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G = C22×C94order 376 = 23·47

Abelian group of type [2,2,94]

direct product, abelian, monomial, 2-elementary

Aliases: C22×C94, SmallGroup(376,12)

Series: Derived Chief Lower central Upper central

C1 — C22×C94
C1C47C94C2×C94 — C22×C94
C1 — C22×C94
C1 — C22×C94

Generators and relations for C22×C94
 G = < a,b,c | a2=b2=c94=1, ab=ba, ac=ca, bc=cb >


Smallest permutation representation of C22×C94
Regular action on 376 points
Generators in S376
(1 258)(2 259)(3 260)(4 261)(5 262)(6 263)(7 264)(8 265)(9 266)(10 267)(11 268)(12 269)(13 270)(14 271)(15 272)(16 273)(17 274)(18 275)(19 276)(20 277)(21 278)(22 279)(23 280)(24 281)(25 282)(26 189)(27 190)(28 191)(29 192)(30 193)(31 194)(32 195)(33 196)(34 197)(35 198)(36 199)(37 200)(38 201)(39 202)(40 203)(41 204)(42 205)(43 206)(44 207)(45 208)(46 209)(47 210)(48 211)(49 212)(50 213)(51 214)(52 215)(53 216)(54 217)(55 218)(56 219)(57 220)(58 221)(59 222)(60 223)(61 224)(62 225)(63 226)(64 227)(65 228)(66 229)(67 230)(68 231)(69 232)(70 233)(71 234)(72 235)(73 236)(74 237)(75 238)(76 239)(77 240)(78 241)(79 242)(80 243)(81 244)(82 245)(83 246)(84 247)(85 248)(86 249)(87 250)(88 251)(89 252)(90 253)(91 254)(92 255)(93 256)(94 257)(95 317)(96 318)(97 319)(98 320)(99 321)(100 322)(101 323)(102 324)(103 325)(104 326)(105 327)(106 328)(107 329)(108 330)(109 331)(110 332)(111 333)(112 334)(113 335)(114 336)(115 337)(116 338)(117 339)(118 340)(119 341)(120 342)(121 343)(122 344)(123 345)(124 346)(125 347)(126 348)(127 349)(128 350)(129 351)(130 352)(131 353)(132 354)(133 355)(134 356)(135 357)(136 358)(137 359)(138 360)(139 361)(140 362)(141 363)(142 364)(143 365)(144 366)(145 367)(146 368)(147 369)(148 370)(149 371)(150 372)(151 373)(152 374)(153 375)(154 376)(155 283)(156 284)(157 285)(158 286)(159 287)(160 288)(161 289)(162 290)(163 291)(164 292)(165 293)(166 294)(167 295)(168 296)(169 297)(170 298)(171 299)(172 300)(173 301)(174 302)(175 303)(176 304)(177 305)(178 306)(179 307)(180 308)(181 309)(182 310)(183 311)(184 312)(185 313)(186 314)(187 315)(188 316)
(1 145)(2 146)(3 147)(4 148)(5 149)(6 150)(7 151)(8 152)(9 153)(10 154)(11 155)(12 156)(13 157)(14 158)(15 159)(16 160)(17 161)(18 162)(19 163)(20 164)(21 165)(22 166)(23 167)(24 168)(25 169)(26 170)(27 171)(28 172)(29 173)(30 174)(31 175)(32 176)(33 177)(34 178)(35 179)(36 180)(37 181)(38 182)(39 183)(40 184)(41 185)(42 186)(43 187)(44 188)(45 95)(46 96)(47 97)(48 98)(49 99)(50 100)(51 101)(52 102)(53 103)(54 104)(55 105)(56 106)(57 107)(58 108)(59 109)(60 110)(61 111)(62 112)(63 113)(64 114)(65 115)(66 116)(67 117)(68 118)(69 119)(70 120)(71 121)(72 122)(73 123)(74 124)(75 125)(76 126)(77 127)(78 128)(79 129)(80 130)(81 131)(82 132)(83 133)(84 134)(85 135)(86 136)(87 137)(88 138)(89 139)(90 140)(91 141)(92 142)(93 143)(94 144)(189 298)(190 299)(191 300)(192 301)(193 302)(194 303)(195 304)(196 305)(197 306)(198 307)(199 308)(200 309)(201 310)(202 311)(203 312)(204 313)(205 314)(206 315)(207 316)(208 317)(209 318)(210 319)(211 320)(212 321)(213 322)(214 323)(215 324)(216 325)(217 326)(218 327)(219 328)(220 329)(221 330)(222 331)(223 332)(224 333)(225 334)(226 335)(227 336)(228 337)(229 338)(230 339)(231 340)(232 341)(233 342)(234 343)(235 344)(236 345)(237 346)(238 347)(239 348)(240 349)(241 350)(242 351)(243 352)(244 353)(245 354)(246 355)(247 356)(248 357)(249 358)(250 359)(251 360)(252 361)(253 362)(254 363)(255 364)(256 365)(257 366)(258 367)(259 368)(260 369)(261 370)(262 371)(263 372)(264 373)(265 374)(266 375)(267 376)(268 283)(269 284)(270 285)(271 286)(272 287)(273 288)(274 289)(275 290)(276 291)(277 292)(278 293)(279 294)(280 295)(281 296)(282 297)
(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)(283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376)

G:=sub<Sym(376)| (1,258)(2,259)(3,260)(4,261)(5,262)(6,263)(7,264)(8,265)(9,266)(10,267)(11,268)(12,269)(13,270)(14,271)(15,272)(16,273)(17,274)(18,275)(19,276)(20,277)(21,278)(22,279)(23,280)(24,281)(25,282)(26,189)(27,190)(28,191)(29,192)(30,193)(31,194)(32,195)(33,196)(34,197)(35,198)(36,199)(37,200)(38,201)(39,202)(40,203)(41,204)(42,205)(43,206)(44,207)(45,208)(46,209)(47,210)(48,211)(49,212)(50,213)(51,214)(52,215)(53,216)(54,217)(55,218)(56,219)(57,220)(58,221)(59,222)(60,223)(61,224)(62,225)(63,226)(64,227)(65,228)(66,229)(67,230)(68,231)(69,232)(70,233)(71,234)(72,235)(73,236)(74,237)(75,238)(76,239)(77,240)(78,241)(79,242)(80,243)(81,244)(82,245)(83,246)(84,247)(85,248)(86,249)(87,250)(88,251)(89,252)(90,253)(91,254)(92,255)(93,256)(94,257)(95,317)(96,318)(97,319)(98,320)(99,321)(100,322)(101,323)(102,324)(103,325)(104,326)(105,327)(106,328)(107,329)(108,330)(109,331)(110,332)(111,333)(112,334)(113,335)(114,336)(115,337)(116,338)(117,339)(118,340)(119,341)(120,342)(121,343)(122,344)(123,345)(124,346)(125,347)(126,348)(127,349)(128,350)(129,351)(130,352)(131,353)(132,354)(133,355)(134,356)(135,357)(136,358)(137,359)(138,360)(139,361)(140,362)(141,363)(142,364)(143,365)(144,366)(145,367)(146,368)(147,369)(148,370)(149,371)(150,372)(151,373)(152,374)(153,375)(154,376)(155,283)(156,284)(157,285)(158,286)(159,287)(160,288)(161,289)(162,290)(163,291)(164,292)(165,293)(166,294)(167,295)(168,296)(169,297)(170,298)(171,299)(172,300)(173,301)(174,302)(175,303)(176,304)(177,305)(178,306)(179,307)(180,308)(181,309)(182,310)(183,311)(184,312)(185,313)(186,314)(187,315)(188,316), (1,145)(2,146)(3,147)(4,148)(5,149)(6,150)(7,151)(8,152)(9,153)(10,154)(11,155)(12,156)(13,157)(14,158)(15,159)(16,160)(17,161)(18,162)(19,163)(20,164)(21,165)(22,166)(23,167)(24,168)(25,169)(26,170)(27,171)(28,172)(29,173)(30,174)(31,175)(32,176)(33,177)(34,178)(35,179)(36,180)(37,181)(38,182)(39,183)(40,184)(41,185)(42,186)(43,187)(44,188)(45,95)(46,96)(47,97)(48,98)(49,99)(50,100)(51,101)(52,102)(53,103)(54,104)(55,105)(56,106)(57,107)(58,108)(59,109)(60,110)(61,111)(62,112)(63,113)(64,114)(65,115)(66,116)(67,117)(68,118)(69,119)(70,120)(71,121)(72,122)(73,123)(74,124)(75,125)(76,126)(77,127)(78,128)(79,129)(80,130)(81,131)(82,132)(83,133)(84,134)(85,135)(86,136)(87,137)(88,138)(89,139)(90,140)(91,141)(92,142)(93,143)(94,144)(189,298)(190,299)(191,300)(192,301)(193,302)(194,303)(195,304)(196,305)(197,306)(198,307)(199,308)(200,309)(201,310)(202,311)(203,312)(204,313)(205,314)(206,315)(207,316)(208,317)(209,318)(210,319)(211,320)(212,321)(213,322)(214,323)(215,324)(216,325)(217,326)(218,327)(219,328)(220,329)(221,330)(222,331)(223,332)(224,333)(225,334)(226,335)(227,336)(228,337)(229,338)(230,339)(231,340)(232,341)(233,342)(234,343)(235,344)(236,345)(237,346)(238,347)(239,348)(240,349)(241,350)(242,351)(243,352)(244,353)(245,354)(246,355)(247,356)(248,357)(249,358)(250,359)(251,360)(252,361)(253,362)(254,363)(255,364)(256,365)(257,366)(258,367)(259,368)(260,369)(261,370)(262,371)(263,372)(264,373)(265,374)(266,375)(267,376)(268,283)(269,284)(270,285)(271,286)(272,287)(273,288)(274,289)(275,290)(276,291)(277,292)(278,293)(279,294)(280,295)(281,296)(282,297), (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)(283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376)>;

G:=Group( (1,258)(2,259)(3,260)(4,261)(5,262)(6,263)(7,264)(8,265)(9,266)(10,267)(11,268)(12,269)(13,270)(14,271)(15,272)(16,273)(17,274)(18,275)(19,276)(20,277)(21,278)(22,279)(23,280)(24,281)(25,282)(26,189)(27,190)(28,191)(29,192)(30,193)(31,194)(32,195)(33,196)(34,197)(35,198)(36,199)(37,200)(38,201)(39,202)(40,203)(41,204)(42,205)(43,206)(44,207)(45,208)(46,209)(47,210)(48,211)(49,212)(50,213)(51,214)(52,215)(53,216)(54,217)(55,218)(56,219)(57,220)(58,221)(59,222)(60,223)(61,224)(62,225)(63,226)(64,227)(65,228)(66,229)(67,230)(68,231)(69,232)(70,233)(71,234)(72,235)(73,236)(74,237)(75,238)(76,239)(77,240)(78,241)(79,242)(80,243)(81,244)(82,245)(83,246)(84,247)(85,248)(86,249)(87,250)(88,251)(89,252)(90,253)(91,254)(92,255)(93,256)(94,257)(95,317)(96,318)(97,319)(98,320)(99,321)(100,322)(101,323)(102,324)(103,325)(104,326)(105,327)(106,328)(107,329)(108,330)(109,331)(110,332)(111,333)(112,334)(113,335)(114,336)(115,337)(116,338)(117,339)(118,340)(119,341)(120,342)(121,343)(122,344)(123,345)(124,346)(125,347)(126,348)(127,349)(128,350)(129,351)(130,352)(131,353)(132,354)(133,355)(134,356)(135,357)(136,358)(137,359)(138,360)(139,361)(140,362)(141,363)(142,364)(143,365)(144,366)(145,367)(146,368)(147,369)(148,370)(149,371)(150,372)(151,373)(152,374)(153,375)(154,376)(155,283)(156,284)(157,285)(158,286)(159,287)(160,288)(161,289)(162,290)(163,291)(164,292)(165,293)(166,294)(167,295)(168,296)(169,297)(170,298)(171,299)(172,300)(173,301)(174,302)(175,303)(176,304)(177,305)(178,306)(179,307)(180,308)(181,309)(182,310)(183,311)(184,312)(185,313)(186,314)(187,315)(188,316), (1,145)(2,146)(3,147)(4,148)(5,149)(6,150)(7,151)(8,152)(9,153)(10,154)(11,155)(12,156)(13,157)(14,158)(15,159)(16,160)(17,161)(18,162)(19,163)(20,164)(21,165)(22,166)(23,167)(24,168)(25,169)(26,170)(27,171)(28,172)(29,173)(30,174)(31,175)(32,176)(33,177)(34,178)(35,179)(36,180)(37,181)(38,182)(39,183)(40,184)(41,185)(42,186)(43,187)(44,188)(45,95)(46,96)(47,97)(48,98)(49,99)(50,100)(51,101)(52,102)(53,103)(54,104)(55,105)(56,106)(57,107)(58,108)(59,109)(60,110)(61,111)(62,112)(63,113)(64,114)(65,115)(66,116)(67,117)(68,118)(69,119)(70,120)(71,121)(72,122)(73,123)(74,124)(75,125)(76,126)(77,127)(78,128)(79,129)(80,130)(81,131)(82,132)(83,133)(84,134)(85,135)(86,136)(87,137)(88,138)(89,139)(90,140)(91,141)(92,142)(93,143)(94,144)(189,298)(190,299)(191,300)(192,301)(193,302)(194,303)(195,304)(196,305)(197,306)(198,307)(199,308)(200,309)(201,310)(202,311)(203,312)(204,313)(205,314)(206,315)(207,316)(208,317)(209,318)(210,319)(211,320)(212,321)(213,322)(214,323)(215,324)(216,325)(217,326)(218,327)(219,328)(220,329)(221,330)(222,331)(223,332)(224,333)(225,334)(226,335)(227,336)(228,337)(229,338)(230,339)(231,340)(232,341)(233,342)(234,343)(235,344)(236,345)(237,346)(238,347)(239,348)(240,349)(241,350)(242,351)(243,352)(244,353)(245,354)(246,355)(247,356)(248,357)(249,358)(250,359)(251,360)(252,361)(253,362)(254,363)(255,364)(256,365)(257,366)(258,367)(259,368)(260,369)(261,370)(262,371)(263,372)(264,373)(265,374)(266,375)(267,376)(268,283)(269,284)(270,285)(271,286)(272,287)(273,288)(274,289)(275,290)(276,291)(277,292)(278,293)(279,294)(280,295)(281,296)(282,297), (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)(283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376) );

G=PermutationGroup([(1,258),(2,259),(3,260),(4,261),(5,262),(6,263),(7,264),(8,265),(9,266),(10,267),(11,268),(12,269),(13,270),(14,271),(15,272),(16,273),(17,274),(18,275),(19,276),(20,277),(21,278),(22,279),(23,280),(24,281),(25,282),(26,189),(27,190),(28,191),(29,192),(30,193),(31,194),(32,195),(33,196),(34,197),(35,198),(36,199),(37,200),(38,201),(39,202),(40,203),(41,204),(42,205),(43,206),(44,207),(45,208),(46,209),(47,210),(48,211),(49,212),(50,213),(51,214),(52,215),(53,216),(54,217),(55,218),(56,219),(57,220),(58,221),(59,222),(60,223),(61,224),(62,225),(63,226),(64,227),(65,228),(66,229),(67,230),(68,231),(69,232),(70,233),(71,234),(72,235),(73,236),(74,237),(75,238),(76,239),(77,240),(78,241),(79,242),(80,243),(81,244),(82,245),(83,246),(84,247),(85,248),(86,249),(87,250),(88,251),(89,252),(90,253),(91,254),(92,255),(93,256),(94,257),(95,317),(96,318),(97,319),(98,320),(99,321),(100,322),(101,323),(102,324),(103,325),(104,326),(105,327),(106,328),(107,329),(108,330),(109,331),(110,332),(111,333),(112,334),(113,335),(114,336),(115,337),(116,338),(117,339),(118,340),(119,341),(120,342),(121,343),(122,344),(123,345),(124,346),(125,347),(126,348),(127,349),(128,350),(129,351),(130,352),(131,353),(132,354),(133,355),(134,356),(135,357),(136,358),(137,359),(138,360),(139,361),(140,362),(141,363),(142,364),(143,365),(144,366),(145,367),(146,368),(147,369),(148,370),(149,371),(150,372),(151,373),(152,374),(153,375),(154,376),(155,283),(156,284),(157,285),(158,286),(159,287),(160,288),(161,289),(162,290),(163,291),(164,292),(165,293),(166,294),(167,295),(168,296),(169,297),(170,298),(171,299),(172,300),(173,301),(174,302),(175,303),(176,304),(177,305),(178,306),(179,307),(180,308),(181,309),(182,310),(183,311),(184,312),(185,313),(186,314),(187,315),(188,316)], [(1,145),(2,146),(3,147),(4,148),(5,149),(6,150),(7,151),(8,152),(9,153),(10,154),(11,155),(12,156),(13,157),(14,158),(15,159),(16,160),(17,161),(18,162),(19,163),(20,164),(21,165),(22,166),(23,167),(24,168),(25,169),(26,170),(27,171),(28,172),(29,173),(30,174),(31,175),(32,176),(33,177),(34,178),(35,179),(36,180),(37,181),(38,182),(39,183),(40,184),(41,185),(42,186),(43,187),(44,188),(45,95),(46,96),(47,97),(48,98),(49,99),(50,100),(51,101),(52,102),(53,103),(54,104),(55,105),(56,106),(57,107),(58,108),(59,109),(60,110),(61,111),(62,112),(63,113),(64,114),(65,115),(66,116),(67,117),(68,118),(69,119),(70,120),(71,121),(72,122),(73,123),(74,124),(75,125),(76,126),(77,127),(78,128),(79,129),(80,130),(81,131),(82,132),(83,133),(84,134),(85,135),(86,136),(87,137),(88,138),(89,139),(90,140),(91,141),(92,142),(93,143),(94,144),(189,298),(190,299),(191,300),(192,301),(193,302),(194,303),(195,304),(196,305),(197,306),(198,307),(199,308),(200,309),(201,310),(202,311),(203,312),(204,313),(205,314),(206,315),(207,316),(208,317),(209,318),(210,319),(211,320),(212,321),(213,322),(214,323),(215,324),(216,325),(217,326),(218,327),(219,328),(220,329),(221,330),(222,331),(223,332),(224,333),(225,334),(226,335),(227,336),(228,337),(229,338),(230,339),(231,340),(232,341),(233,342),(234,343),(235,344),(236,345),(237,346),(238,347),(239,348),(240,349),(241,350),(242,351),(243,352),(244,353),(245,354),(246,355),(247,356),(248,357),(249,358),(250,359),(251,360),(252,361),(253,362),(254,363),(255,364),(256,365),(257,366),(258,367),(259,368),(260,369),(261,370),(262,371),(263,372),(264,373),(265,374),(266,375),(267,376),(268,283),(269,284),(270,285),(271,286),(272,287),(273,288),(274,289),(275,290),(276,291),(277,292),(278,293),(279,294),(280,295),(281,296),(282,297)], [(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),(283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376)])

376 conjugacy classes

class 1 2A···2G47A···47AT94A···94LJ
order12···247···4794···94
size11···11···11···1

376 irreducible representations

dim1111
type++
imageC1C2C47C94
kernelC22×C94C2×C94C23C22
# reps1746322

Matrix representation of C22×C94 in GL3(𝔽283) generated by

100
02820
001
,
28200
02820
001
,
14100
010
00254
G:=sub<GL(3,GF(283))| [1,0,0,0,282,0,0,0,1],[282,0,0,0,282,0,0,0,1],[141,0,0,0,1,0,0,0,254] >;

C22×C94 in GAP, Magma, Sage, TeX

C_2^2\times C_{94}
% in TeX

G:=Group("C2^2xC94");
// GroupNames label

G:=SmallGroup(376,12);
// by ID

G=gap.SmallGroup(376,12);
# by ID

G:=PCGroup([4,-2,-2,-2,-47]);
// Polycyclic

G:=Group<a,b,c|a^2=b^2=c^94=1,a*b=b*a,a*c=c*a,b*c=c*b>;
// generators/relations

Export

Subgroup lattice of C22×C94 in TeX

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𝔽