direct product, abelian, monomial, 2-elementary
Aliases: C22×C98, SmallGroup(392,13)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C22×C98 |
| C1 — C22×C98 |
| C1 — C22×C98 |
Generators and relations for C22×C98
G = < a,b,c | a2=b2=c98=1, ab=ba, ac=ca, bc=cb >
Smallest permutation representation of C22×C98
►Regular action on 392 points
Generators in S392
(1 217)(2 218)(3 219)(4 220)(5 221)(6 222)(7 223)(8 224)(9 225)(10 226)(11 227)(12 228)(13 229)(14 230)(15 231)(16 232)(17 233)(18 234)(19 235)(20 236)(21 237)(22 238)(23 239)(24 240)(25 241)(26 242)(27 243)(28 244)(29 245)(30 246)(31 247)(32 248)(33 249)(34 250)(35 251)(36 252)(37 253)(38 254)(39 255)(40 256)(41 257)(42 258)(43 259)(44 260)(45 261)(46 262)(47 263)(48 264)(49 265)(50 266)(51 267)(52 268)(53 269)(54 270)(55 271)(56 272)(57 273)(58 274)(59 275)(60 276)(61 277)(62 278)(63 279)(64 280)(65 281)(66 282)(67 283)(68 284)(69 285)(70 286)(71 287)(72 288)(73 289)(74 290)(75 291)(76 292)(77 293)(78 294)(79 197)(80 198)(81 199)(82 200)(83 201)(84 202)(85 203)(86 204)(87 205)(88 206)(89 207)(90 208)(91 209)(92 210)(93 211)(94 212)(95 213)(96 214)(97 215)(98 216)(99 348)(100 349)(101 350)(102 351)(103 352)(104 353)(105 354)(106 355)(107 356)(108 357)(109 358)(110 359)(111 360)(112 361)(113 362)(114 363)(115 364)(116 365)(117 366)(118 367)(119 368)(120 369)(121 370)(122 371)(123 372)(124 373)(125 374)(126 375)(127 376)(128 377)(129 378)(130 379)(131 380)(132 381)(133 382)(134 383)(135 384)(136 385)(137 386)(138 387)(139 388)(140 389)(141 390)(142 391)(143 392)(144 295)(145 296)(146 297)(147 298)(148 299)(149 300)(150 301)(151 302)(152 303)(153 304)(154 305)(155 306)(156 307)(157 308)(158 309)(159 310)(160 311)(161 312)(162 313)(163 314)(164 315)(165 316)(166 317)(167 318)(168 319)(169 320)(170 321)(171 322)(172 323)(173 324)(174 325)(175 326)(176 327)(177 328)(178 329)(179 330)(180 331)(181 332)(182 333)(183 334)(184 335)(185 336)(186 337)(187 338)(188 339)(189 340)(190 341)(191 342)(192 343)(193 344)(194 345)(195 346)(196 347)
(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)(45 189)(46 190)(47 191)(48 192)(49 193)(50 194)(51 195)(52 196)(53 99)(54 100)(55 101)(56 102)(57 103)(58 104)(59 105)(60 106)(61 107)(62 108)(63 109)(64 110)(65 111)(66 112)(67 113)(68 114)(69 115)(70 116)(71 117)(72 118)(73 119)(74 120)(75 121)(76 122)(77 123)(78 124)(79 125)(80 126)(81 127)(82 128)(83 129)(84 130)(85 131)(86 132)(87 133)(88 134)(89 135)(90 136)(91 137)(92 138)(93 139)(94 140)(95 141)(96 142)(97 143)(98 144)(197 374)(198 375)(199 376)(200 377)(201 378)(202 379)(203 380)(204 381)(205 382)(206 383)(207 384)(208 385)(209 386)(210 387)(211 388)(212 389)(213 390)(214 391)(215 392)(216 295)(217 296)(218 297)(219 298)(220 299)(221 300)(222 301)(223 302)(224 303)(225 304)(226 305)(227 306)(228 307)(229 308)(230 309)(231 310)(232 311)(233 312)(234 313)(235 314)(236 315)(237 316)(238 317)(239 318)(240 319)(241 320)(242 321)(243 322)(244 323)(245 324)(246 325)(247 326)(248 327)(249 328)(250 329)(251 330)(252 331)(253 332)(254 333)(255 334)(256 335)(257 336)(258 337)(259 338)(260 339)(261 340)(262 341)(263 342)(264 343)(265 344)(266 345)(267 346)(268 347)(269 348)(270 349)(271 350)(272 351)(273 352)(274 353)(275 354)(276 355)(277 356)(278 357)(279 358)(280 359)(281 360)(282 361)(283 362)(284 363)(285 364)(286 365)(287 366)(288 367)(289 368)(290 369)(291 370)(292 371)(293 372)(294 373)
(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)(295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392)
G:=sub<Sym(392)| (1,217)(2,218)(3,219)(4,220)(5,221)(6,222)(7,223)(8,224)(9,225)(10,226)(11,227)(12,228)(13,229)(14,230)(15,231)(16,232)(17,233)(18,234)(19,235)(20,236)(21,237)(22,238)(23,239)(24,240)(25,241)(26,242)(27,243)(28,244)(29,245)(30,246)(31,247)(32,248)(33,249)(34,250)(35,251)(36,252)(37,253)(38,254)(39,255)(40,256)(41,257)(42,258)(43,259)(44,260)(45,261)(46,262)(47,263)(48,264)(49,265)(50,266)(51,267)(52,268)(53,269)(54,270)(55,271)(56,272)(57,273)(58,274)(59,275)(60,276)(61,277)(62,278)(63,279)(64,280)(65,281)(66,282)(67,283)(68,284)(69,285)(70,286)(71,287)(72,288)(73,289)(74,290)(75,291)(76,292)(77,293)(78,294)(79,197)(80,198)(81,199)(82,200)(83,201)(84,202)(85,203)(86,204)(87,205)(88,206)(89,207)(90,208)(91,209)(92,210)(93,211)(94,212)(95,213)(96,214)(97,215)(98,216)(99,348)(100,349)(101,350)(102,351)(103,352)(104,353)(105,354)(106,355)(107,356)(108,357)(109,358)(110,359)(111,360)(112,361)(113,362)(114,363)(115,364)(116,365)(117,366)(118,367)(119,368)(120,369)(121,370)(122,371)(123,372)(124,373)(125,374)(126,375)(127,376)(128,377)(129,378)(130,379)(131,380)(132,381)(133,382)(134,383)(135,384)(136,385)(137,386)(138,387)(139,388)(140,389)(141,390)(142,391)(143,392)(144,295)(145,296)(146,297)(147,298)(148,299)(149,300)(150,301)(151,302)(152,303)(153,304)(154,305)(155,306)(156,307)(157,308)(158,309)(159,310)(160,311)(161,312)(162,313)(163,314)(164,315)(165,316)(166,317)(167,318)(168,319)(169,320)(170,321)(171,322)(172,323)(173,324)(174,325)(175,326)(176,327)(177,328)(178,329)(179,330)(180,331)(181,332)(182,333)(183,334)(184,335)(185,336)(186,337)(187,338)(188,339)(189,340)(190,341)(191,342)(192,343)(193,344)(194,345)(195,346)(196,347), (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)(45,189)(46,190)(47,191)(48,192)(49,193)(50,194)(51,195)(52,196)(53,99)(54,100)(55,101)(56,102)(57,103)(58,104)(59,105)(60,106)(61,107)(62,108)(63,109)(64,110)(65,111)(66,112)(67,113)(68,114)(69,115)(70,116)(71,117)(72,118)(73,119)(74,120)(75,121)(76,122)(77,123)(78,124)(79,125)(80,126)(81,127)(82,128)(83,129)(84,130)(85,131)(86,132)(87,133)(88,134)(89,135)(90,136)(91,137)(92,138)(93,139)(94,140)(95,141)(96,142)(97,143)(98,144)(197,374)(198,375)(199,376)(200,377)(201,378)(202,379)(203,380)(204,381)(205,382)(206,383)(207,384)(208,385)(209,386)(210,387)(211,388)(212,389)(213,390)(214,391)(215,392)(216,295)(217,296)(218,297)(219,298)(220,299)(221,300)(222,301)(223,302)(224,303)(225,304)(226,305)(227,306)(228,307)(229,308)(230,309)(231,310)(232,311)(233,312)(234,313)(235,314)(236,315)(237,316)(238,317)(239,318)(240,319)(241,320)(242,321)(243,322)(244,323)(245,324)(246,325)(247,326)(248,327)(249,328)(250,329)(251,330)(252,331)(253,332)(254,333)(255,334)(256,335)(257,336)(258,337)(259,338)(260,339)(261,340)(262,341)(263,342)(264,343)(265,344)(266,345)(267,346)(268,347)(269,348)(270,349)(271,350)(272,351)(273,352)(274,353)(275,354)(276,355)(277,356)(278,357)(279,358)(280,359)(281,360)(282,361)(283,362)(284,363)(285,364)(286,365)(287,366)(288,367)(289,368)(290,369)(291,370)(292,371)(293,372)(294,373), (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)(295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392)>;
G:=Group( (1,217)(2,218)(3,219)(4,220)(5,221)(6,222)(7,223)(8,224)(9,225)(10,226)(11,227)(12,228)(13,229)(14,230)(15,231)(16,232)(17,233)(18,234)(19,235)(20,236)(21,237)(22,238)(23,239)(24,240)(25,241)(26,242)(27,243)(28,244)(29,245)(30,246)(31,247)(32,248)(33,249)(34,250)(35,251)(36,252)(37,253)(38,254)(39,255)(40,256)(41,257)(42,258)(43,259)(44,260)(45,261)(46,262)(47,263)(48,264)(49,265)(50,266)(51,267)(52,268)(53,269)(54,270)(55,271)(56,272)(57,273)(58,274)(59,275)(60,276)(61,277)(62,278)(63,279)(64,280)(65,281)(66,282)(67,283)(68,284)(69,285)(70,286)(71,287)(72,288)(73,289)(74,290)(75,291)(76,292)(77,293)(78,294)(79,197)(80,198)(81,199)(82,200)(83,201)(84,202)(85,203)(86,204)(87,205)(88,206)(89,207)(90,208)(91,209)(92,210)(93,211)(94,212)(95,213)(96,214)(97,215)(98,216)(99,348)(100,349)(101,350)(102,351)(103,352)(104,353)(105,354)(106,355)(107,356)(108,357)(109,358)(110,359)(111,360)(112,361)(113,362)(114,363)(115,364)(116,365)(117,366)(118,367)(119,368)(120,369)(121,370)(122,371)(123,372)(124,373)(125,374)(126,375)(127,376)(128,377)(129,378)(130,379)(131,380)(132,381)(133,382)(134,383)(135,384)(136,385)(137,386)(138,387)(139,388)(140,389)(141,390)(142,391)(143,392)(144,295)(145,296)(146,297)(147,298)(148,299)(149,300)(150,301)(151,302)(152,303)(153,304)(154,305)(155,306)(156,307)(157,308)(158,309)(159,310)(160,311)(161,312)(162,313)(163,314)(164,315)(165,316)(166,317)(167,318)(168,319)(169,320)(170,321)(171,322)(172,323)(173,324)(174,325)(175,326)(176,327)(177,328)(178,329)(179,330)(180,331)(181,332)(182,333)(183,334)(184,335)(185,336)(186,337)(187,338)(188,339)(189,340)(190,341)(191,342)(192,343)(193,344)(194,345)(195,346)(196,347), (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)(45,189)(46,190)(47,191)(48,192)(49,193)(50,194)(51,195)(52,196)(53,99)(54,100)(55,101)(56,102)(57,103)(58,104)(59,105)(60,106)(61,107)(62,108)(63,109)(64,110)(65,111)(66,112)(67,113)(68,114)(69,115)(70,116)(71,117)(72,118)(73,119)(74,120)(75,121)(76,122)(77,123)(78,124)(79,125)(80,126)(81,127)(82,128)(83,129)(84,130)(85,131)(86,132)(87,133)(88,134)(89,135)(90,136)(91,137)(92,138)(93,139)(94,140)(95,141)(96,142)(97,143)(98,144)(197,374)(198,375)(199,376)(200,377)(201,378)(202,379)(203,380)(204,381)(205,382)(206,383)(207,384)(208,385)(209,386)(210,387)(211,388)(212,389)(213,390)(214,391)(215,392)(216,295)(217,296)(218,297)(219,298)(220,299)(221,300)(222,301)(223,302)(224,303)(225,304)(226,305)(227,306)(228,307)(229,308)(230,309)(231,310)(232,311)(233,312)(234,313)(235,314)(236,315)(237,316)(238,317)(239,318)(240,319)(241,320)(242,321)(243,322)(244,323)(245,324)(246,325)(247,326)(248,327)(249,328)(250,329)(251,330)(252,331)(253,332)(254,333)(255,334)(256,335)(257,336)(258,337)(259,338)(260,339)(261,340)(262,341)(263,342)(264,343)(265,344)(266,345)(267,346)(268,347)(269,348)(270,349)(271,350)(272,351)(273,352)(274,353)(275,354)(276,355)(277,356)(278,357)(279,358)(280,359)(281,360)(282,361)(283,362)(284,363)(285,364)(286,365)(287,366)(288,367)(289,368)(290,369)(291,370)(292,371)(293,372)(294,373), (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)(295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392) );
G=PermutationGroup([[(1,217),(2,218),(3,219),(4,220),(5,221),(6,222),(7,223),(8,224),(9,225),(10,226),(11,227),(12,228),(13,229),(14,230),(15,231),(16,232),(17,233),(18,234),(19,235),(20,236),(21,237),(22,238),(23,239),(24,240),(25,241),(26,242),(27,243),(28,244),(29,245),(30,246),(31,247),(32,248),(33,249),(34,250),(35,251),(36,252),(37,253),(38,254),(39,255),(40,256),(41,257),(42,258),(43,259),(44,260),(45,261),(46,262),(47,263),(48,264),(49,265),(50,266),(51,267),(52,268),(53,269),(54,270),(55,271),(56,272),(57,273),(58,274),(59,275),(60,276),(61,277),(62,278),(63,279),(64,280),(65,281),(66,282),(67,283),(68,284),(69,285),(70,286),(71,287),(72,288),(73,289),(74,290),(75,291),(76,292),(77,293),(78,294),(79,197),(80,198),(81,199),(82,200),(83,201),(84,202),(85,203),(86,204),(87,205),(88,206),(89,207),(90,208),(91,209),(92,210),(93,211),(94,212),(95,213),(96,214),(97,215),(98,216),(99,348),(100,349),(101,350),(102,351),(103,352),(104,353),(105,354),(106,355),(107,356),(108,357),(109,358),(110,359),(111,360),(112,361),(113,362),(114,363),(115,364),(116,365),(117,366),(118,367),(119,368),(120,369),(121,370),(122,371),(123,372),(124,373),(125,374),(126,375),(127,376),(128,377),(129,378),(130,379),(131,380),(132,381),(133,382),(134,383),(135,384),(136,385),(137,386),(138,387),(139,388),(140,389),(141,390),(142,391),(143,392),(144,295),(145,296),(146,297),(147,298),(148,299),(149,300),(150,301),(151,302),(152,303),(153,304),(154,305),(155,306),(156,307),(157,308),(158,309),(159,310),(160,311),(161,312),(162,313),(163,314),(164,315),(165,316),(166,317),(167,318),(168,319),(169,320),(170,321),(171,322),(172,323),(173,324),(174,325),(175,326),(176,327),(177,328),(178,329),(179,330),(180,331),(181,332),(182,333),(183,334),(184,335),(185,336),(186,337),(187,338),(188,339),(189,340),(190,341),(191,342),(192,343),(193,344),(194,345),(195,346),(196,347)], [(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),(45,189),(46,190),(47,191),(48,192),(49,193),(50,194),(51,195),(52,196),(53,99),(54,100),(55,101),(56,102),(57,103),(58,104),(59,105),(60,106),(61,107),(62,108),(63,109),(64,110),(65,111),(66,112),(67,113),(68,114),(69,115),(70,116),(71,117),(72,118),(73,119),(74,120),(75,121),(76,122),(77,123),(78,124),(79,125),(80,126),(81,127),(82,128),(83,129),(84,130),(85,131),(86,132),(87,133),(88,134),(89,135),(90,136),(91,137),(92,138),(93,139),(94,140),(95,141),(96,142),(97,143),(98,144),(197,374),(198,375),(199,376),(200,377),(201,378),(202,379),(203,380),(204,381),(205,382),(206,383),(207,384),(208,385),(209,386),(210,387),(211,388),(212,389),(213,390),(214,391),(215,392),(216,295),(217,296),(218,297),(219,298),(220,299),(221,300),(222,301),(223,302),(224,303),(225,304),(226,305),(227,306),(228,307),(229,308),(230,309),(231,310),(232,311),(233,312),(234,313),(235,314),(236,315),(237,316),(238,317),(239,318),(240,319),(241,320),(242,321),(243,322),(244,323),(245,324),(246,325),(247,326),(248,327),(249,328),(250,329),(251,330),(252,331),(253,332),(254,333),(255,334),(256,335),(257,336),(258,337),(259,338),(260,339),(261,340),(262,341),(263,342),(264,343),(265,344),(266,345),(267,346),(268,347),(269,348),(270,349),(271,350),(272,351),(273,352),(274,353),(275,354),(276,355),(277,356),(278,357),(279,358),(280,359),(281,360),(282,361),(283,362),(284,363),(285,364),(286,365),(287,366),(288,367),(289,368),(290,369),(291,370),(292,371),(293,372),(294,373)], [(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),(295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392)]])
392 conjugacy classes
| class | 1 | 2A | ··· | 2G | 7A | ··· | 7F | 14A | ··· | 14AP | 49A | ··· | 49AP | 98A | ··· | 98KH |
| order | 1 | 2 | ··· | 2 | 7 | ··· | 7 | 14 | ··· | 14 | 49 | ··· | 49 | 98 | ··· | 98 |
| size | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
392 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 |
| type | + | + | ||||
| image | C1 | C2 | C7 | C14 | C49 | C98 |
| kernel | C22×C98 | C2×C98 | C22×C14 | C2×C14 | C23 | C22 |
| # reps | 1 | 7 | 6 | 42 | 42 | 294 |
Matrix representation of C22×C98 ►in GL3(𝔽197) generated by
| 1 | 0 | 0 |
| 0 | 196 | 0 |
| 0 | 0 | 196 |
| 1 | 0 | 0 |
| 0 | 196 | 0 |
| 0 | 0 | 1 |
| 181 | 0 | 0 |
| 0 | 55 | 0 |
| 0 | 0 | 134 |
G:=sub<GL(3,GF(197))| [1,0,0,0,196,0,0,0,196],[1,0,0,0,196,0,0,0,1],[181,0,0,0,55,0,0,0,134] >;
C22×C98 in GAP, Magma, Sage, TeX
C_2^2\times C_{98} % in TeX
G:=Group("C2^2xC98"); // GroupNames label
G:=SmallGroup(392,13);
// by ID
G=gap.SmallGroup(392,13);
# by ID
G:=PCGroup([5,-2,-2,-2,-7,-7,158]);
// Polycyclic
G:=Group<a,b,c|a^2=b^2=c^98=1,a*b=b*a,a*c=c*a,b*c=c*b>;
// generators/relations
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