Copied to
clipboard

G = C22×C98order 392 = 23·72

Abelian group of type [2,2,98]

direct product, abelian, monomial, 2-elementary

Aliases: C22×C98, SmallGroup(392,13)

Series: Derived Chief Lower central Upper central

C1 — C22×C98
C1C7C49C98C2×C98 — 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)(99 334)(100 335)(101 336)(102 337)(103 338)(104 339)(105 340)(106 341)(107 342)(108 343)(109 344)(110 345)(111 346)(112 347)(113 348)(114 349)(115 350)(116 351)(117 352)(118 353)(119 354)(120 355)(121 356)(122 357)(123 358)(124 359)(125 360)(126 361)(127 362)(128 363)(129 364)(130 365)(131 366)(132 367)(133 368)(134 369)(135 370)(136 371)(137 372)(138 373)(139 374)(140 375)(141 376)(142 377)(143 378)(144 379)(145 380)(146 381)(147 382)(148 383)(149 384)(150 385)(151 386)(152 387)(153 388)(154 389)(155 390)(156 391)(157 392)(158 295)(159 296)(160 297)(161 298)(162 299)(163 300)(164 301)(165 302)(166 303)(167 304)(168 305)(169 306)(170 307)(171 308)(172 309)(173 310)(174 311)(175 312)(176 313)(177 314)(178 315)(179 316)(180 317)(181 318)(182 319)(183 320)(184 321)(185 322)(186 323)(187 324)(188 325)(189 326)(190 327)(191 328)(192 329)(193 330)(194 331)(195 332)(196 333)
(1 119)(2 120)(3 121)(4 122)(5 123)(6 124)(7 125)(8 126)(9 127)(10 128)(11 129)(12 130)(13 131)(14 132)(15 133)(16 134)(17 135)(18 136)(19 137)(20 138)(21 139)(22 140)(23 141)(24 142)(25 143)(26 144)(27 145)(28 146)(29 147)(30 148)(31 149)(32 150)(33 151)(34 152)(35 153)(36 154)(37 155)(38 156)(39 157)(40 158)(41 159)(42 160)(43 161)(44 162)(45 163)(46 164)(47 165)(48 166)(49 167)(50 168)(51 169)(52 170)(53 171)(54 172)(55 173)(56 174)(57 175)(58 176)(59 177)(60 178)(61 179)(62 180)(63 181)(64 182)(65 183)(66 184)(67 185)(68 186)(69 187)(70 188)(71 189)(72 190)(73 191)(74 192)(75 193)(76 194)(77 195)(78 196)(79 99)(80 100)(81 101)(82 102)(83 103)(84 104)(85 105)(86 106)(87 107)(88 108)(89 109)(90 110)(91 111)(92 112)(93 113)(94 114)(95 115)(96 116)(97 117)(98 118)(197 334)(198 335)(199 336)(200 337)(201 338)(202 339)(203 340)(204 341)(205 342)(206 343)(207 344)(208 345)(209 346)(210 347)(211 348)(212 349)(213 350)(214 351)(215 352)(216 353)(217 354)(218 355)(219 356)(220 357)(221 358)(222 359)(223 360)(224 361)(225 362)(226 363)(227 364)(228 365)(229 366)(230 367)(231 368)(232 369)(233 370)(234 371)(235 372)(236 373)(237 374)(238 375)(239 376)(240 377)(241 378)(242 379)(243 380)(244 381)(245 382)(246 383)(247 384)(248 385)(249 386)(250 387)(251 388)(252 389)(253 390)(254 391)(255 392)(256 295)(257 296)(258 297)(259 298)(260 299)(261 300)(262 301)(263 302)(264 303)(265 304)(266 305)(267 306)(268 307)(269 308)(270 309)(271 310)(272 311)(273 312)(274 313)(275 314)(276 315)(277 316)(278 317)(279 318)(280 319)(281 320)(282 321)(283 322)(284 323)(285 324)(286 325)(287 326)(288 327)(289 328)(290 329)(291 330)(292 331)(293 332)(294 333)
(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)(99,334)(100,335)(101,336)(102,337)(103,338)(104,339)(105,340)(106,341)(107,342)(108,343)(109,344)(110,345)(111,346)(112,347)(113,348)(114,349)(115,350)(116,351)(117,352)(118,353)(119,354)(120,355)(121,356)(122,357)(123,358)(124,359)(125,360)(126,361)(127,362)(128,363)(129,364)(130,365)(131,366)(132,367)(133,368)(134,369)(135,370)(136,371)(137,372)(138,373)(139,374)(140,375)(141,376)(142,377)(143,378)(144,379)(145,380)(146,381)(147,382)(148,383)(149,384)(150,385)(151,386)(152,387)(153,388)(154,389)(155,390)(156,391)(157,392)(158,295)(159,296)(160,297)(161,298)(162,299)(163,300)(164,301)(165,302)(166,303)(167,304)(168,305)(169,306)(170,307)(171,308)(172,309)(173,310)(174,311)(175,312)(176,313)(177,314)(178,315)(179,316)(180,317)(181,318)(182,319)(183,320)(184,321)(185,322)(186,323)(187,324)(188,325)(189,326)(190,327)(191,328)(192,329)(193,330)(194,331)(195,332)(196,333), (1,119)(2,120)(3,121)(4,122)(5,123)(6,124)(7,125)(8,126)(9,127)(10,128)(11,129)(12,130)(13,131)(14,132)(15,133)(16,134)(17,135)(18,136)(19,137)(20,138)(21,139)(22,140)(23,141)(24,142)(25,143)(26,144)(27,145)(28,146)(29,147)(30,148)(31,149)(32,150)(33,151)(34,152)(35,153)(36,154)(37,155)(38,156)(39,157)(40,158)(41,159)(42,160)(43,161)(44,162)(45,163)(46,164)(47,165)(48,166)(49,167)(50,168)(51,169)(52,170)(53,171)(54,172)(55,173)(56,174)(57,175)(58,176)(59,177)(60,178)(61,179)(62,180)(63,181)(64,182)(65,183)(66,184)(67,185)(68,186)(69,187)(70,188)(71,189)(72,190)(73,191)(74,192)(75,193)(76,194)(77,195)(78,196)(79,99)(80,100)(81,101)(82,102)(83,103)(84,104)(85,105)(86,106)(87,107)(88,108)(89,109)(90,110)(91,111)(92,112)(93,113)(94,114)(95,115)(96,116)(97,117)(98,118)(197,334)(198,335)(199,336)(200,337)(201,338)(202,339)(203,340)(204,341)(205,342)(206,343)(207,344)(208,345)(209,346)(210,347)(211,348)(212,349)(213,350)(214,351)(215,352)(216,353)(217,354)(218,355)(219,356)(220,357)(221,358)(222,359)(223,360)(224,361)(225,362)(226,363)(227,364)(228,365)(229,366)(230,367)(231,368)(232,369)(233,370)(234,371)(235,372)(236,373)(237,374)(238,375)(239,376)(240,377)(241,378)(242,379)(243,380)(244,381)(245,382)(246,383)(247,384)(248,385)(249,386)(250,387)(251,388)(252,389)(253,390)(254,391)(255,392)(256,295)(257,296)(258,297)(259,298)(260,299)(261,300)(262,301)(263,302)(264,303)(265,304)(266,305)(267,306)(268,307)(269,308)(270,309)(271,310)(272,311)(273,312)(274,313)(275,314)(276,315)(277,316)(278,317)(279,318)(280,319)(281,320)(282,321)(283,322)(284,323)(285,324)(286,325)(287,326)(288,327)(289,328)(290,329)(291,330)(292,331)(293,332)(294,333), (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)(99,334)(100,335)(101,336)(102,337)(103,338)(104,339)(105,340)(106,341)(107,342)(108,343)(109,344)(110,345)(111,346)(112,347)(113,348)(114,349)(115,350)(116,351)(117,352)(118,353)(119,354)(120,355)(121,356)(122,357)(123,358)(124,359)(125,360)(126,361)(127,362)(128,363)(129,364)(130,365)(131,366)(132,367)(133,368)(134,369)(135,370)(136,371)(137,372)(138,373)(139,374)(140,375)(141,376)(142,377)(143,378)(144,379)(145,380)(146,381)(147,382)(148,383)(149,384)(150,385)(151,386)(152,387)(153,388)(154,389)(155,390)(156,391)(157,392)(158,295)(159,296)(160,297)(161,298)(162,299)(163,300)(164,301)(165,302)(166,303)(167,304)(168,305)(169,306)(170,307)(171,308)(172,309)(173,310)(174,311)(175,312)(176,313)(177,314)(178,315)(179,316)(180,317)(181,318)(182,319)(183,320)(184,321)(185,322)(186,323)(187,324)(188,325)(189,326)(190,327)(191,328)(192,329)(193,330)(194,331)(195,332)(196,333), (1,119)(2,120)(3,121)(4,122)(5,123)(6,124)(7,125)(8,126)(9,127)(10,128)(11,129)(12,130)(13,131)(14,132)(15,133)(16,134)(17,135)(18,136)(19,137)(20,138)(21,139)(22,140)(23,141)(24,142)(25,143)(26,144)(27,145)(28,146)(29,147)(30,148)(31,149)(32,150)(33,151)(34,152)(35,153)(36,154)(37,155)(38,156)(39,157)(40,158)(41,159)(42,160)(43,161)(44,162)(45,163)(46,164)(47,165)(48,166)(49,167)(50,168)(51,169)(52,170)(53,171)(54,172)(55,173)(56,174)(57,175)(58,176)(59,177)(60,178)(61,179)(62,180)(63,181)(64,182)(65,183)(66,184)(67,185)(68,186)(69,187)(70,188)(71,189)(72,190)(73,191)(74,192)(75,193)(76,194)(77,195)(78,196)(79,99)(80,100)(81,101)(82,102)(83,103)(84,104)(85,105)(86,106)(87,107)(88,108)(89,109)(90,110)(91,111)(92,112)(93,113)(94,114)(95,115)(96,116)(97,117)(98,118)(197,334)(198,335)(199,336)(200,337)(201,338)(202,339)(203,340)(204,341)(205,342)(206,343)(207,344)(208,345)(209,346)(210,347)(211,348)(212,349)(213,350)(214,351)(215,352)(216,353)(217,354)(218,355)(219,356)(220,357)(221,358)(222,359)(223,360)(224,361)(225,362)(226,363)(227,364)(228,365)(229,366)(230,367)(231,368)(232,369)(233,370)(234,371)(235,372)(236,373)(237,374)(238,375)(239,376)(240,377)(241,378)(242,379)(243,380)(244,381)(245,382)(246,383)(247,384)(248,385)(249,386)(250,387)(251,388)(252,389)(253,390)(254,391)(255,392)(256,295)(257,296)(258,297)(259,298)(260,299)(261,300)(262,301)(263,302)(264,303)(265,304)(266,305)(267,306)(268,307)(269,308)(270,309)(271,310)(272,311)(273,312)(274,313)(275,314)(276,315)(277,316)(278,317)(279,318)(280,319)(281,320)(282,321)(283,322)(284,323)(285,324)(286,325)(287,326)(288,327)(289,328)(290,329)(291,330)(292,331)(293,332)(294,333), (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),(99,334),(100,335),(101,336),(102,337),(103,338),(104,339),(105,340),(106,341),(107,342),(108,343),(109,344),(110,345),(111,346),(112,347),(113,348),(114,349),(115,350),(116,351),(117,352),(118,353),(119,354),(120,355),(121,356),(122,357),(123,358),(124,359),(125,360),(126,361),(127,362),(128,363),(129,364),(130,365),(131,366),(132,367),(133,368),(134,369),(135,370),(136,371),(137,372),(138,373),(139,374),(140,375),(141,376),(142,377),(143,378),(144,379),(145,380),(146,381),(147,382),(148,383),(149,384),(150,385),(151,386),(152,387),(153,388),(154,389),(155,390),(156,391),(157,392),(158,295),(159,296),(160,297),(161,298),(162,299),(163,300),(164,301),(165,302),(166,303),(167,304),(168,305),(169,306),(170,307),(171,308),(172,309),(173,310),(174,311),(175,312),(176,313),(177,314),(178,315),(179,316),(180,317),(181,318),(182,319),(183,320),(184,321),(185,322),(186,323),(187,324),(188,325),(189,326),(190,327),(191,328),(192,329),(193,330),(194,331),(195,332),(196,333)], [(1,119),(2,120),(3,121),(4,122),(5,123),(6,124),(7,125),(8,126),(9,127),(10,128),(11,129),(12,130),(13,131),(14,132),(15,133),(16,134),(17,135),(18,136),(19,137),(20,138),(21,139),(22,140),(23,141),(24,142),(25,143),(26,144),(27,145),(28,146),(29,147),(30,148),(31,149),(32,150),(33,151),(34,152),(35,153),(36,154),(37,155),(38,156),(39,157),(40,158),(41,159),(42,160),(43,161),(44,162),(45,163),(46,164),(47,165),(48,166),(49,167),(50,168),(51,169),(52,170),(53,171),(54,172),(55,173),(56,174),(57,175),(58,176),(59,177),(60,178),(61,179),(62,180),(63,181),(64,182),(65,183),(66,184),(67,185),(68,186),(69,187),(70,188),(71,189),(72,190),(73,191),(74,192),(75,193),(76,194),(77,195),(78,196),(79,99),(80,100),(81,101),(82,102),(83,103),(84,104),(85,105),(86,106),(87,107),(88,108),(89,109),(90,110),(91,111),(92,112),(93,113),(94,114),(95,115),(96,116),(97,117),(98,118),(197,334),(198,335),(199,336),(200,337),(201,338),(202,339),(203,340),(204,341),(205,342),(206,343),(207,344),(208,345),(209,346),(210,347),(211,348),(212,349),(213,350),(214,351),(215,352),(216,353),(217,354),(218,355),(219,356),(220,357),(221,358),(222,359),(223,360),(224,361),(225,362),(226,363),(227,364),(228,365),(229,366),(230,367),(231,368),(232,369),(233,370),(234,371),(235,372),(236,373),(237,374),(238,375),(239,376),(240,377),(241,378),(242,379),(243,380),(244,381),(245,382),(246,383),(247,384),(248,385),(249,386),(250,387),(251,388),(252,389),(253,390),(254,391),(255,392),(256,295),(257,296),(258,297),(259,298),(260,299),(261,300),(262,301),(263,302),(264,303),(265,304),(266,305),(267,306),(268,307),(269,308),(270,309),(271,310),(272,311),(273,312),(274,313),(275,314),(276,315),(277,316),(278,317),(279,318),(280,319),(281,320),(282,321),(283,322),(284,323),(285,324),(286,325),(287,326),(288,327),(289,328),(290,329),(291,330),(292,331),(293,332),(294,333)], [(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···2G7A···7F14A···14AP49A···49AP98A···98KH
order12···27···714···1449···4998···98
size11···11···11···11···11···1

392 irreducible representations

dim111111
type++
imageC1C2C7C14C49C98
kernelC22×C98C2×C98C22×C14C2×C14C23C22
# reps1764242294

Matrix representation of C22×C98 in GL3(𝔽197) generated by

100
01960
00196
,
100
01960
001
,
18100
0550
00134
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

Export

Subgroup lattice of C22×C98 in TeX

׿
×
𝔽