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G = C22×C86order 344 = 23·43

Abelian group of type [2,2,86]

direct product, abelian, monomial, 2-elementary

Aliases: C22×C86, SmallGroup(344,12)

Series: Derived Chief Lower central Upper central

C1 — C22×C86
C1C43C86C2×C86 — C22×C86
C1 — C22×C86
C1 — C22×C86

Generators and relations for C22×C86
 G = < a,b,c | a2=b2=c86=1, ab=ba, ac=ca, bc=cb >


Smallest permutation representation of C22×C86
Regular action on 344 points
Generators in S344
(1 228)(2 229)(3 230)(4 231)(5 232)(6 233)(7 234)(8 235)(9 236)(10 237)(11 238)(12 239)(13 240)(14 241)(15 242)(16 243)(17 244)(18 245)(19 246)(20 247)(21 248)(22 249)(23 250)(24 251)(25 252)(26 253)(27 254)(28 255)(29 256)(30 257)(31 258)(32 173)(33 174)(34 175)(35 176)(36 177)(37 178)(38 179)(39 180)(40 181)(41 182)(42 183)(43 184)(44 185)(45 186)(46 187)(47 188)(48 189)(49 190)(50 191)(51 192)(52 193)(53 194)(54 195)(55 196)(56 197)(57 198)(58 199)(59 200)(60 201)(61 202)(62 203)(63 204)(64 205)(65 206)(66 207)(67 208)(68 209)(69 210)(70 211)(71 212)(72 213)(73 214)(74 215)(75 216)(76 217)(77 218)(78 219)(79 220)(80 221)(81 222)(82 223)(83 224)(84 225)(85 226)(86 227)(87 305)(88 306)(89 307)(90 308)(91 309)(92 310)(93 311)(94 312)(95 313)(96 314)(97 315)(98 316)(99 317)(100 318)(101 319)(102 320)(103 321)(104 322)(105 323)(106 324)(107 325)(108 326)(109 327)(110 328)(111 329)(112 330)(113 331)(114 332)(115 333)(116 334)(117 335)(118 336)(119 337)(120 338)(121 339)(122 340)(123 341)(124 342)(125 343)(126 344)(127 259)(128 260)(129 261)(130 262)(131 263)(132 264)(133 265)(134 266)(135 267)(136 268)(137 269)(138 270)(139 271)(140 272)(141 273)(142 274)(143 275)(144 276)(145 277)(146 278)(147 279)(148 280)(149 281)(150 282)(151 283)(152 284)(153 285)(154 286)(155 287)(156 288)(157 289)(158 290)(159 291)(160 292)(161 293)(162 294)(163 295)(164 296)(165 297)(166 298)(167 299)(168 300)(169 301)(170 302)(171 303)(172 304)
(1 172)(2 87)(3 88)(4 89)(5 90)(6 91)(7 92)(8 93)(9 94)(10 95)(11 96)(12 97)(13 98)(14 99)(15 100)(16 101)(17 102)(18 103)(19 104)(20 105)(21 106)(22 107)(23 108)(24 109)(25 110)(26 111)(27 112)(28 113)(29 114)(30 115)(31 116)(32 117)(33 118)(34 119)(35 120)(36 121)(37 122)(38 123)(39 124)(40 125)(41 126)(42 127)(43 128)(44 129)(45 130)(46 131)(47 132)(48 133)(49 134)(50 135)(51 136)(52 137)(53 138)(54 139)(55 140)(56 141)(57 142)(58 143)(59 144)(60 145)(61 146)(62 147)(63 148)(64 149)(65 150)(66 151)(67 152)(68 153)(69 154)(70 155)(71 156)(72 157)(73 158)(74 159)(75 160)(76 161)(77 162)(78 163)(79 164)(80 165)(81 166)(82 167)(83 168)(84 169)(85 170)(86 171)(173 335)(174 336)(175 337)(176 338)(177 339)(178 340)(179 341)(180 342)(181 343)(182 344)(183 259)(184 260)(185 261)(186 262)(187 263)(188 264)(189 265)(190 266)(191 267)(192 268)(193 269)(194 270)(195 271)(196 272)(197 273)(198 274)(199 275)(200 276)(201 277)(202 278)(203 279)(204 280)(205 281)(206 282)(207 283)(208 284)(209 285)(210 286)(211 287)(212 288)(213 289)(214 290)(215 291)(216 292)(217 293)(218 294)(219 295)(220 296)(221 297)(222 298)(223 299)(224 300)(225 301)(226 302)(227 303)(228 304)(229 305)(230 306)(231 307)(232 308)(233 309)(234 310)(235 311)(236 312)(237 313)(238 314)(239 315)(240 316)(241 317)(242 318)(243 319)(244 320)(245 321)(246 322)(247 323)(248 324)(249 325)(250 326)(251 327)(252 328)(253 329)(254 330)(255 331)(256 332)(257 333)(258 334)
(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)

G:=sub<Sym(344)| (1,228)(2,229)(3,230)(4,231)(5,232)(6,233)(7,234)(8,235)(9,236)(10,237)(11,238)(12,239)(13,240)(14,241)(15,242)(16,243)(17,244)(18,245)(19,246)(20,247)(21,248)(22,249)(23,250)(24,251)(25,252)(26,253)(27,254)(28,255)(29,256)(30,257)(31,258)(32,173)(33,174)(34,175)(35,176)(36,177)(37,178)(38,179)(39,180)(40,181)(41,182)(42,183)(43,184)(44,185)(45,186)(46,187)(47,188)(48,189)(49,190)(50,191)(51,192)(52,193)(53,194)(54,195)(55,196)(56,197)(57,198)(58,199)(59,200)(60,201)(61,202)(62,203)(63,204)(64,205)(65,206)(66,207)(67,208)(68,209)(69,210)(70,211)(71,212)(72,213)(73,214)(74,215)(75,216)(76,217)(77,218)(78,219)(79,220)(80,221)(81,222)(82,223)(83,224)(84,225)(85,226)(86,227)(87,305)(88,306)(89,307)(90,308)(91,309)(92,310)(93,311)(94,312)(95,313)(96,314)(97,315)(98,316)(99,317)(100,318)(101,319)(102,320)(103,321)(104,322)(105,323)(106,324)(107,325)(108,326)(109,327)(110,328)(111,329)(112,330)(113,331)(114,332)(115,333)(116,334)(117,335)(118,336)(119,337)(120,338)(121,339)(122,340)(123,341)(124,342)(125,343)(126,344)(127,259)(128,260)(129,261)(130,262)(131,263)(132,264)(133,265)(134,266)(135,267)(136,268)(137,269)(138,270)(139,271)(140,272)(141,273)(142,274)(143,275)(144,276)(145,277)(146,278)(147,279)(148,280)(149,281)(150,282)(151,283)(152,284)(153,285)(154,286)(155,287)(156,288)(157,289)(158,290)(159,291)(160,292)(161,293)(162,294)(163,295)(164,296)(165,297)(166,298)(167,299)(168,300)(169,301)(170,302)(171,303)(172,304), (1,172)(2,87)(3,88)(4,89)(5,90)(6,91)(7,92)(8,93)(9,94)(10,95)(11,96)(12,97)(13,98)(14,99)(15,100)(16,101)(17,102)(18,103)(19,104)(20,105)(21,106)(22,107)(23,108)(24,109)(25,110)(26,111)(27,112)(28,113)(29,114)(30,115)(31,116)(32,117)(33,118)(34,119)(35,120)(36,121)(37,122)(38,123)(39,124)(40,125)(41,126)(42,127)(43,128)(44,129)(45,130)(46,131)(47,132)(48,133)(49,134)(50,135)(51,136)(52,137)(53,138)(54,139)(55,140)(56,141)(57,142)(58,143)(59,144)(60,145)(61,146)(62,147)(63,148)(64,149)(65,150)(66,151)(67,152)(68,153)(69,154)(70,155)(71,156)(72,157)(73,158)(74,159)(75,160)(76,161)(77,162)(78,163)(79,164)(80,165)(81,166)(82,167)(83,168)(84,169)(85,170)(86,171)(173,335)(174,336)(175,337)(176,338)(177,339)(178,340)(179,341)(180,342)(181,343)(182,344)(183,259)(184,260)(185,261)(186,262)(187,263)(188,264)(189,265)(190,266)(191,267)(192,268)(193,269)(194,270)(195,271)(196,272)(197,273)(198,274)(199,275)(200,276)(201,277)(202,278)(203,279)(204,280)(205,281)(206,282)(207,283)(208,284)(209,285)(210,286)(211,287)(212,288)(213,289)(214,290)(215,291)(216,292)(217,293)(218,294)(219,295)(220,296)(221,297)(222,298)(223,299)(224,300)(225,301)(226,302)(227,303)(228,304)(229,305)(230,306)(231,307)(232,308)(233,309)(234,310)(235,311)(236,312)(237,313)(238,314)(239,315)(240,316)(241,317)(242,318)(243,319)(244,320)(245,321)(246,322)(247,323)(248,324)(249,325)(250,326)(251,327)(252,328)(253,329)(254,330)(255,331)(256,332)(257,333)(258,334), (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)>;

G:=Group( (1,228)(2,229)(3,230)(4,231)(5,232)(6,233)(7,234)(8,235)(9,236)(10,237)(11,238)(12,239)(13,240)(14,241)(15,242)(16,243)(17,244)(18,245)(19,246)(20,247)(21,248)(22,249)(23,250)(24,251)(25,252)(26,253)(27,254)(28,255)(29,256)(30,257)(31,258)(32,173)(33,174)(34,175)(35,176)(36,177)(37,178)(38,179)(39,180)(40,181)(41,182)(42,183)(43,184)(44,185)(45,186)(46,187)(47,188)(48,189)(49,190)(50,191)(51,192)(52,193)(53,194)(54,195)(55,196)(56,197)(57,198)(58,199)(59,200)(60,201)(61,202)(62,203)(63,204)(64,205)(65,206)(66,207)(67,208)(68,209)(69,210)(70,211)(71,212)(72,213)(73,214)(74,215)(75,216)(76,217)(77,218)(78,219)(79,220)(80,221)(81,222)(82,223)(83,224)(84,225)(85,226)(86,227)(87,305)(88,306)(89,307)(90,308)(91,309)(92,310)(93,311)(94,312)(95,313)(96,314)(97,315)(98,316)(99,317)(100,318)(101,319)(102,320)(103,321)(104,322)(105,323)(106,324)(107,325)(108,326)(109,327)(110,328)(111,329)(112,330)(113,331)(114,332)(115,333)(116,334)(117,335)(118,336)(119,337)(120,338)(121,339)(122,340)(123,341)(124,342)(125,343)(126,344)(127,259)(128,260)(129,261)(130,262)(131,263)(132,264)(133,265)(134,266)(135,267)(136,268)(137,269)(138,270)(139,271)(140,272)(141,273)(142,274)(143,275)(144,276)(145,277)(146,278)(147,279)(148,280)(149,281)(150,282)(151,283)(152,284)(153,285)(154,286)(155,287)(156,288)(157,289)(158,290)(159,291)(160,292)(161,293)(162,294)(163,295)(164,296)(165,297)(166,298)(167,299)(168,300)(169,301)(170,302)(171,303)(172,304), (1,172)(2,87)(3,88)(4,89)(5,90)(6,91)(7,92)(8,93)(9,94)(10,95)(11,96)(12,97)(13,98)(14,99)(15,100)(16,101)(17,102)(18,103)(19,104)(20,105)(21,106)(22,107)(23,108)(24,109)(25,110)(26,111)(27,112)(28,113)(29,114)(30,115)(31,116)(32,117)(33,118)(34,119)(35,120)(36,121)(37,122)(38,123)(39,124)(40,125)(41,126)(42,127)(43,128)(44,129)(45,130)(46,131)(47,132)(48,133)(49,134)(50,135)(51,136)(52,137)(53,138)(54,139)(55,140)(56,141)(57,142)(58,143)(59,144)(60,145)(61,146)(62,147)(63,148)(64,149)(65,150)(66,151)(67,152)(68,153)(69,154)(70,155)(71,156)(72,157)(73,158)(74,159)(75,160)(76,161)(77,162)(78,163)(79,164)(80,165)(81,166)(82,167)(83,168)(84,169)(85,170)(86,171)(173,335)(174,336)(175,337)(176,338)(177,339)(178,340)(179,341)(180,342)(181,343)(182,344)(183,259)(184,260)(185,261)(186,262)(187,263)(188,264)(189,265)(190,266)(191,267)(192,268)(193,269)(194,270)(195,271)(196,272)(197,273)(198,274)(199,275)(200,276)(201,277)(202,278)(203,279)(204,280)(205,281)(206,282)(207,283)(208,284)(209,285)(210,286)(211,287)(212,288)(213,289)(214,290)(215,291)(216,292)(217,293)(218,294)(219,295)(220,296)(221,297)(222,298)(223,299)(224,300)(225,301)(226,302)(227,303)(228,304)(229,305)(230,306)(231,307)(232,308)(233,309)(234,310)(235,311)(236,312)(237,313)(238,314)(239,315)(240,316)(241,317)(242,318)(243,319)(244,320)(245,321)(246,322)(247,323)(248,324)(249,325)(250,326)(251,327)(252,328)(253,329)(254,330)(255,331)(256,332)(257,333)(258,334), (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) );

G=PermutationGroup([(1,228),(2,229),(3,230),(4,231),(5,232),(6,233),(7,234),(8,235),(9,236),(10,237),(11,238),(12,239),(13,240),(14,241),(15,242),(16,243),(17,244),(18,245),(19,246),(20,247),(21,248),(22,249),(23,250),(24,251),(25,252),(26,253),(27,254),(28,255),(29,256),(30,257),(31,258),(32,173),(33,174),(34,175),(35,176),(36,177),(37,178),(38,179),(39,180),(40,181),(41,182),(42,183),(43,184),(44,185),(45,186),(46,187),(47,188),(48,189),(49,190),(50,191),(51,192),(52,193),(53,194),(54,195),(55,196),(56,197),(57,198),(58,199),(59,200),(60,201),(61,202),(62,203),(63,204),(64,205),(65,206),(66,207),(67,208),(68,209),(69,210),(70,211),(71,212),(72,213),(73,214),(74,215),(75,216),(76,217),(77,218),(78,219),(79,220),(80,221),(81,222),(82,223),(83,224),(84,225),(85,226),(86,227),(87,305),(88,306),(89,307),(90,308),(91,309),(92,310),(93,311),(94,312),(95,313),(96,314),(97,315),(98,316),(99,317),(100,318),(101,319),(102,320),(103,321),(104,322),(105,323),(106,324),(107,325),(108,326),(109,327),(110,328),(111,329),(112,330),(113,331),(114,332),(115,333),(116,334),(117,335),(118,336),(119,337),(120,338),(121,339),(122,340),(123,341),(124,342),(125,343),(126,344),(127,259),(128,260),(129,261),(130,262),(131,263),(132,264),(133,265),(134,266),(135,267),(136,268),(137,269),(138,270),(139,271),(140,272),(141,273),(142,274),(143,275),(144,276),(145,277),(146,278),(147,279),(148,280),(149,281),(150,282),(151,283),(152,284),(153,285),(154,286),(155,287),(156,288),(157,289),(158,290),(159,291),(160,292),(161,293),(162,294),(163,295),(164,296),(165,297),(166,298),(167,299),(168,300),(169,301),(170,302),(171,303),(172,304)], [(1,172),(2,87),(3,88),(4,89),(5,90),(6,91),(7,92),(8,93),(9,94),(10,95),(11,96),(12,97),(13,98),(14,99),(15,100),(16,101),(17,102),(18,103),(19,104),(20,105),(21,106),(22,107),(23,108),(24,109),(25,110),(26,111),(27,112),(28,113),(29,114),(30,115),(31,116),(32,117),(33,118),(34,119),(35,120),(36,121),(37,122),(38,123),(39,124),(40,125),(41,126),(42,127),(43,128),(44,129),(45,130),(46,131),(47,132),(48,133),(49,134),(50,135),(51,136),(52,137),(53,138),(54,139),(55,140),(56,141),(57,142),(58,143),(59,144),(60,145),(61,146),(62,147),(63,148),(64,149),(65,150),(66,151),(67,152),(68,153),(69,154),(70,155),(71,156),(72,157),(73,158),(74,159),(75,160),(76,161),(77,162),(78,163),(79,164),(80,165),(81,166),(82,167),(83,168),(84,169),(85,170),(86,171),(173,335),(174,336),(175,337),(176,338),(177,339),(178,340),(179,341),(180,342),(181,343),(182,344),(183,259),(184,260),(185,261),(186,262),(187,263),(188,264),(189,265),(190,266),(191,267),(192,268),(193,269),(194,270),(195,271),(196,272),(197,273),(198,274),(199,275),(200,276),(201,277),(202,278),(203,279),(204,280),(205,281),(206,282),(207,283),(208,284),(209,285),(210,286),(211,287),(212,288),(213,289),(214,290),(215,291),(216,292),(217,293),(218,294),(219,295),(220,296),(221,297),(222,298),(223,299),(224,300),(225,301),(226,302),(227,303),(228,304),(229,305),(230,306),(231,307),(232,308),(233,309),(234,310),(235,311),(236,312),(237,313),(238,314),(239,315),(240,316),(241,317),(242,318),(243,319),(244,320),(245,321),(246,322),(247,323),(248,324),(249,325),(250,326),(251,327),(252,328),(253,329),(254,330),(255,331),(256,332),(257,333),(258,334)], [(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)])

344 conjugacy classes

class 1 2A···2G43A···43AP86A···86KH
order12···243···4386···86
size11···11···11···1

344 irreducible representations

dim1111
type++
imageC1C2C43C86
kernelC22×C86C2×C86C23C22
# reps1742294

Matrix representation of C22×C86 in GL3(𝔽173) generated by

17200
01720
001
,
100
01720
00172
,
11800
040
0014
G:=sub<GL(3,GF(173))| [172,0,0,0,172,0,0,0,1],[1,0,0,0,172,0,0,0,172],[118,0,0,0,4,0,0,0,14] >;

C22×C86 in GAP, Magma, Sage, TeX

C_2^2\times C_{86}
% in TeX

G:=Group("C2^2xC86");
// GroupNames label

G:=SmallGroup(344,12);
// by ID

G=gap.SmallGroup(344,12);
# by ID

G:=PCGroup([4,-2,-2,-2,-43]);
// Polycyclic

G:=Group<a,b,c|a^2=b^2=c^86=1,a*b=b*a,a*c=c*a,b*c=c*b>;
// generators/relations

Export

Subgroup lattice of C22×C86 in TeX

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