direct product, abelian, monomial, 2-elementary
Aliases: C22×C86, SmallGroup(344,12)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — 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
(1 238)(2 239)(3 240)(4 241)(5 242)(6 243)(7 244)(8 245)(9 246)(10 247)(11 248)(12 249)(13 250)(14 251)(15 252)(16 253)(17 254)(18 255)(19 256)(20 257)(21 258)(22 173)(23 174)(24 175)(25 176)(26 177)(27 178)(28 179)(29 180)(30 181)(31 182)(32 183)(33 184)(34 185)(35 186)(36 187)(37 188)(38 189)(39 190)(40 191)(41 192)(42 193)(43 194)(44 195)(45 196)(46 197)(47 198)(48 199)(49 200)(50 201)(51 202)(52 203)(53 204)(54 205)(55 206)(56 207)(57 208)(58 209)(59 210)(60 211)(61 212)(62 213)(63 214)(64 215)(65 216)(66 217)(67 218)(68 219)(69 220)(70 221)(71 222)(72 223)(73 224)(74 225)(75 226)(76 227)(77 228)(78 229)(79 230)(80 231)(81 232)(82 233)(83 234)(84 235)(85 236)(86 237)(87 284)(88 285)(89 286)(90 287)(91 288)(92 289)(93 290)(94 291)(95 292)(96 293)(97 294)(98 295)(99 296)(100 297)(101 298)(102 299)(103 300)(104 301)(105 302)(106 303)(107 304)(108 305)(109 306)(110 307)(111 308)(112 309)(113 310)(114 311)(115 312)(116 313)(117 314)(118 315)(119 316)(120 317)(121 318)(122 319)(123 320)(124 321)(125 322)(126 323)(127 324)(128 325)(129 326)(130 327)(131 328)(132 329)(133 330)(134 331)(135 332)(136 333)(137 334)(138 335)(139 336)(140 337)(141 338)(142 339)(143 340)(144 341)(145 342)(146 343)(147 344)(148 259)(149 260)(150 261)(151 262)(152 263)(153 264)(154 265)(155 266)(156 267)(157 268)(158 269)(159 270)(160 271)(161 272)(162 273)(163 274)(164 275)(165 276)(166 277)(167 278)(168 279)(169 280)(170 281)(171 282)(172 283)
(1 140)(2 141)(3 142)(4 143)(5 144)(6 145)(7 146)(8 147)(9 148)(10 149)(11 150)(12 151)(13 152)(14 153)(15 154)(16 155)(17 156)(18 157)(19 158)(20 159)(21 160)(22 161)(23 162)(24 163)(25 164)(26 165)(27 166)(28 167)(29 168)(30 169)(31 170)(32 171)(33 172)(34 87)(35 88)(36 89)(37 90)(38 91)(39 92)(40 93)(41 94)(42 95)(43 96)(44 97)(45 98)(46 99)(47 100)(48 101)(49 102)(50 103)(51 104)(52 105)(53 106)(54 107)(55 108)(56 109)(57 110)(58 111)(59 112)(60 113)(61 114)(62 115)(63 116)(64 117)(65 118)(66 119)(67 120)(68 121)(69 122)(70 123)(71 124)(72 125)(73 126)(74 127)(75 128)(76 129)(77 130)(78 131)(79 132)(80 133)(81 134)(82 135)(83 136)(84 137)(85 138)(86 139)(173 272)(174 273)(175 274)(176 275)(177 276)(178 277)(179 278)(180 279)(181 280)(182 281)(183 282)(184 283)(185 284)(186 285)(187 286)(188 287)(189 288)(190 289)(191 290)(192 291)(193 292)(194 293)(195 294)(196 295)(197 296)(198 297)(199 298)(200 299)(201 300)(202 301)(203 302)(204 303)(205 304)(206 305)(207 306)(208 307)(209 308)(210 309)(211 310)(212 311)(213 312)(214 313)(215 314)(216 315)(217 316)(218 317)(219 318)(220 319)(221 320)(222 321)(223 322)(224 323)(225 324)(226 325)(227 326)(228 327)(229 328)(230 329)(231 330)(232 331)(233 332)(234 333)(235 334)(236 335)(237 336)(238 337)(239 338)(240 339)(241 340)(242 341)(243 342)(244 343)(245 344)(246 259)(247 260)(248 261)(249 262)(250 263)(251 264)(252 265)(253 266)(254 267)(255 268)(256 269)(257 270)(258 271)
(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)| (1,238)(2,239)(3,240)(4,241)(5,242)(6,243)(7,244)(8,245)(9,246)(10,247)(11,248)(12,249)(13,250)(14,251)(15,252)(16,253)(17,254)(18,255)(19,256)(20,257)(21,258)(22,173)(23,174)(24,175)(25,176)(26,177)(27,178)(28,179)(29,180)(30,181)(31,182)(32,183)(33,184)(34,185)(35,186)(36,187)(37,188)(38,189)(39,190)(40,191)(41,192)(42,193)(43,194)(44,195)(45,196)(46,197)(47,198)(48,199)(49,200)(50,201)(51,202)(52,203)(53,204)(54,205)(55,206)(56,207)(57,208)(58,209)(59,210)(60,211)(61,212)(62,213)(63,214)(64,215)(65,216)(66,217)(67,218)(68,219)(69,220)(70,221)(71,222)(72,223)(73,224)(74,225)(75,226)(76,227)(77,228)(78,229)(79,230)(80,231)(81,232)(82,233)(83,234)(84,235)(85,236)(86,237)(87,284)(88,285)(89,286)(90,287)(91,288)(92,289)(93,290)(94,291)(95,292)(96,293)(97,294)(98,295)(99,296)(100,297)(101,298)(102,299)(103,300)(104,301)(105,302)(106,303)(107,304)(108,305)(109,306)(110,307)(111,308)(112,309)(113,310)(114,311)(115,312)(116,313)(117,314)(118,315)(119,316)(120,317)(121,318)(122,319)(123,320)(124,321)(125,322)(126,323)(127,324)(128,325)(129,326)(130,327)(131,328)(132,329)(133,330)(134,331)(135,332)(136,333)(137,334)(138,335)(139,336)(140,337)(141,338)(142,339)(143,340)(144,341)(145,342)(146,343)(147,344)(148,259)(149,260)(150,261)(151,262)(152,263)(153,264)(154,265)(155,266)(156,267)(157,268)(158,269)(159,270)(160,271)(161,272)(162,273)(163,274)(164,275)(165,276)(166,277)(167,278)(168,279)(169,280)(170,281)(171,282)(172,283), (1,140)(2,141)(3,142)(4,143)(5,144)(6,145)(7,146)(8,147)(9,148)(10,149)(11,150)(12,151)(13,152)(14,153)(15,154)(16,155)(17,156)(18,157)(19,158)(20,159)(21,160)(22,161)(23,162)(24,163)(25,164)(26,165)(27,166)(28,167)(29,168)(30,169)(31,170)(32,171)(33,172)(34,87)(35,88)(36,89)(37,90)(38,91)(39,92)(40,93)(41,94)(42,95)(43,96)(44,97)(45,98)(46,99)(47,100)(48,101)(49,102)(50,103)(51,104)(52,105)(53,106)(54,107)(55,108)(56,109)(57,110)(58,111)(59,112)(60,113)(61,114)(62,115)(63,116)(64,117)(65,118)(66,119)(67,120)(68,121)(69,122)(70,123)(71,124)(72,125)(73,126)(74,127)(75,128)(76,129)(77,130)(78,131)(79,132)(80,133)(81,134)(82,135)(83,136)(84,137)(85,138)(86,139)(173,272)(174,273)(175,274)(176,275)(177,276)(178,277)(179,278)(180,279)(181,280)(182,281)(183,282)(184,283)(185,284)(186,285)(187,286)(188,287)(189,288)(190,289)(191,290)(192,291)(193,292)(194,293)(195,294)(196,295)(197,296)(198,297)(199,298)(200,299)(201,300)(202,301)(203,302)(204,303)(205,304)(206,305)(207,306)(208,307)(209,308)(210,309)(211,310)(212,311)(213,312)(214,313)(215,314)(216,315)(217,316)(218,317)(219,318)(220,319)(221,320)(222,321)(223,322)(224,323)(225,324)(226,325)(227,326)(228,327)(229,328)(230,329)(231,330)(232,331)(233,332)(234,333)(235,334)(236,335)(237,336)(238,337)(239,338)(240,339)(241,340)(242,341)(243,342)(244,343)(245,344)(246,259)(247,260)(248,261)(249,262)(250,263)(251,264)(252,265)(253,266)(254,267)(255,268)(256,269)(257,270)(258,271), (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( (1,238)(2,239)(3,240)(4,241)(5,242)(6,243)(7,244)(8,245)(9,246)(10,247)(11,248)(12,249)(13,250)(14,251)(15,252)(16,253)(17,254)(18,255)(19,256)(20,257)(21,258)(22,173)(23,174)(24,175)(25,176)(26,177)(27,178)(28,179)(29,180)(30,181)(31,182)(32,183)(33,184)(34,185)(35,186)(36,187)(37,188)(38,189)(39,190)(40,191)(41,192)(42,193)(43,194)(44,195)(45,196)(46,197)(47,198)(48,199)(49,200)(50,201)(51,202)(52,203)(53,204)(54,205)(55,206)(56,207)(57,208)(58,209)(59,210)(60,211)(61,212)(62,213)(63,214)(64,215)(65,216)(66,217)(67,218)(68,219)(69,220)(70,221)(71,222)(72,223)(73,224)(74,225)(75,226)(76,227)(77,228)(78,229)(79,230)(80,231)(81,232)(82,233)(83,234)(84,235)(85,236)(86,237)(87,284)(88,285)(89,286)(90,287)(91,288)(92,289)(93,290)(94,291)(95,292)(96,293)(97,294)(98,295)(99,296)(100,297)(101,298)(102,299)(103,300)(104,301)(105,302)(106,303)(107,304)(108,305)(109,306)(110,307)(111,308)(112,309)(113,310)(114,311)(115,312)(116,313)(117,314)(118,315)(119,316)(120,317)(121,318)(122,319)(123,320)(124,321)(125,322)(126,323)(127,324)(128,325)(129,326)(130,327)(131,328)(132,329)(133,330)(134,331)(135,332)(136,333)(137,334)(138,335)(139,336)(140,337)(141,338)(142,339)(143,340)(144,341)(145,342)(146,343)(147,344)(148,259)(149,260)(150,261)(151,262)(152,263)(153,264)(154,265)(155,266)(156,267)(157,268)(158,269)(159,270)(160,271)(161,272)(162,273)(163,274)(164,275)(165,276)(166,277)(167,278)(168,279)(169,280)(170,281)(171,282)(172,283), (1,140)(2,141)(3,142)(4,143)(5,144)(6,145)(7,146)(8,147)(9,148)(10,149)(11,150)(12,151)(13,152)(14,153)(15,154)(16,155)(17,156)(18,157)(19,158)(20,159)(21,160)(22,161)(23,162)(24,163)(25,164)(26,165)(27,166)(28,167)(29,168)(30,169)(31,170)(32,171)(33,172)(34,87)(35,88)(36,89)(37,90)(38,91)(39,92)(40,93)(41,94)(42,95)(43,96)(44,97)(45,98)(46,99)(47,100)(48,101)(49,102)(50,103)(51,104)(52,105)(53,106)(54,107)(55,108)(56,109)(57,110)(58,111)(59,112)(60,113)(61,114)(62,115)(63,116)(64,117)(65,118)(66,119)(67,120)(68,121)(69,122)(70,123)(71,124)(72,125)(73,126)(74,127)(75,128)(76,129)(77,130)(78,131)(79,132)(80,133)(81,134)(82,135)(83,136)(84,137)(85,138)(86,139)(173,272)(174,273)(175,274)(176,275)(177,276)(178,277)(179,278)(180,279)(181,280)(182,281)(183,282)(184,283)(185,284)(186,285)(187,286)(188,287)(189,288)(190,289)(191,290)(192,291)(193,292)(194,293)(195,294)(196,295)(197,296)(198,297)(199,298)(200,299)(201,300)(202,301)(203,302)(204,303)(205,304)(206,305)(207,306)(208,307)(209,308)(210,309)(211,310)(212,311)(213,312)(214,313)(215,314)(216,315)(217,316)(218,317)(219,318)(220,319)(221,320)(222,321)(223,322)(224,323)(225,324)(226,325)(227,326)(228,327)(229,328)(230,329)(231,330)(232,331)(233,332)(234,333)(235,334)(236,335)(237,336)(238,337)(239,338)(240,339)(241,340)(242,341)(243,342)(244,343)(245,344)(246,259)(247,260)(248,261)(249,262)(250,263)(251,264)(252,265)(253,266)(254,267)(255,268)(256,269)(257,270)(258,271), (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([[(1,238),(2,239),(3,240),(4,241),(5,242),(6,243),(7,244),(8,245),(9,246),(10,247),(11,248),(12,249),(13,250),(14,251),(15,252),(16,253),(17,254),(18,255),(19,256),(20,257),(21,258),(22,173),(23,174),(24,175),(25,176),(26,177),(27,178),(28,179),(29,180),(30,181),(31,182),(32,183),(33,184),(34,185),(35,186),(36,187),(37,188),(38,189),(39,190),(40,191),(41,192),(42,193),(43,194),(44,195),(45,196),(46,197),(47,198),(48,199),(49,200),(50,201),(51,202),(52,203),(53,204),(54,205),(55,206),(56,207),(57,208),(58,209),(59,210),(60,211),(61,212),(62,213),(63,214),(64,215),(65,216),(66,217),(67,218),(68,219),(69,220),(70,221),(71,222),(72,223),(73,224),(74,225),(75,226),(76,227),(77,228),(78,229),(79,230),(80,231),(81,232),(82,233),(83,234),(84,235),(85,236),(86,237),(87,284),(88,285),(89,286),(90,287),(91,288),(92,289),(93,290),(94,291),(95,292),(96,293),(97,294),(98,295),(99,296),(100,297),(101,298),(102,299),(103,300),(104,301),(105,302),(106,303),(107,304),(108,305),(109,306),(110,307),(111,308),(112,309),(113,310),(114,311),(115,312),(116,313),(117,314),(118,315),(119,316),(120,317),(121,318),(122,319),(123,320),(124,321),(125,322),(126,323),(127,324),(128,325),(129,326),(130,327),(131,328),(132,329),(133,330),(134,331),(135,332),(136,333),(137,334),(138,335),(139,336),(140,337),(141,338),(142,339),(143,340),(144,341),(145,342),(146,343),(147,344),(148,259),(149,260),(150,261),(151,262),(152,263),(153,264),(154,265),(155,266),(156,267),(157,268),(158,269),(159,270),(160,271),(161,272),(162,273),(163,274),(164,275),(165,276),(166,277),(167,278),(168,279),(169,280),(170,281),(171,282),(172,283)], [(1,140),(2,141),(3,142),(4,143),(5,144),(6,145),(7,146),(8,147),(9,148),(10,149),(11,150),(12,151),(13,152),(14,153),(15,154),(16,155),(17,156),(18,157),(19,158),(20,159),(21,160),(22,161),(23,162),(24,163),(25,164),(26,165),(27,166),(28,167),(29,168),(30,169),(31,170),(32,171),(33,172),(34,87),(35,88),(36,89),(37,90),(38,91),(39,92),(40,93),(41,94),(42,95),(43,96),(44,97),(45,98),(46,99),(47,100),(48,101),(49,102),(50,103),(51,104),(52,105),(53,106),(54,107),(55,108),(56,109),(57,110),(58,111),(59,112),(60,113),(61,114),(62,115),(63,116),(64,117),(65,118),(66,119),(67,120),(68,121),(69,122),(70,123),(71,124),(72,125),(73,126),(74,127),(75,128),(76,129),(77,130),(78,131),(79,132),(80,133),(81,134),(82,135),(83,136),(84,137),(85,138),(86,139),(173,272),(174,273),(175,274),(176,275),(177,276),(178,277),(179,278),(180,279),(181,280),(182,281),(183,282),(184,283),(185,284),(186,285),(187,286),(188,287),(189,288),(190,289),(191,290),(192,291),(193,292),(194,293),(195,294),(196,295),(197,296),(198,297),(199,298),(200,299),(201,300),(202,301),(203,302),(204,303),(205,304),(206,305),(207,306),(208,307),(209,308),(210,309),(211,310),(212,311),(213,312),(214,313),(215,314),(216,315),(217,316),(218,317),(219,318),(220,319),(221,320),(222,321),(223,322),(224,323),(225,324),(226,325),(227,326),(228,327),(229,328),(230,329),(231,330),(232,331),(233,332),(234,333),(235,334),(236,335),(237,336),(238,337),(239,338),(240,339),(241,340),(242,341),(243,342),(244,343),(245,344),(246,259),(247,260),(248,261),(249,262),(250,263),(251,264),(252,265),(253,266),(254,267),(255,268),(256,269),(257,270),(258,271)], [(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 | ··· | 2G | 43A | ··· | 43AP | 86A | ··· | 86KH |
| order | 1 | 2 | ··· | 2 | 43 | ··· | 43 | 86 | ··· | 86 |
| size | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
344 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | + | ||
| image | C1 | C2 | C43 | C86 |
| kernel | C22×C86 | C2×C86 | C23 | C22 |
| # reps | 1 | 7 | 42 | 294 |
Matrix representation of C22×C86 ►in GL3(𝔽173) generated by
| 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 |
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
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