),(18,199,61,242),(19,198,62,241),(20,197,63,240),(21,196,64,239),(22,195,65,238),(23,194,66,237),(24,193,67,236),(25,192,68,235),(26,191,69,234),(27,190,70,233),(28,189,71,232),(29,188,72,231),(30,187,73,230),(31,186,74,229),(32,185,75,228),(33,184,76,227),(34,183,77,226),(35,182,78,225),(36,181,79,224),(37,180,80,223),(38,179,81,222),(39,178,82,221),(40,177,83,220),(41,176,84,219),(42,175,85,218),(43,174,86,217),(87,311,130,268),(88,310,131,267),(89,309,132,266),(90,308,133,265),(91,307,134,264),(92,306,135,263),(93,305,136,262),(94,304,137,261),(95,303,138,260),(96,302,139,259),(97,301,140,344),(98,300,141,343),(99,299,142,342),(100,298,143,341),(101,297,144,340),(102,296,145,339),(103,295,146,338),(104,294,147,337),(105,293,148,336),(106,292,149,335),(107,291,150,334),(108,290,151,333),(109,289,152,332),(110,288,153,331),(111,287,154,330),(112,286,155,329),(113,285,156,328),(114,284,157,327),(115,283,158,326),(116,282,159,325),(117,281,160,324),(118,280,161,323),(119,279,162,322),(120,278,163,321),(121,277,164,320),(122,276,165,319),(123,275,166,318),(124,274,167,317),(125,273,168,316),(126,272,169,315),(127,271,170,314),(128,270,171,313),(129,269,172,312)]])
92 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 43A | ··· | 43U | 86A | ··· | 86BK |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 43 | ··· | 43 | 86 | ··· | 86 |
| size | 1 | 1 | 1 | 1 | 43 | 43 | 43 | 43 | 2 | ··· | 2 | 2 | ··· | 2 |
92 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | |
| image | C1 | C2 | C2 | C4 | D43 | Dic43 | D86 |
| kernel | C2×Dic43 | Dic43 | C2×C86 | C86 | C22 | C2 | C2 |
| # reps | 1 | 2 | 1 | 4 | 21 | 42 | 21 |
Matrix representation of C2×Dic43 ►in GL3(𝔽173) generated by
| 172 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 1 |
| 1 | 0 | 0 |
| 0 | 0 | 172 |
| 0 | 1 | 162 |
| 1 | 0 | 0 |
| 0 | 56 | 65 |
| 0 | 162 | 117 |
G:=sub<GL(3,GF(173))| [172,0,0,0,1,0,0,0,1],[1,0,0,0,0,1,0,172,162],[1,0,0,0,56,162,0,65,117] >;
C2×Dic43 in GAP, Magma, Sage, TeX
C_2\times {\rm Dic}_{43} % in TeX
G:=Group("C2xDic43"); // GroupNames label
G:=SmallGroup(344,6);
// by ID
G=gap.SmallGroup(344,6);
# by ID
G:=PCGroup([4,-2,-2,-2,-43,16,5379]);
// Polycyclic
G:=Group<a,b,c|a^2=b^86=1,c^2=b^43,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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