direct product, abelian, monomial, 2-elementary
Aliases: C22×C88, SmallGroup(352,164)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C22×C88 |
| C1 — C22×C88 |
| C1 — C22×C88 |
Generators and relations for C22×C88
G = < a,b,c | a2=b2=c88=1, ab=ba, ac=ca, bc=cb >
Subgroups: 76, all normal (12 characteristic)
C1, C2, C2, C4, C4, C22, C8, C2×C4, C23, C11, C2×C8, C22×C4, C22, C22, C22×C8, C44, C44, C2×C22, C88, C2×C44, C22×C22, C2×C88, C22×C44, C22×C88
Quotients: C1, C2, C4, C22, C8, C2×C4, C23, C11, C2×C8, C22×C4, C22, C22×C8, C44, C2×C22, C88, C2×C44, C22×C22, C2×C88, C22×C44, C22×C88
►Regular action on 352 points
Generators in S352
(1 210)(2 211)(3 212)(4 213)(5 214)(6 215)(7 216)(8 217)(9 218)(10 219)(11 220)(12 221)(13 222)(14 223)(15 224)(16 225)(17 226)(18 227)(19 228)(20 229)(21 230)(22 231)(23 232)(24 233)(25 234)(26 235)(27 236)(28 237)(29 238)(30 239)(31 240)(32 241)(33 242)(34 243)(35 244)(36 245)(37 246)(38 247)(39 248)(40 249)(41 250)(42 251)(43 252)(44 253)(45 254)(46 255)(47 256)(48 257)(49 258)(50 259)(51 260)(52 261)(53 262)(54 263)(55 264)(56 177)(57 178)(58 179)(59 180)(60 181)(61 182)(62 183)(63 184)(64 185)(65 186)(66 187)(67 188)(68 189)(69 190)(70 191)(71 192)(72 193)(73 194)(74 195)(75 196)(76 197)(77 198)(78 199)(79 200)(80 201)(81 202)(82 203)(83 204)(84 205)(85 206)(86 207)(87 208)(88 209)(89 315)(90 316)(91 317)(92 318)(93 319)(94 320)(95 321)(96 322)(97 323)(98 324)(99 325)(100 326)(101 327)(102 328)(103 329)(104 330)(105 331)(106 332)(107 333)(108 334)(109 335)(110 336)(111 337)(112 338)(113 339)(114 340)(115 341)(116 342)(117 343)(118 344)(119 345)(120 346)(121 347)(122 348)(123 349)(124 350)(125 351)(126 352)(127 265)(128 266)(129 267)(130 268)(131 269)(132 270)(133 271)(134 272)(135 273)(136 274)(137 275)(138 276)(139 277)(140 278)(141 279)(142 280)(143 281)(144 282)(145 283)(146 284)(147 285)(148 286)(149 287)(150 288)(151 289)(152 290)(153 291)(154 292)(155 293)(156 294)(157 295)(158 296)(159 297)(160 298)(161 299)(162 300)(163 301)(164 302)(165 303)(166 304)(167 305)(168 306)(169 307)(170 308)(171 309)(172 310)(173 311)(174 312)(175 313)(176 314)
(1 126)(2 127)(3 128)(4 129)(5 130)(6 131)(7 132)(8 133)(9 134)(10 135)(11 136)(12 137)(13 138)(14 139)(15 140)(16 141)(17 142)(18 143)(19 144)(20 145)(21 146)(22 147)(23 148)(24 149)(25 150)(26 151)(27 152)(28 153)(29 154)(30 155)(31 156)(32 157)(33 158)(34 159)(35 160)(36 161)(37 162)(38 163)(39 164)(40 165)(41 166)(42 167)(43 168)(44 169)(45 170)(46 171)(47 172)(48 173)(49 174)(50 175)(51 176)(52 89)(53 90)(54 91)(55 92)(56 93)(57 94)(58 95)(59 96)(60 97)(61 98)(62 99)(63 100)(64 101)(65 102)(66 103)(67 104)(68 105)(69 106)(70 107)(71 108)(72 109)(73 110)(74 111)(75 112)(76 113)(77 114)(78 115)(79 116)(80 117)(81 118)(82 119)(83 120)(84 121)(85 122)(86 123)(87 124)(88 125)(177 319)(178 320)(179 321)(180 322)(181 323)(182 324)(183 325)(184 326)(185 327)(186 328)(187 329)(188 330)(189 331)(190 332)(191 333)(192 334)(193 335)(194 336)(195 337)(196 338)(197 339)(198 340)(199 341)(200 342)(201 343)(202 344)(203 345)(204 346)(205 347)(206 348)(207 349)(208 350)(209 351)(210 352)(211 265)(212 266)(213 267)(214 268)(215 269)(216 270)(217 271)(218 272)(219 273)(220 274)(221 275)(222 276)(223 277)(224 278)(225 279)(226 280)(227 281)(228 282)(229 283)(230 284)(231 285)(232 286)(233 287)(234 288)(235 289)(236 290)(237 291)(238 292)(239 293)(240 294)(241 295)(242 296)(243 297)(244 298)(245 299)(246 300)(247 301)(248 302)(249 303)(250 304)(251 305)(252 306)(253 307)(254 308)(255 309)(256 310)(257 311)(258 312)(259 313)(260 314)(261 315)(262 316)(263 317)(264 318)
(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)(265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352)
G:=sub<Sym(352)| (1,210)(2,211)(3,212)(4,213)(5,214)(6,215)(7,216)(8,217)(9,218)(10,219)(11,220)(12,221)(13,222)(14,223)(15,224)(16,225)(17,226)(18,227)(19,228)(20,229)(21,230)(22,231)(23,232)(24,233)(25,234)(26,235)(27,236)(28,237)(29,238)(30,239)(31,240)(32,241)(33,242)(34,243)(35,244)(36,245)(37,246)(38,247)(39,248)(40,249)(41,250)(42,251)(43,252)(44,253)(45,254)(46,255)(47,256)(48,257)(49,258)(50,259)(51,260)(52,261)(53,262)(54,263)(55,264)(56,177)(57,178)(58,179)(59,180)(60,181)(61,182)(62,183)(63,184)(64,185)(65,186)(66,187)(67,188)(68,189)(69,190)(70,191)(71,192)(72,193)(73,194)(74,195)(75,196)(76,197)(77,198)(78,199)(79,200)(80,201)(81,202)(82,203)(83,204)(84,205)(85,206)(86,207)(87,208)(88,209)(89,315)(90,316)(91,317)(92,318)(93,319)(94,320)(95,321)(96,322)(97,323)(98,324)(99,325)(100,326)(101,327)(102,328)(103,329)(104,330)(105,331)(106,332)(107,333)(108,334)(109,335)(110,336)(111,337)(112,338)(113,339)(114,340)(115,341)(116,342)(117,343)(118,344)(119,345)(120,346)(121,347)(122,348)(123,349)(124,350)(125,351)(126,352)(127,265)(128,266)(129,267)(130,268)(131,269)(132,270)(133,271)(134,272)(135,273)(136,274)(137,275)(138,276)(139,277)(140,278)(141,279)(142,280)(143,281)(144,282)(145,283)(146,284)(147,285)(148,286)(149,287)(150,288)(151,289)(152,290)(153,291)(154,292)(155,293)(156,294)(157,295)(158,296)(159,297)(160,298)(161,299)(162,300)(163,301)(164,302)(165,303)(166,304)(167,305)(168,306)(169,307)(170,308)(171,309)(172,310)(173,311)(174,312)(175,313)(176,314), (1,126)(2,127)(3,128)(4,129)(5,130)(6,131)(7,132)(8,133)(9,134)(10,135)(11,136)(12,137)(13,138)(14,139)(15,140)(16,141)(17,142)(18,143)(19,144)(20,145)(21,146)(22,147)(23,148)(24,149)(25,150)(26,151)(27,152)(28,153)(29,154)(30,155)(31,156)(32,157)(33,158)(34,159)(35,160)(36,161)(37,162)(38,163)(39,164)(40,165)(41,166)(42,167)(43,168)(44,169)(45,170)(46,171)(47,172)(48,173)(49,174)(50,175)(51,176)(52,89)(53,90)(54,91)(55,92)(56,93)(57,94)(58,95)(59,96)(60,97)(61,98)(62,99)(63,100)(64,101)(65,102)(66,103)(67,104)(68,105)(69,106)(70,107)(71,108)(72,109)(73,110)(74,111)(75,112)(76,113)(77,114)(78,115)(79,116)(80,117)(81,118)(82,119)(83,120)(84,121)(85,122)(86,123)(87,124)(88,125)(177,319)(178,320)(179,321)(180,322)(181,323)(182,324)(183,325)(184,326)(185,327)(186,328)(187,329)(188,330)(189,331)(190,332)(191,333)(192,334)(193,335)(194,336)(195,337)(196,338)(197,339)(198,340)(199,341)(200,342)(201,343)(202,344)(203,345)(204,346)(205,347)(206,348)(207,349)(208,350)(209,351)(210,352)(211,265)(212,266)(213,267)(214,268)(215,269)(216,270)(217,271)(218,272)(219,273)(220,274)(221,275)(222,276)(223,277)(224,278)(225,279)(226,280)(227,281)(228,282)(229,283)(230,284)(231,285)(232,286)(233,287)(234,288)(235,289)(236,290)(237,291)(238,292)(239,293)(240,294)(241,295)(242,296)(243,297)(244,298)(245,299)(246,300)(247,301)(248,302)(249,303)(250,304)(251,305)(252,306)(253,307)(254,308)(255,309)(256,310)(257,311)(258,312)(259,313)(260,314)(261,315)(262,316)(263,317)(264,318), (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)(265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352)>;
G:=Group( (1,210)(2,211)(3,212)(4,213)(5,214)(6,215)(7,216)(8,217)(9,218)(10,219)(11,220)(12,221)(13,222)(14,223)(15,224)(16,225)(17,226)(18,227)(19,228)(20,229)(21,230)(22,231)(23,232)(24,233)(25,234)(26,235)(27,236)(28,237)(29,238)(30,239)(31,240)(32,241)(33,242)(34,243)(35,244)(36,245)(37,246)(38,247)(39,248)(40,249)(41,250)(42,251)(43,252)(44,253)(45,254)(46,255)(47,256)(48,257)(49,258)(50,259)(51,260)(52,261)(53,262)(54,263)(55,264)(56,177)(57,178)(58,179)(59,180)(60,181)(61,182)(62,183)(63,184)(64,185)(65,186)(66,187)(67,188)(68,189)(69,190)(70,191)(71,192)(72,193)(73,194)(74,195)(75,196)(76,197)(77,198)(78,199)(79,200)(80,201)(81,202)(82,203)(83,204)(84,205)(85,206)(86,207)(87,208)(88,209)(89,315)(90,316)(91,317)(92,318)(93,319)(94,320)(95,321)(96,322)(97,323)(98,324)(99,325)(100,326)(101,327)(102,328)(103,329)(104,330)(105,331)(106,332)(107,333)(108,334)(109,335)(110,336)(111,337)(112,338)(113,339)(114,340)(115,341)(116,342)(117,343)(118,344)(119,345)(120,346)(121,347)(122,348)(123,349)(124,350)(125,351)(126,352)(127,265)(128,266)(129,267)(130,268)(131,269)(132,270)(133,271)(134,272)(135,273)(136,274)(137,275)(138,276)(139,277)(140,278)(141,279)(142,280)(143,281)(144,282)(145,283)(146,284)(147,285)(148,286)(149,287)(150,288)(151,289)(152,290)(153,291)(154,292)(155,293)(156,294)(157,295)(158,296)(159,297)(160,298)(161,299)(162,300)(163,301)(164,302)(165,303)(166,304)(167,305)(168,306)(169,307)(170,308)(171,309)(172,310)(173,311)(174,312)(175,313)(176,314), (1,126)(2,127)(3,128)(4,129)(5,130)(6,131)(7,132)(8,133)(9,134)(10,135)(11,136)(12,137)(13,138)(14,139)(15,140)(16,141)(17,142)(18,143)(19,144)(20,145)(21,146)(22,147)(23,148)(24,149)(25,150)(26,151)(27,152)(28,153)(29,154)(30,155)(31,156)(32,157)(33,158)(34,159)(35,160)(36,161)(37,162)(38,163)(39,164)(40,165)(41,166)(42,167)(43,168)(44,169)(45,170)(46,171)(47,172)(48,173)(49,174)(50,175)(51,176)(52,89)(53,90)(54,91)(55,92)(56,93)(57,94)(58,95)(59,96)(60,97)(61,98)(62,99)(63,100)(64,101)(65,102)(66,103)(67,104)(68,105)(69,106)(70,107)(71,108)(72,109)(73,110)(74,111)(75,112)(76,113)(77,114)(78,115)(79,116)(80,117)(81,118)(82,119)(83,120)(84,121)(85,122)(86,123)(87,124)(88,125)(177,319)(178,320)(179,321)(180,322)(181,323)(182,324)(183,325)(184,326)(185,327)(186,328)(187,329)(188,330)(189,331)(190,332)(191,333)(192,334)(193,335)(194,336)(195,337)(196,338)(197,339)(198,340)(199,341)(200,342)(201,343)(202,344)(203,345)(204,346)(205,347)(206,348)(207,349)(208,350)(209,351)(210,352)(211,265)(212,266)(213,267)(214,268)(215,269)(216,270)(217,271)(218,272)(219,273)(220,274)(221,275)(222,276)(223,277)(224,278)(225,279)(226,280)(227,281)(228,282)(229,283)(230,284)(231,285)(232,286)(233,287)(234,288)(235,289)(236,290)(237,291)(238,292)(239,293)(240,294)(241,295)(242,296)(243,297)(244,298)(245,299)(246,300)(247,301)(248,302)(249,303)(250,304)(251,305)(252,306)(253,307)(254,308)(255,309)(256,310)(257,311)(258,312)(259,313)(260,314)(261,315)(262,316)(263,317)(264,318), (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)(265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352) );
G=PermutationGroup([[(1,210),(2,211),(3,212),(4,213),(5,214),(6,215),(7,216),(8,217),(9,218),(10,219),(11,220),(12,221),(13,222),(14,223),(15,224),(16,225),(17,226),(18,227),(19,228),(20,229),(21,230),(22,231),(23,232),(24,233),(25,234),(26,235),(27,236),(28,237),(29,238),(30,239),(31,240),(32,241),(33,242),(34,243),(35,244),(36,245),(37,246),(38,247),(39,248),(40,249),(41,250),(42,251),(43,252),(44,253),(45,254),(46,255),(47,256),(48,257),(49,258),(50,259),(51,260),(52,261),(53,262),(54,263),(55,264),(56,177),(57,178),(58,179),(59,180),(60,181),(61,182),(62,183),(63,184),(64,185),(65,186),(66,187),(67,188),(68,189),(69,190),(70,191),(71,192),(72,193),(73,194),(74,195),(75,196),(76,197),(77,198),(78,199),(79,200),(80,201),(81,202),(82,203),(83,204),(84,205),(85,206),(86,207),(87,208),(88,209),(89,315),(90,316),(91,317),(92,318),(93,319),(94,320),(95,321),(96,322),(97,323),(98,324),(99,325),(100,326),(101,327),(102,328),(103,329),(104,330),(105,331),(106,332),(107,333),(108,334),(109,335),(110,336),(111,337),(112,338),(113,339),(114,340),(115,341),(116,342),(117,343),(118,344),(119,345),(120,346),(121,347),(122,348),(123,349),(124,350),(125,351),(126,352),(127,265),(128,266),(129,267),(130,268),(131,269),(132,270),(133,271),(134,272),(135,273),(136,274),(137,275),(138,276),(139,277),(140,278),(141,279),(142,280),(143,281),(144,282),(145,283),(146,284),(147,285),(148,286),(149,287),(150,288),(151,289),(152,290),(153,291),(154,292),(155,293),(156,294),(157,295),(158,296),(159,297),(160,298),(161,299),(162,300),(163,301),(164,302),(165,303),(166,304),(167,305),(168,306),(169,307),(170,308),(171,309),(172,310),(173,311),(174,312),(175,313),(176,314)], [(1,126),(2,127),(3,128),(4,129),(5,130),(6,131),(7,132),(8,133),(9,134),(10,135),(11,136),(12,137),(13,138),(14,139),(15,140),(16,141),(17,142),(18,143),(19,144),(20,145),(21,146),(22,147),(23,148),(24,149),(25,150),(26,151),(27,152),(28,153),(29,154),(30,155),(31,156),(32,157),(33,158),(34,159),(35,160),(36,161),(37,162),(38,163),(39,164),(40,165),(41,166),(42,167),(43,168),(44,169),(45,170),(46,171),(47,172),(48,173),(49,174),(50,175),(51,176),(52,89),(53,90),(54,91),(55,92),(56,93),(57,94),(58,95),(59,96),(60,97),(61,98),(62,99),(63,100),(64,101),(65,102),(66,103),(67,104),(68,105),(69,106),(70,107),(71,108),(72,109),(73,110),(74,111),(75,112),(76,113),(77,114),(78,115),(79,116),(80,117),(81,118),(82,119),(83,120),(84,121),(85,122),(86,123),(87,124),(88,125),(177,319),(178,320),(179,321),(180,322),(181,323),(182,324),(183,325),(184,326),(185,327),(186,328),(187,329),(188,330),(189,331),(190,332),(191,333),(192,334),(193,335),(194,336),(195,337),(196,338),(197,339),(198,340),(199,341),(200,342),(201,343),(202,344),(203,345),(204,346),(205,347),(206,348),(207,349),(208,350),(209,351),(210,352),(211,265),(212,266),(213,267),(214,268),(215,269),(216,270),(217,271),(218,272),(219,273),(220,274),(221,275),(222,276),(223,277),(224,278),(225,279),(226,280),(227,281),(228,282),(229,283),(230,284),(231,285),(232,286),(233,287),(234,288),(235,289),(236,290),(237,291),(238,292),(239,293),(240,294),(241,295),(242,296),(243,297),(244,298),(245,299),(246,300),(247,301),(248,302),(249,303),(250,304),(251,305),(252,306),(253,307),(254,308),(255,309),(256,310),(257,311),(258,312),(259,313),(260,314),(261,315),(262,316),(263,317),(264,318)], [(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),(265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352)]])
352 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | ··· | 4H | 8A | ··· | 8P | 11A | ··· | 11J | 22A | ··· | 22BR | 44A | ··· | 44CB | 88A | ··· | 88FD |
| order | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 11 | ··· | 11 | 22 | ··· | 22 | 44 | ··· | 44 | 88 | ··· | 88 |
| size | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
352 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| type | + | + | + | |||||||||
| image | C1 | C2 | C2 | C4 | C4 | C8 | C11 | C22 | C22 | C44 | C44 | C88 |
| kernel | C22×C88 | C2×C88 | C22×C44 | C2×C44 | C22×C22 | C2×C22 | C22×C8 | C2×C8 | C22×C4 | C2×C4 | C23 | C22 |
| # reps | 1 | 6 | 1 | 6 | 2 | 16 | 10 | 60 | 10 | 60 | 20 | 160 |
Matrix representation of C22×C88 ►in GL3(𝔽89) generated by
| 88 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 1 |
| 88 | 0 | 0 |
| 0 | 88 | 0 |
| 0 | 0 | 88 |
| 55 | 0 | 0 |
| 0 | 81 | 0 |
| 0 | 0 | 48 |
G:=sub<GL(3,GF(89))| [88,0,0,0,1,0,0,0,1],[88,0,0,0,88,0,0,0,88],[55,0,0,0,81,0,0,0,48] >;
C22×C88 in GAP, Magma, Sage, TeX
C_2^2\times C_{88} % in TeX
G:=Group("C2^2xC88"); // GroupNames label
G:=SmallGroup(352,164);
// by ID
G=gap.SmallGroup(352,164);
# by ID
G:=PCGroup([6,-2,-2,-2,-11,-2,-2,528,88]);
// Polycyclic
G:=Group<a,b,c|a^2=b^2=c^88=1,a*b=b*a,a*c=c*a,b*c=c*b>;
// generators/relations