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G = C22×C88order 352 = 25·11

Abelian group of type [2,2,88]

direct product, abelian, monomial, 2-elementary

Aliases: C22×C88, SmallGroup(352,164)

Series: Derived Chief Lower central Upper central

C1 — C22×C88
C1C2C4C44C88C2×C88 — 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 [×6], C4, C4 [×3], C22 [×7], C8 [×4], C2×C4 [×6], C23, C11, C2×C8 [×6], C22×C4, C22, C22 [×6], C22×C8, C44, C44 [×3], C2×C22 [×7], C88 [×4], C2×C44 [×6], C22×C22, C2×C88 [×6], C22×C44, C22×C88
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C8 [×4], C2×C4 [×6], C23, C11, C2×C8 [×6], C22×C4, C22 [×7], C22×C8, C44 [×4], C2×C22 [×7], C88 [×4], C2×C44 [×6], C22×C22, C2×C88 [×6], C22×C44, C22×C88

Smallest permutation representation of C22×C88
Regular action on 352 points
Generators in S352
(1 220)(2 221)(3 222)(4 223)(5 224)(6 225)(7 226)(8 227)(9 228)(10 229)(11 230)(12 231)(13 232)(14 233)(15 234)(16 235)(17 236)(18 237)(19 238)(20 239)(21 240)(22 241)(23 242)(24 243)(25 244)(26 245)(27 246)(28 247)(29 248)(30 249)(31 250)(32 251)(33 252)(34 253)(35 254)(36 255)(37 256)(38 257)(39 258)(40 259)(41 260)(42 261)(43 262)(44 263)(45 264)(46 177)(47 178)(48 179)(49 180)(50 181)(51 182)(52 183)(53 184)(54 185)(55 186)(56 187)(57 188)(58 189)(59 190)(60 191)(61 192)(62 193)(63 194)(64 195)(65 196)(66 197)(67 198)(68 199)(69 200)(70 201)(71 202)(72 203)(73 204)(74 205)(75 206)(76 207)(77 208)(78 209)(79 210)(80 211)(81 212)(82 213)(83 214)(84 215)(85 216)(86 217)(87 218)(88 219)(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)(148 345)(149 346)(150 347)(151 348)(152 349)(153 350)(154 351)(155 352)(156 265)(157 266)(158 267)(159 268)(160 269)(161 270)(162 271)(163 272)(164 273)(165 274)(166 275)(167 276)(168 277)(169 278)(170 279)(171 280)(172 281)(173 282)(174 283)(175 284)(176 285)
(1 96)(2 97)(3 98)(4 99)(5 100)(6 101)(7 102)(8 103)(9 104)(10 105)(11 106)(12 107)(13 108)(14 109)(15 110)(16 111)(17 112)(18 113)(19 114)(20 115)(21 116)(22 117)(23 118)(24 119)(25 120)(26 121)(27 122)(28 123)(29 124)(30 125)(31 126)(32 127)(33 128)(34 129)(35 130)(36 131)(37 132)(38 133)(39 134)(40 135)(41 136)(42 137)(43 138)(44 139)(45 140)(46 141)(47 142)(48 143)(49 144)(50 145)(51 146)(52 147)(53 148)(54 149)(55 150)(56 151)(57 152)(58 153)(59 154)(60 155)(61 156)(62 157)(63 158)(64 159)(65 160)(66 161)(67 162)(68 163)(69 164)(70 165)(71 166)(72 167)(73 168)(74 169)(75 170)(76 171)(77 172)(78 173)(79 174)(80 175)(81 176)(82 89)(83 90)(84 91)(85 92)(86 93)(87 94)(88 95)(177 338)(178 339)(179 340)(180 341)(181 342)(182 343)(183 344)(184 345)(185 346)(186 347)(187 348)(188 349)(189 350)(190 351)(191 352)(192 265)(193 266)(194 267)(195 268)(196 269)(197 270)(198 271)(199 272)(200 273)(201 274)(202 275)(203 276)(204 277)(205 278)(206 279)(207 280)(208 281)(209 282)(210 283)(211 284)(212 285)(213 286)(214 287)(215 288)(216 289)(217 290)(218 291)(219 292)(220 293)(221 294)(222 295)(223 296)(224 297)(225 298)(226 299)(227 300)(228 301)(229 302)(230 303)(231 304)(232 305)(233 306)(234 307)(235 308)(236 309)(237 310)(238 311)(239 312)(240 313)(241 314)(242 315)(243 316)(244 317)(245 318)(246 319)(247 320)(248 321)(249 322)(250 323)(251 324)(252 325)(253 326)(254 327)(255 328)(256 329)(257 330)(258 331)(259 332)(260 333)(261 334)(262 335)(263 336)(264 337)
(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)| (1,220)(2,221)(3,222)(4,223)(5,224)(6,225)(7,226)(8,227)(9,228)(10,229)(11,230)(12,231)(13,232)(14,233)(15,234)(16,235)(17,236)(18,237)(19,238)(20,239)(21,240)(22,241)(23,242)(24,243)(25,244)(26,245)(27,246)(28,247)(29,248)(30,249)(31,250)(32,251)(33,252)(34,253)(35,254)(36,255)(37,256)(38,257)(39,258)(40,259)(41,260)(42,261)(43,262)(44,263)(45,264)(46,177)(47,178)(48,179)(49,180)(50,181)(51,182)(52,183)(53,184)(54,185)(55,186)(56,187)(57,188)(58,189)(59,190)(60,191)(61,192)(62,193)(63,194)(64,195)(65,196)(66,197)(67,198)(68,199)(69,200)(70,201)(71,202)(72,203)(73,204)(74,205)(75,206)(76,207)(77,208)(78,209)(79,210)(80,211)(81,212)(82,213)(83,214)(84,215)(85,216)(86,217)(87,218)(88,219)(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)(148,345)(149,346)(150,347)(151,348)(152,349)(153,350)(154,351)(155,352)(156,265)(157,266)(158,267)(159,268)(160,269)(161,270)(162,271)(163,272)(164,273)(165,274)(166,275)(167,276)(168,277)(169,278)(170,279)(171,280)(172,281)(173,282)(174,283)(175,284)(176,285), (1,96)(2,97)(3,98)(4,99)(5,100)(6,101)(7,102)(8,103)(9,104)(10,105)(11,106)(12,107)(13,108)(14,109)(15,110)(16,111)(17,112)(18,113)(19,114)(20,115)(21,116)(22,117)(23,118)(24,119)(25,120)(26,121)(27,122)(28,123)(29,124)(30,125)(31,126)(32,127)(33,128)(34,129)(35,130)(36,131)(37,132)(38,133)(39,134)(40,135)(41,136)(42,137)(43,138)(44,139)(45,140)(46,141)(47,142)(48,143)(49,144)(50,145)(51,146)(52,147)(53,148)(54,149)(55,150)(56,151)(57,152)(58,153)(59,154)(60,155)(61,156)(62,157)(63,158)(64,159)(65,160)(66,161)(67,162)(68,163)(69,164)(70,165)(71,166)(72,167)(73,168)(74,169)(75,170)(76,171)(77,172)(78,173)(79,174)(80,175)(81,176)(82,89)(83,90)(84,91)(85,92)(86,93)(87,94)(88,95)(177,338)(178,339)(179,340)(180,341)(181,342)(182,343)(183,344)(184,345)(185,346)(186,347)(187,348)(188,349)(189,350)(190,351)(191,352)(192,265)(193,266)(194,267)(195,268)(196,269)(197,270)(198,271)(199,272)(200,273)(201,274)(202,275)(203,276)(204,277)(205,278)(206,279)(207,280)(208,281)(209,282)(210,283)(211,284)(212,285)(213,286)(214,287)(215,288)(216,289)(217,290)(218,291)(219,292)(220,293)(221,294)(222,295)(223,296)(224,297)(225,298)(226,299)(227,300)(228,301)(229,302)(230,303)(231,304)(232,305)(233,306)(234,307)(235,308)(236,309)(237,310)(238,311)(239,312)(240,313)(241,314)(242,315)(243,316)(244,317)(245,318)(246,319)(247,320)(248,321)(249,322)(250,323)(251,324)(252,325)(253,326)(254,327)(255,328)(256,329)(257,330)(258,331)(259,332)(260,333)(261,334)(262,335)(263,336)(264,337), (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( (1,220)(2,221)(3,222)(4,223)(5,224)(6,225)(7,226)(8,227)(9,228)(10,229)(11,230)(12,231)(13,232)(14,233)(15,234)(16,235)(17,236)(18,237)(19,238)(20,239)(21,240)(22,241)(23,242)(24,243)(25,244)(26,245)(27,246)(28,247)(29,248)(30,249)(31,250)(32,251)(33,252)(34,253)(35,254)(36,255)(37,256)(38,257)(39,258)(40,259)(41,260)(42,261)(43,262)(44,263)(45,264)(46,177)(47,178)(48,179)(49,180)(50,181)(51,182)(52,183)(53,184)(54,185)(55,186)(56,187)(57,188)(58,189)(59,190)(60,191)(61,192)(62,193)(63,194)(64,195)(65,196)(66,197)(67,198)(68,199)(69,200)(70,201)(71,202)(72,203)(73,204)(74,205)(75,206)(76,207)(77,208)(78,209)(79,210)(80,211)(81,212)(82,213)(83,214)(84,215)(85,216)(86,217)(87,218)(88,219)(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)(148,345)(149,346)(150,347)(151,348)(152,349)(153,350)(154,351)(155,352)(156,265)(157,266)(158,267)(159,268)(160,269)(161,270)(162,271)(163,272)(164,273)(165,274)(166,275)(167,276)(168,277)(169,278)(170,279)(171,280)(172,281)(173,282)(174,283)(175,284)(176,285), (1,96)(2,97)(3,98)(4,99)(5,100)(6,101)(7,102)(8,103)(9,104)(10,105)(11,106)(12,107)(13,108)(14,109)(15,110)(16,111)(17,112)(18,113)(19,114)(20,115)(21,116)(22,117)(23,118)(24,119)(25,120)(26,121)(27,122)(28,123)(29,124)(30,125)(31,126)(32,127)(33,128)(34,129)(35,130)(36,131)(37,132)(38,133)(39,134)(40,135)(41,136)(42,137)(43,138)(44,139)(45,140)(46,141)(47,142)(48,143)(49,144)(50,145)(51,146)(52,147)(53,148)(54,149)(55,150)(56,151)(57,152)(58,153)(59,154)(60,155)(61,156)(62,157)(63,158)(64,159)(65,160)(66,161)(67,162)(68,163)(69,164)(70,165)(71,166)(72,167)(73,168)(74,169)(75,170)(76,171)(77,172)(78,173)(79,174)(80,175)(81,176)(82,89)(83,90)(84,91)(85,92)(86,93)(87,94)(88,95)(177,338)(178,339)(179,340)(180,341)(181,342)(182,343)(183,344)(184,345)(185,346)(186,347)(187,348)(188,349)(189,350)(190,351)(191,352)(192,265)(193,266)(194,267)(195,268)(196,269)(197,270)(198,271)(199,272)(200,273)(201,274)(202,275)(203,276)(204,277)(205,278)(206,279)(207,280)(208,281)(209,282)(210,283)(211,284)(212,285)(213,286)(214,287)(215,288)(216,289)(217,290)(218,291)(219,292)(220,293)(221,294)(222,295)(223,296)(224,297)(225,298)(226,299)(227,300)(228,301)(229,302)(230,303)(231,304)(232,305)(233,306)(234,307)(235,308)(236,309)(237,310)(238,311)(239,312)(240,313)(241,314)(242,315)(243,316)(244,317)(245,318)(246,319)(247,320)(248,321)(249,322)(250,323)(251,324)(252,325)(253,326)(254,327)(255,328)(256,329)(257,330)(258,331)(259,332)(260,333)(261,334)(262,335)(263,336)(264,337), (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([(1,220),(2,221),(3,222),(4,223),(5,224),(6,225),(7,226),(8,227),(9,228),(10,229),(11,230),(12,231),(13,232),(14,233),(15,234),(16,235),(17,236),(18,237),(19,238),(20,239),(21,240),(22,241),(23,242),(24,243),(25,244),(26,245),(27,246),(28,247),(29,248),(30,249),(31,250),(32,251),(33,252),(34,253),(35,254),(36,255),(37,256),(38,257),(39,258),(40,259),(41,260),(42,261),(43,262),(44,263),(45,264),(46,177),(47,178),(48,179),(49,180),(50,181),(51,182),(52,183),(53,184),(54,185),(55,186),(56,187),(57,188),(58,189),(59,190),(60,191),(61,192),(62,193),(63,194),(64,195),(65,196),(66,197),(67,198),(68,199),(69,200),(70,201),(71,202),(72,203),(73,204),(74,205),(75,206),(76,207),(77,208),(78,209),(79,210),(80,211),(81,212),(82,213),(83,214),(84,215),(85,216),(86,217),(87,218),(88,219),(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),(148,345),(149,346),(150,347),(151,348),(152,349),(153,350),(154,351),(155,352),(156,265),(157,266),(158,267),(159,268),(160,269),(161,270),(162,271),(163,272),(164,273),(165,274),(166,275),(167,276),(168,277),(169,278),(170,279),(171,280),(172,281),(173,282),(174,283),(175,284),(176,285)], [(1,96),(2,97),(3,98),(4,99),(5,100),(6,101),(7,102),(8,103),(9,104),(10,105),(11,106),(12,107),(13,108),(14,109),(15,110),(16,111),(17,112),(18,113),(19,114),(20,115),(21,116),(22,117),(23,118),(24,119),(25,120),(26,121),(27,122),(28,123),(29,124),(30,125),(31,126),(32,127),(33,128),(34,129),(35,130),(36,131),(37,132),(38,133),(39,134),(40,135),(41,136),(42,137),(43,138),(44,139),(45,140),(46,141),(47,142),(48,143),(49,144),(50,145),(51,146),(52,147),(53,148),(54,149),(55,150),(56,151),(57,152),(58,153),(59,154),(60,155),(61,156),(62,157),(63,158),(64,159),(65,160),(66,161),(67,162),(68,163),(69,164),(70,165),(71,166),(72,167),(73,168),(74,169),(75,170),(76,171),(77,172),(78,173),(79,174),(80,175),(81,176),(82,89),(83,90),(84,91),(85,92),(86,93),(87,94),(88,95),(177,338),(178,339),(179,340),(180,341),(181,342),(182,343),(183,344),(184,345),(185,346),(186,347),(187,348),(188,349),(189,350),(190,351),(191,352),(192,265),(193,266),(194,267),(195,268),(196,269),(197,270),(198,271),(199,272),(200,273),(201,274),(202,275),(203,276),(204,277),(205,278),(206,279),(207,280),(208,281),(209,282),(210,283),(211,284),(212,285),(213,286),(214,287),(215,288),(216,289),(217,290),(218,291),(219,292),(220,293),(221,294),(222,295),(223,296),(224,297),(225,298),(226,299),(227,300),(228,301),(229,302),(230,303),(231,304),(232,305),(233,306),(234,307),(235,308),(236,309),(237,310),(238,311),(239,312),(240,313),(241,314),(242,315),(243,316),(244,317),(245,318),(246,319),(247,320),(248,321),(249,322),(250,323),(251,324),(252,325),(253,326),(254,327),(255,328),(256,329),(257,330),(258,331),(259,332),(260,333),(261,334),(262,335),(263,336),(264,337)], [(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···2G4A···4H8A···8P11A···11J22A···22BR44A···44CB88A···88FD
order12···24···48···811···1122···2244···4488···88
size11···11···11···11···11···11···11···1

352 irreducible representations

dim111111111111
type+++
imageC1C2C2C4C4C8C11C22C22C44C44C88
kernelC22×C88C2×C88C22×C44C2×C44C22×C22C2×C22C22×C8C2×C8C22×C4C2×C4C23C22
# reps16162161060106020160

Matrix representation of C22×C88 in GL3(𝔽89) generated by

8800
010
001
,
8800
0880
0088
,
5500
0810
0048
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

׿
×
𝔽