direct product, abelian, monomial, 2-elementary
Aliases: C22×C92, SmallGroup(368,37)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C22×C92 |
| C1 — C22×C92 |
| C1 — C22×C92 |
Generators and relations for C22×C92
G = < a,b,c | a2=b2=c92=1, ab=ba, ac=ca, bc=cb >
Subgroups: 54, all normal (8 characteristic)
C1, C2, C2, C4, C22, C2×C4, C23, C22×C4, C23, C46, C46, C92, C2×C46, C2×C92, C22×C46, C22×C92
Quotients: C1, C2, C4, C22, C2×C4, C23, C22×C4, C23, C46, C92, C2×C46, C2×C92, C22×C46, C22×C92
►Regular action on 368 points
Generators in S368
(1 356)(2 357)(3 358)(4 359)(5 360)(6 361)(7 362)(8 363)(9 364)(10 365)(11 366)(12 367)(13 368)(14 277)(15 278)(16 279)(17 280)(18 281)(19 282)(20 283)(21 284)(22 285)(23 286)(24 287)(25 288)(26 289)(27 290)(28 291)(29 292)(30 293)(31 294)(32 295)(33 296)(34 297)(35 298)(36 299)(37 300)(38 301)(39 302)(40 303)(41 304)(42 305)(43 306)(44 307)(45 308)(46 309)(47 310)(48 311)(49 312)(50 313)(51 314)(52 315)(53 316)(54 317)(55 318)(56 319)(57 320)(58 321)(59 322)(60 323)(61 324)(62 325)(63 326)(64 327)(65 328)(66 329)(67 330)(68 331)(69 332)(70 333)(71 334)(72 335)(73 336)(74 337)(75 338)(76 339)(77 340)(78 341)(79 342)(80 343)(81 344)(82 345)(83 346)(84 347)(85 348)(86 349)(87 350)(88 351)(89 352)(90 353)(91 354)(92 355)(93 187)(94 188)(95 189)(96 190)(97 191)(98 192)(99 193)(100 194)(101 195)(102 196)(103 197)(104 198)(105 199)(106 200)(107 201)(108 202)(109 203)(110 204)(111 205)(112 206)(113 207)(114 208)(115 209)(116 210)(117 211)(118 212)(119 213)(120 214)(121 215)(122 216)(123 217)(124 218)(125 219)(126 220)(127 221)(128 222)(129 223)(130 224)(131 225)(132 226)(133 227)(134 228)(135 229)(136 230)(137 231)(138 232)(139 233)(140 234)(141 235)(142 236)(143 237)(144 238)(145 239)(146 240)(147 241)(148 242)(149 243)(150 244)(151 245)(152 246)(153 247)(154 248)(155 249)(156 250)(157 251)(158 252)(159 253)(160 254)(161 255)(162 256)(163 257)(164 258)(165 259)(166 260)(167 261)(168 262)(169 263)(170 264)(171 265)(172 266)(173 267)(174 268)(175 269)(176 270)(177 271)(178 272)(179 273)(180 274)(181 275)(182 276)(183 185)(184 186)
(1 162)(2 163)(3 164)(4 165)(5 166)(6 167)(7 168)(8 169)(9 170)(10 171)(11 172)(12 173)(13 174)(14 175)(15 176)(16 177)(17 178)(18 179)(19 180)(20 181)(21 182)(22 183)(23 184)(24 93)(25 94)(26 95)(27 96)(28 97)(29 98)(30 99)(31 100)(32 101)(33 102)(34 103)(35 104)(36 105)(37 106)(38 107)(39 108)(40 109)(41 110)(42 111)(43 112)(44 113)(45 114)(46 115)(47 116)(48 117)(49 118)(50 119)(51 120)(52 121)(53 122)(54 123)(55 124)(56 125)(57 126)(58 127)(59 128)(60 129)(61 130)(62 131)(63 132)(64 133)(65 134)(66 135)(67 136)(68 137)(69 138)(70 139)(71 140)(72 141)(73 142)(74 143)(75 144)(76 145)(77 146)(78 147)(79 148)(80 149)(81 150)(82 151)(83 152)(84 153)(85 154)(86 155)(87 156)(88 157)(89 158)(90 159)(91 160)(92 161)(185 285)(186 286)(187 287)(188 288)(189 289)(190 290)(191 291)(192 292)(193 293)(194 294)(195 295)(196 296)(197 297)(198 298)(199 299)(200 300)(201 301)(202 302)(203 303)(204 304)(205 305)(206 306)(207 307)(208 308)(209 309)(210 310)(211 311)(212 312)(213 313)(214 314)(215 315)(216 316)(217 317)(218 318)(219 319)(220 320)(221 321)(222 322)(223 323)(224 324)(225 325)(226 326)(227 327)(228 328)(229 329)(230 330)(231 331)(232 332)(233 333)(234 334)(235 335)(236 336)(237 337)(238 338)(239 339)(240 340)(241 341)(242 342)(243 343)(244 344)(245 345)(246 346)(247 347)(248 348)(249 349)(250 350)(251 351)(252 352)(253 353)(254 354)(255 355)(256 356)(257 357)(258 358)(259 359)(260 360)(261 361)(262 362)(263 363)(264 364)(265 365)(266 366)(267 367)(268 368)(269 277)(270 278)(271 279)(272 280)(273 281)(274 282)(275 283)(276 284)
(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)(277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368)
G:=sub<Sym(368)| (1,356)(2,357)(3,358)(4,359)(5,360)(6,361)(7,362)(8,363)(9,364)(10,365)(11,366)(12,367)(13,368)(14,277)(15,278)(16,279)(17,280)(18,281)(19,282)(20,283)(21,284)(22,285)(23,286)(24,287)(25,288)(26,289)(27,290)(28,291)(29,292)(30,293)(31,294)(32,295)(33,296)(34,297)(35,298)(36,299)(37,300)(38,301)(39,302)(40,303)(41,304)(42,305)(43,306)(44,307)(45,308)(46,309)(47,310)(48,311)(49,312)(50,313)(51,314)(52,315)(53,316)(54,317)(55,318)(56,319)(57,320)(58,321)(59,322)(60,323)(61,324)(62,325)(63,326)(64,327)(65,328)(66,329)(67,330)(68,331)(69,332)(70,333)(71,334)(72,335)(73,336)(74,337)(75,338)(76,339)(77,340)(78,341)(79,342)(80,343)(81,344)(82,345)(83,346)(84,347)(85,348)(86,349)(87,350)(88,351)(89,352)(90,353)(91,354)(92,355)(93,187)(94,188)(95,189)(96,190)(97,191)(98,192)(99,193)(100,194)(101,195)(102,196)(103,197)(104,198)(105,199)(106,200)(107,201)(108,202)(109,203)(110,204)(111,205)(112,206)(113,207)(114,208)(115,209)(116,210)(117,211)(118,212)(119,213)(120,214)(121,215)(122,216)(123,217)(124,218)(125,219)(126,220)(127,221)(128,222)(129,223)(130,224)(131,225)(132,226)(133,227)(134,228)(135,229)(136,230)(137,231)(138,232)(139,233)(140,234)(141,235)(142,236)(143,237)(144,238)(145,239)(146,240)(147,241)(148,242)(149,243)(150,244)(151,245)(152,246)(153,247)(154,248)(155,249)(156,250)(157,251)(158,252)(159,253)(160,254)(161,255)(162,256)(163,257)(164,258)(165,259)(166,260)(167,261)(168,262)(169,263)(170,264)(171,265)(172,266)(173,267)(174,268)(175,269)(176,270)(177,271)(178,272)(179,273)(180,274)(181,275)(182,276)(183,185)(184,186), (1,162)(2,163)(3,164)(4,165)(5,166)(6,167)(7,168)(8,169)(9,170)(10,171)(11,172)(12,173)(13,174)(14,175)(15,176)(16,177)(17,178)(18,179)(19,180)(20,181)(21,182)(22,183)(23,184)(24,93)(25,94)(26,95)(27,96)(28,97)(29,98)(30,99)(31,100)(32,101)(33,102)(34,103)(35,104)(36,105)(37,106)(38,107)(39,108)(40,109)(41,110)(42,111)(43,112)(44,113)(45,114)(46,115)(47,116)(48,117)(49,118)(50,119)(51,120)(52,121)(53,122)(54,123)(55,124)(56,125)(57,126)(58,127)(59,128)(60,129)(61,130)(62,131)(63,132)(64,133)(65,134)(66,135)(67,136)(68,137)(69,138)(70,139)(71,140)(72,141)(73,142)(74,143)(75,144)(76,145)(77,146)(78,147)(79,148)(80,149)(81,150)(82,151)(83,152)(84,153)(85,154)(86,155)(87,156)(88,157)(89,158)(90,159)(91,160)(92,161)(185,285)(186,286)(187,287)(188,288)(189,289)(190,290)(191,291)(192,292)(193,293)(194,294)(195,295)(196,296)(197,297)(198,298)(199,299)(200,300)(201,301)(202,302)(203,303)(204,304)(205,305)(206,306)(207,307)(208,308)(209,309)(210,310)(211,311)(212,312)(213,313)(214,314)(215,315)(216,316)(217,317)(218,318)(219,319)(220,320)(221,321)(222,322)(223,323)(224,324)(225,325)(226,326)(227,327)(228,328)(229,329)(230,330)(231,331)(232,332)(233,333)(234,334)(235,335)(236,336)(237,337)(238,338)(239,339)(240,340)(241,341)(242,342)(243,343)(244,344)(245,345)(246,346)(247,347)(248,348)(249,349)(250,350)(251,351)(252,352)(253,353)(254,354)(255,355)(256,356)(257,357)(258,358)(259,359)(260,360)(261,361)(262,362)(263,363)(264,364)(265,365)(266,366)(267,367)(268,368)(269,277)(270,278)(271,279)(272,280)(273,281)(274,282)(275,283)(276,284), (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)(277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368)>;
G:=Group( (1,356)(2,357)(3,358)(4,359)(5,360)(6,361)(7,362)(8,363)(9,364)(10,365)(11,366)(12,367)(13,368)(14,277)(15,278)(16,279)(17,280)(18,281)(19,282)(20,283)(21,284)(22,285)(23,286)(24,287)(25,288)(26,289)(27,290)(28,291)(29,292)(30,293)(31,294)(32,295)(33,296)(34,297)(35,298)(36,299)(37,300)(38,301)(39,302)(40,303)(41,304)(42,305)(43,306)(44,307)(45,308)(46,309)(47,310)(48,311)(49,312)(50,313)(51,314)(52,315)(53,316)(54,317)(55,318)(56,319)(57,320)(58,321)(59,322)(60,323)(61,324)(62,325)(63,326)(64,327)(65,328)(66,329)(67,330)(68,331)(69,332)(70,333)(71,334)(72,335)(73,336)(74,337)(75,338)(76,339)(77,340)(78,341)(79,342)(80,343)(81,344)(82,345)(83,346)(84,347)(85,348)(86,349)(87,350)(88,351)(89,352)(90,353)(91,354)(92,355)(93,187)(94,188)(95,189)(96,190)(97,191)(98,192)(99,193)(100,194)(101,195)(102,196)(103,197)(104,198)(105,199)(106,200)(107,201)(108,202)(109,203)(110,204)(111,205)(112,206)(113,207)(114,208)(115,209)(116,210)(117,211)(118,212)(119,213)(120,214)(121,215)(122,216)(123,217)(124,218)(125,219)(126,220)(127,221)(128,222)(129,223)(130,224)(131,225)(132,226)(133,227)(134,228)(135,229)(136,230)(137,231)(138,232)(139,233)(140,234)(141,235)(142,236)(143,237)(144,238)(145,239)(146,240)(147,241)(148,242)(149,243)(150,244)(151,245)(152,246)(153,247)(154,248)(155,249)(156,250)(157,251)(158,252)(159,253)(160,254)(161,255)(162,256)(163,257)(164,258)(165,259)(166,260)(167,261)(168,262)(169,263)(170,264)(171,265)(172,266)(173,267)(174,268)(175,269)(176,270)(177,271)(178,272)(179,273)(180,274)(181,275)(182,276)(183,185)(184,186), (1,162)(2,163)(3,164)(4,165)(5,166)(6,167)(7,168)(8,169)(9,170)(10,171)(11,172)(12,173)(13,174)(14,175)(15,176)(16,177)(17,178)(18,179)(19,180)(20,181)(21,182)(22,183)(23,184)(24,93)(25,94)(26,95)(27,96)(28,97)(29,98)(30,99)(31,100)(32,101)(33,102)(34,103)(35,104)(36,105)(37,106)(38,107)(39,108)(40,109)(41,110)(42,111)(43,112)(44,113)(45,114)(46,115)(47,116)(48,117)(49,118)(50,119)(51,120)(52,121)(53,122)(54,123)(55,124)(56,125)(57,126)(58,127)(59,128)(60,129)(61,130)(62,131)(63,132)(64,133)(65,134)(66,135)(67,136)(68,137)(69,138)(70,139)(71,140)(72,141)(73,142)(74,143)(75,144)(76,145)(77,146)(78,147)(79,148)(80,149)(81,150)(82,151)(83,152)(84,153)(85,154)(86,155)(87,156)(88,157)(89,158)(90,159)(91,160)(92,161)(185,285)(186,286)(187,287)(188,288)(189,289)(190,290)(191,291)(192,292)(193,293)(194,294)(195,295)(196,296)(197,297)(198,298)(199,299)(200,300)(201,301)(202,302)(203,303)(204,304)(205,305)(206,306)(207,307)(208,308)(209,309)(210,310)(211,311)(212,312)(213,313)(214,314)(215,315)(216,316)(217,317)(218,318)(219,319)(220,320)(221,321)(222,322)(223,323)(224,324)(225,325)(226,326)(227,327)(228,328)(229,329)(230,330)(231,331)(232,332)(233,333)(234,334)(235,335)(236,336)(237,337)(238,338)(239,339)(240,340)(241,341)(242,342)(243,343)(244,344)(245,345)(246,346)(247,347)(248,348)(249,349)(250,350)(251,351)(252,352)(253,353)(254,354)(255,355)(256,356)(257,357)(258,358)(259,359)(260,360)(261,361)(262,362)(263,363)(264,364)(265,365)(266,366)(267,367)(268,368)(269,277)(270,278)(271,279)(272,280)(273,281)(274,282)(275,283)(276,284), (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)(277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368) );
G=PermutationGroup([[(1,356),(2,357),(3,358),(4,359),(5,360),(6,361),(7,362),(8,363),(9,364),(10,365),(11,366),(12,367),(13,368),(14,277),(15,278),(16,279),(17,280),(18,281),(19,282),(20,283),(21,284),(22,285),(23,286),(24,287),(25,288),(26,289),(27,290),(28,291),(29,292),(30,293),(31,294),(32,295),(33,296),(34,297),(35,298),(36,299),(37,300),(38,301),(39,302),(40,303),(41,304),(42,305),(43,306),(44,307),(45,308),(46,309),(47,310),(48,311),(49,312),(50,313),(51,314),(52,315),(53,316),(54,317),(55,318),(56,319),(57,320),(58,321),(59,322),(60,323),(61,324),(62,325),(63,326),(64,327),(65,328),(66,329),(67,330),(68,331),(69,332),(70,333),(71,334),(72,335),(73,336),(74,337),(75,338),(76,339),(77,340),(78,341),(79,342),(80,343),(81,344),(82,345),(83,346),(84,347),(85,348),(86,349),(87,350),(88,351),(89,352),(90,353),(91,354),(92,355),(93,187),(94,188),(95,189),(96,190),(97,191),(98,192),(99,193),(100,194),(101,195),(102,196),(103,197),(104,198),(105,199),(106,200),(107,201),(108,202),(109,203),(110,204),(111,205),(112,206),(113,207),(114,208),(115,209),(116,210),(117,211),(118,212),(119,213),(120,214),(121,215),(122,216),(123,217),(124,218),(125,219),(126,220),(127,221),(128,222),(129,223),(130,224),(131,225),(132,226),(133,227),(134,228),(135,229),(136,230),(137,231),(138,232),(139,233),(140,234),(141,235),(142,236),(143,237),(144,238),(145,239),(146,240),(147,241),(148,242),(149,243),(150,244),(151,245),(152,246),(153,247),(154,248),(155,249),(156,250),(157,251),(158,252),(159,253),(160,254),(161,255),(162,256),(163,257),(164,258),(165,259),(166,260),(167,261),(168,262),(169,263),(170,264),(171,265),(172,266),(173,267),(174,268),(175,269),(176,270),(177,271),(178,272),(179,273),(180,274),(181,275),(182,276),(183,185),(184,186)], [(1,162),(2,163),(3,164),(4,165),(5,166),(6,167),(7,168),(8,169),(9,170),(10,171),(11,172),(12,173),(13,174),(14,175),(15,176),(16,177),(17,178),(18,179),(19,180),(20,181),(21,182),(22,183),(23,184),(24,93),(25,94),(26,95),(27,96),(28,97),(29,98),(30,99),(31,100),(32,101),(33,102),(34,103),(35,104),(36,105),(37,106),(38,107),(39,108),(40,109),(41,110),(42,111),(43,112),(44,113),(45,114),(46,115),(47,116),(48,117),(49,118),(50,119),(51,120),(52,121),(53,122),(54,123),(55,124),(56,125),(57,126),(58,127),(59,128),(60,129),(61,130),(62,131),(63,132),(64,133),(65,134),(66,135),(67,136),(68,137),(69,138),(70,139),(71,140),(72,141),(73,142),(74,143),(75,144),(76,145),(77,146),(78,147),(79,148),(80,149),(81,150),(82,151),(83,152),(84,153),(85,154),(86,155),(87,156),(88,157),(89,158),(90,159),(91,160),(92,161),(185,285),(186,286),(187,287),(188,288),(189,289),(190,290),(191,291),(192,292),(193,293),(194,294),(195,295),(196,296),(197,297),(198,298),(199,299),(200,300),(201,301),(202,302),(203,303),(204,304),(205,305),(206,306),(207,307),(208,308),(209,309),(210,310),(211,311),(212,312),(213,313),(214,314),(215,315),(216,316),(217,317),(218,318),(219,319),(220,320),(221,321),(222,322),(223,323),(224,324),(225,325),(226,326),(227,327),(228,328),(229,329),(230,330),(231,331),(232,332),(233,333),(234,334),(235,335),(236,336),(237,337),(238,338),(239,339),(240,340),(241,341),(242,342),(243,343),(244,344),(245,345),(246,346),(247,347),(248,348),(249,349),(250,350),(251,351),(252,352),(253,353),(254,354),(255,355),(256,356),(257,357),(258,358),(259,359),(260,360),(261,361),(262,362),(263,363),(264,364),(265,365),(266,366),(267,367),(268,368),(269,277),(270,278),(271,279),(272,280),(273,281),(274,282),(275,283),(276,284)], [(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),(277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368)]])
368 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | ··· | 4H | 23A | ··· | 23V | 46A | ··· | 46EX | 92A | ··· | 92FT |
| order | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 23 | ··· | 23 | 46 | ··· | 46 | 92 | ··· | 92 |
| size | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
368 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| type | + | + | + | |||||
| image | C1 | C2 | C2 | C4 | C23 | C46 | C46 | C92 |
| kernel | C22×C92 | C2×C92 | C22×C46 | C2×C46 | C22×C4 | C2×C4 | C23 | C22 |
| # reps | 1 | 6 | 1 | 8 | 22 | 132 | 22 | 176 |
Matrix representation of C22×C92 ►in GL3(𝔽277) generated by
| 1 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 276 |
| 276 | 0 | 0 |
| 0 | 276 | 0 |
| 0 | 0 | 1 |
| 19 | 0 | 0 |
| 0 | 152 | 0 |
| 0 | 0 | 82 |
G:=sub<GL(3,GF(277))| [1,0,0,0,1,0,0,0,276],[276,0,0,0,276,0,0,0,1],[19,0,0,0,152,0,0,0,82] >;
C22×C92 in GAP, Magma, Sage, TeX
C_2^2\times C_{92} % in TeX
G:=Group("C2^2xC92"); // GroupNames label
G:=SmallGroup(368,37);
// by ID
G=gap.SmallGroup(368,37);
# by ID
G:=PCGroup([5,-2,-2,-2,-23,-2,920]);
// Polycyclic
G:=Group<a,b,c|a^2=b^2=c^92=1,a*b=b*a,a*c=c*a,b*c=c*b>;
// generators/relations