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## G = C22×C92order 368 = 24·23

### Abelian group of type [2,2,92]

Aliases: C22×C92, SmallGroup(368,37)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C22×C92
 Chief series C1 — C2 — C46 — C92 — C2×C92 — C22×C92
 Lower central C1 — C22×C92
 Upper central 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 [×6], C4 [×4], C22 [×7], C2×C4 [×6], C23, C22×C4, C23, C46, C46 [×6], C92 [×4], C2×C46 [×7], C2×C92 [×6], C22×C46, C22×C92
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C2×C4 [×6], C23, C22×C4, C23, C46 [×7], C92 [×4], C2×C46 [×7], C2×C92 [×6], C22×C46, C22×C92

Smallest permutation representation of C22×C92
Regular action on 368 points
Generators in S368
(1 249)(2 250)(3 251)(4 252)(5 253)(6 254)(7 255)(8 256)(9 257)(10 258)(11 259)(12 260)(13 261)(14 262)(15 263)(16 264)(17 265)(18 266)(19 267)(20 268)(21 269)(22 270)(23 271)(24 272)(25 273)(26 274)(27 275)(28 276)(29 185)(30 186)(31 187)(32 188)(33 189)(34 190)(35 191)(36 192)(37 193)(38 194)(39 195)(40 196)(41 197)(42 198)(43 199)(44 200)(45 201)(46 202)(47 203)(48 204)(49 205)(50 206)(51 207)(52 208)(53 209)(54 210)(55 211)(56 212)(57 213)(58 214)(59 215)(60 216)(61 217)(62 218)(63 219)(64 220)(65 221)(66 222)(67 223)(68 224)(69 225)(70 226)(71 227)(72 228)(73 229)(74 230)(75 231)(76 232)(77 233)(78 234)(79 235)(80 236)(81 237)(82 238)(83 239)(84 240)(85 241)(86 242)(87 243)(88 244)(89 245)(90 246)(91 247)(92 248)(93 302)(94 303)(95 304)(96 305)(97 306)(98 307)(99 308)(100 309)(101 310)(102 311)(103 312)(104 313)(105 314)(106 315)(107 316)(108 317)(109 318)(110 319)(111 320)(112 321)(113 322)(114 323)(115 324)(116 325)(117 326)(118 327)(119 328)(120 329)(121 330)(122 331)(123 332)(124 333)(125 334)(126 335)(127 336)(128 337)(129 338)(130 339)(131 340)(132 341)(133 342)(134 343)(135 344)(136 345)(137 346)(138 347)(139 348)(140 349)(141 350)(142 351)(143 352)(144 353)(145 354)(146 355)(147 356)(148 357)(149 358)(150 359)(151 360)(152 361)(153 362)(154 363)(155 364)(156 365)(157 366)(158 367)(159 368)(160 277)(161 278)(162 279)(163 280)(164 281)(165 282)(166 283)(167 284)(168 285)(169 286)(170 287)(171 288)(172 289)(173 290)(174 291)(175 292)(176 293)(177 294)(178 295)(179 296)(180 297)(181 298)(182 299)(183 300)(184 301)
(1 172)(2 173)(3 174)(4 175)(5 176)(6 177)(7 178)(8 179)(9 180)(10 181)(11 182)(12 183)(13 184)(14 93)(15 94)(16 95)(17 96)(18 97)(19 98)(20 99)(21 100)(22 101)(23 102)(24 103)(25 104)(26 105)(27 106)(28 107)(29 108)(30 109)(31 110)(32 111)(33 112)(34 113)(35 114)(36 115)(37 116)(38 117)(39 118)(40 119)(41 120)(42 121)(43 122)(44 123)(45 124)(46 125)(47 126)(48 127)(49 128)(50 129)(51 130)(52 131)(53 132)(54 133)(55 134)(56 135)(57 136)(58 137)(59 138)(60 139)(61 140)(62 141)(63 142)(64 143)(65 144)(66 145)(67 146)(68 147)(69 148)(70 149)(71 150)(72 151)(73 152)(74 153)(75 154)(76 155)(77 156)(78 157)(79 158)(80 159)(81 160)(82 161)(83 162)(84 163)(85 164)(86 165)(87 166)(88 167)(89 168)(90 169)(91 170)(92 171)(185 317)(186 318)(187 319)(188 320)(189 321)(190 322)(191 323)(192 324)(193 325)(194 326)(195 327)(196 328)(197 329)(198 330)(199 331)(200 332)(201 333)(202 334)(203 335)(204 336)(205 337)(206 338)(207 339)(208 340)(209 341)(210 342)(211 343)(212 344)(213 345)(214 346)(215 347)(216 348)(217 349)(218 350)(219 351)(220 352)(221 353)(222 354)(223 355)(224 356)(225 357)(226 358)(227 359)(228 360)(229 361)(230 362)(231 363)(232 364)(233 365)(234 366)(235 367)(236 368)(237 277)(238 278)(239 279)(240 280)(241 281)(242 282)(243 283)(244 284)(245 285)(246 286)(247 287)(248 288)(249 289)(250 290)(251 291)(252 292)(253 293)(254 294)(255 295)(256 296)(257 297)(258 298)(259 299)(260 300)(261 301)(262 302)(263 303)(264 304)(265 305)(266 306)(267 307)(268 308)(269 309)(270 310)(271 311)(272 312)(273 313)(274 314)(275 315)(276 316)
(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)| (1,249)(2,250)(3,251)(4,252)(5,253)(6,254)(7,255)(8,256)(9,257)(10,258)(11,259)(12,260)(13,261)(14,262)(15,263)(16,264)(17,265)(18,266)(19,267)(20,268)(21,269)(22,270)(23,271)(24,272)(25,273)(26,274)(27,275)(28,276)(29,185)(30,186)(31,187)(32,188)(33,189)(34,190)(35,191)(36,192)(37,193)(38,194)(39,195)(40,196)(41,197)(42,198)(43,199)(44,200)(45,201)(46,202)(47,203)(48,204)(49,205)(50,206)(51,207)(52,208)(53,209)(54,210)(55,211)(56,212)(57,213)(58,214)(59,215)(60,216)(61,217)(62,218)(63,219)(64,220)(65,221)(66,222)(67,223)(68,224)(69,225)(70,226)(71,227)(72,228)(73,229)(74,230)(75,231)(76,232)(77,233)(78,234)(79,235)(80,236)(81,237)(82,238)(83,239)(84,240)(85,241)(86,242)(87,243)(88,244)(89,245)(90,246)(91,247)(92,248)(93,302)(94,303)(95,304)(96,305)(97,306)(98,307)(99,308)(100,309)(101,310)(102,311)(103,312)(104,313)(105,314)(106,315)(107,316)(108,317)(109,318)(110,319)(111,320)(112,321)(113,322)(114,323)(115,324)(116,325)(117,326)(118,327)(119,328)(120,329)(121,330)(122,331)(123,332)(124,333)(125,334)(126,335)(127,336)(128,337)(129,338)(130,339)(131,340)(132,341)(133,342)(134,343)(135,344)(136,345)(137,346)(138,347)(139,348)(140,349)(141,350)(142,351)(143,352)(144,353)(145,354)(146,355)(147,356)(148,357)(149,358)(150,359)(151,360)(152,361)(153,362)(154,363)(155,364)(156,365)(157,366)(158,367)(159,368)(160,277)(161,278)(162,279)(163,280)(164,281)(165,282)(166,283)(167,284)(168,285)(169,286)(170,287)(171,288)(172,289)(173,290)(174,291)(175,292)(176,293)(177,294)(178,295)(179,296)(180,297)(181,298)(182,299)(183,300)(184,301), (1,172)(2,173)(3,174)(4,175)(5,176)(6,177)(7,178)(8,179)(9,180)(10,181)(11,182)(12,183)(13,184)(14,93)(15,94)(16,95)(17,96)(18,97)(19,98)(20,99)(21,100)(22,101)(23,102)(24,103)(25,104)(26,105)(27,106)(28,107)(29,108)(30,109)(31,110)(32,111)(33,112)(34,113)(35,114)(36,115)(37,116)(38,117)(39,118)(40,119)(41,120)(42,121)(43,122)(44,123)(45,124)(46,125)(47,126)(48,127)(49,128)(50,129)(51,130)(52,131)(53,132)(54,133)(55,134)(56,135)(57,136)(58,137)(59,138)(60,139)(61,140)(62,141)(63,142)(64,143)(65,144)(66,145)(67,146)(68,147)(69,148)(70,149)(71,150)(72,151)(73,152)(74,153)(75,154)(76,155)(77,156)(78,157)(79,158)(80,159)(81,160)(82,161)(83,162)(84,163)(85,164)(86,165)(87,166)(88,167)(89,168)(90,169)(91,170)(92,171)(185,317)(186,318)(187,319)(188,320)(189,321)(190,322)(191,323)(192,324)(193,325)(194,326)(195,327)(196,328)(197,329)(198,330)(199,331)(200,332)(201,333)(202,334)(203,335)(204,336)(205,337)(206,338)(207,339)(208,340)(209,341)(210,342)(211,343)(212,344)(213,345)(214,346)(215,347)(216,348)(217,349)(218,350)(219,351)(220,352)(221,353)(222,354)(223,355)(224,356)(225,357)(226,358)(227,359)(228,360)(229,361)(230,362)(231,363)(232,364)(233,365)(234,366)(235,367)(236,368)(237,277)(238,278)(239,279)(240,280)(241,281)(242,282)(243,283)(244,284)(245,285)(246,286)(247,287)(248,288)(249,289)(250,290)(251,291)(252,292)(253,293)(254,294)(255,295)(256,296)(257,297)(258,298)(259,299)(260,300)(261,301)(262,302)(263,303)(264,304)(265,305)(266,306)(267,307)(268,308)(269,309)(270,310)(271,311)(272,312)(273,313)(274,314)(275,315)(276,316), (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( (1,249)(2,250)(3,251)(4,252)(5,253)(6,254)(7,255)(8,256)(9,257)(10,258)(11,259)(12,260)(13,261)(14,262)(15,263)(16,264)(17,265)(18,266)(19,267)(20,268)(21,269)(22,270)(23,271)(24,272)(25,273)(26,274)(27,275)(28,276)(29,185)(30,186)(31,187)(32,188)(33,189)(34,190)(35,191)(36,192)(37,193)(38,194)(39,195)(40,196)(41,197)(42,198)(43,199)(44,200)(45,201)(46,202)(47,203)(48,204)(49,205)(50,206)(51,207)(52,208)(53,209)(54,210)(55,211)(56,212)(57,213)(58,214)(59,215)(60,216)(61,217)(62,218)(63,219)(64,220)(65,221)(66,222)(67,223)(68,224)(69,225)(70,226)(71,227)(72,228)(73,229)(74,230)(75,231)(76,232)(77,233)(78,234)(79,235)(80,236)(81,237)(82,238)(83,239)(84,240)(85,241)(86,242)(87,243)(88,244)(89,245)(90,246)(91,247)(92,248)(93,302)(94,303)(95,304)(96,305)(97,306)(98,307)(99,308)(100,309)(101,310)(102,311)(103,312)(104,313)(105,314)(106,315)(107,316)(108,317)(109,318)(110,319)(111,320)(112,321)(113,322)(114,323)(115,324)(116,325)(117,326)(118,327)(119,328)(120,329)(121,330)(122,331)(123,332)(124,333)(125,334)(126,335)(127,336)(128,337)(129,338)(130,339)(131,340)(132,341)(133,342)(134,343)(135,344)(136,345)(137,346)(138,347)(139,348)(140,349)(141,350)(142,351)(143,352)(144,353)(145,354)(146,355)(147,356)(148,357)(149,358)(150,359)(151,360)(152,361)(153,362)(154,363)(155,364)(156,365)(157,366)(158,367)(159,368)(160,277)(161,278)(162,279)(163,280)(164,281)(165,282)(166,283)(167,284)(168,285)(169,286)(170,287)(171,288)(172,289)(173,290)(174,291)(175,292)(176,293)(177,294)(178,295)(179,296)(180,297)(181,298)(182,299)(183,300)(184,301), (1,172)(2,173)(3,174)(4,175)(5,176)(6,177)(7,178)(8,179)(9,180)(10,181)(11,182)(12,183)(13,184)(14,93)(15,94)(16,95)(17,96)(18,97)(19,98)(20,99)(21,100)(22,101)(23,102)(24,103)(25,104)(26,105)(27,106)(28,107)(29,108)(30,109)(31,110)(32,111)(33,112)(34,113)(35,114)(36,115)(37,116)(38,117)(39,118)(40,119)(41,120)(42,121)(43,122)(44,123)(45,124)(46,125)(47,126)(48,127)(49,128)(50,129)(51,130)(52,131)(53,132)(54,133)(55,134)(56,135)(57,136)(58,137)(59,138)(60,139)(61,140)(62,141)(63,142)(64,143)(65,144)(66,145)(67,146)(68,147)(69,148)(70,149)(71,150)(72,151)(73,152)(74,153)(75,154)(76,155)(77,156)(78,157)(79,158)(80,159)(81,160)(82,161)(83,162)(84,163)(85,164)(86,165)(87,166)(88,167)(89,168)(90,169)(91,170)(92,171)(185,317)(186,318)(187,319)(188,320)(189,321)(190,322)(191,323)(192,324)(193,325)(194,326)(195,327)(196,328)(197,329)(198,330)(199,331)(200,332)(201,333)(202,334)(203,335)(204,336)(205,337)(206,338)(207,339)(208,340)(209,341)(210,342)(211,343)(212,344)(213,345)(214,346)(215,347)(216,348)(217,349)(218,350)(219,351)(220,352)(221,353)(222,354)(223,355)(224,356)(225,357)(226,358)(227,359)(228,360)(229,361)(230,362)(231,363)(232,364)(233,365)(234,366)(235,367)(236,368)(237,277)(238,278)(239,279)(240,280)(241,281)(242,282)(243,283)(244,284)(245,285)(246,286)(247,287)(248,288)(249,289)(250,290)(251,291)(252,292)(253,293)(254,294)(255,295)(256,296)(257,297)(258,298)(259,299)(260,300)(261,301)(262,302)(263,303)(264,304)(265,305)(266,306)(267,307)(268,308)(269,309)(270,310)(271,311)(272,312)(273,313)(274,314)(275,315)(276,316), (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([(1,249),(2,250),(3,251),(4,252),(5,253),(6,254),(7,255),(8,256),(9,257),(10,258),(11,259),(12,260),(13,261),(14,262),(15,263),(16,264),(17,265),(18,266),(19,267),(20,268),(21,269),(22,270),(23,271),(24,272),(25,273),(26,274),(27,275),(28,276),(29,185),(30,186),(31,187),(32,188),(33,189),(34,190),(35,191),(36,192),(37,193),(38,194),(39,195),(40,196),(41,197),(42,198),(43,199),(44,200),(45,201),(46,202),(47,203),(48,204),(49,205),(50,206),(51,207),(52,208),(53,209),(54,210),(55,211),(56,212),(57,213),(58,214),(59,215),(60,216),(61,217),(62,218),(63,219),(64,220),(65,221),(66,222),(67,223),(68,224),(69,225),(70,226),(71,227),(72,228),(73,229),(74,230),(75,231),(76,232),(77,233),(78,234),(79,235),(80,236),(81,237),(82,238),(83,239),(84,240),(85,241),(86,242),(87,243),(88,244),(89,245),(90,246),(91,247),(92,248),(93,302),(94,303),(95,304),(96,305),(97,306),(98,307),(99,308),(100,309),(101,310),(102,311),(103,312),(104,313),(105,314),(106,315),(107,316),(108,317),(109,318),(110,319),(111,320),(112,321),(113,322),(114,323),(115,324),(116,325),(117,326),(118,327),(119,328),(120,329),(121,330),(122,331),(123,332),(124,333),(125,334),(126,335),(127,336),(128,337),(129,338),(130,339),(131,340),(132,341),(133,342),(134,343),(135,344),(136,345),(137,346),(138,347),(139,348),(140,349),(141,350),(142,351),(143,352),(144,353),(145,354),(146,355),(147,356),(148,357),(149,358),(150,359),(151,360),(152,361),(153,362),(154,363),(155,364),(156,365),(157,366),(158,367),(159,368),(160,277),(161,278),(162,279),(163,280),(164,281),(165,282),(166,283),(167,284),(168,285),(169,286),(170,287),(171,288),(172,289),(173,290),(174,291),(175,292),(176,293),(177,294),(178,295),(179,296),(180,297),(181,298),(182,299),(183,300),(184,301)], [(1,172),(2,173),(3,174),(4,175),(5,176),(6,177),(7,178),(8,179),(9,180),(10,181),(11,182),(12,183),(13,184),(14,93),(15,94),(16,95),(17,96),(18,97),(19,98),(20,99),(21,100),(22,101),(23,102),(24,103),(25,104),(26,105),(27,106),(28,107),(29,108),(30,109),(31,110),(32,111),(33,112),(34,113),(35,114),(36,115),(37,116),(38,117),(39,118),(40,119),(41,120),(42,121),(43,122),(44,123),(45,124),(46,125),(47,126),(48,127),(49,128),(50,129),(51,130),(52,131),(53,132),(54,133),(55,134),(56,135),(57,136),(58,137),(59,138),(60,139),(61,140),(62,141),(63,142),(64,143),(65,144),(66,145),(67,146),(68,147),(69,148),(70,149),(71,150),(72,151),(73,152),(74,153),(75,154),(76,155),(77,156),(78,157),(79,158),(80,159),(81,160),(82,161),(83,162),(84,163),(85,164),(86,165),(87,166),(88,167),(89,168),(90,169),(91,170),(92,171),(185,317),(186,318),(187,319),(188,320),(189,321),(190,322),(191,323),(192,324),(193,325),(194,326),(195,327),(196,328),(197,329),(198,330),(199,331),(200,332),(201,333),(202,334),(203,335),(204,336),(205,337),(206,338),(207,339),(208,340),(209,341),(210,342),(211,343),(212,344),(213,345),(214,346),(215,347),(216,348),(217,349),(218,350),(219,351),(220,352),(221,353),(222,354),(223,355),(224,356),(225,357),(226,358),(227,359),(228,360),(229,361),(230,362),(231,363),(232,364),(233,365),(234,366),(235,367),(236,368),(237,277),(238,278),(239,279),(240,280),(241,281),(242,282),(243,283),(244,284),(245,285),(246,286),(247,287),(248,288),(249,289),(250,290),(251,291),(252,292),(253,293),(254,294),(255,295),(256,296),(257,297),(258,298),(259,299),(260,300),(261,301),(262,302),(263,303),(264,304),(265,305),(266,306),(267,307),(268,308),(269,309),(270,310),(271,311),(272,312),(273,313),(274,314),(275,315),(276,316)], [(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

׿
×
𝔽