Copied to
clipboard

G = C22×C118order 472 = 23·59

Abelian group of type [2,2,118]

direct product, abelian, monomial, 2-elementary

Aliases: C22×C118, SmallGroup(472,12)

Series: Derived Chief Lower central Upper central

C1 — C22×C118
C1C59C118C2×C118 — C22×C118
C1 — C22×C118
C1 — C22×C118

Generators and relations for C22×C118
 G = < a,b,c | a2=b2=c118=1, ab=ba, ac=ca, bc=cb >


Smallest permutation representation of C22×C118
Regular action on 472 points
Generators in S472
(1 353)(2 354)(3 237)(4 238)(5 239)(6 240)(7 241)(8 242)(9 243)(10 244)(11 245)(12 246)(13 247)(14 248)(15 249)(16 250)(17 251)(18 252)(19 253)(20 254)(21 255)(22 256)(23 257)(24 258)(25 259)(26 260)(27 261)(28 262)(29 263)(30 264)(31 265)(32 266)(33 267)(34 268)(35 269)(36 270)(37 271)(38 272)(39 273)(40 274)(41 275)(42 276)(43 277)(44 278)(45 279)(46 280)(47 281)(48 282)(49 283)(50 284)(51 285)(52 286)(53 287)(54 288)(55 289)(56 290)(57 291)(58 292)(59 293)(60 294)(61 295)(62 296)(63 297)(64 298)(65 299)(66 300)(67 301)(68 302)(69 303)(70 304)(71 305)(72 306)(73 307)(74 308)(75 309)(76 310)(77 311)(78 312)(79 313)(80 314)(81 315)(82 316)(83 317)(84 318)(85 319)(86 320)(87 321)(88 322)(89 323)(90 324)(91 325)(92 326)(93 327)(94 328)(95 329)(96 330)(97 331)(98 332)(99 333)(100 334)(101 335)(102 336)(103 337)(104 338)(105 339)(106 340)(107 341)(108 342)(109 343)(110 344)(111 345)(112 346)(113 347)(114 348)(115 349)(116 350)(117 351)(118 352)(119 379)(120 380)(121 381)(122 382)(123 383)(124 384)(125 385)(126 386)(127 387)(128 388)(129 389)(130 390)(131 391)(132 392)(133 393)(134 394)(135 395)(136 396)(137 397)(138 398)(139 399)(140 400)(141 401)(142 402)(143 403)(144 404)(145 405)(146 406)(147 407)(148 408)(149 409)(150 410)(151 411)(152 412)(153 413)(154 414)(155 415)(156 416)(157 417)(158 418)(159 419)(160 420)(161 421)(162 422)(163 423)(164 424)(165 425)(166 426)(167 427)(168 428)(169 429)(170 430)(171 431)(172 432)(173 433)(174 434)(175 435)(176 436)(177 437)(178 438)(179 439)(180 440)(181 441)(182 442)(183 443)(184 444)(185 445)(186 446)(187 447)(188 448)(189 449)(190 450)(191 451)(192 452)(193 453)(194 454)(195 455)(196 456)(197 457)(198 458)(199 459)(200 460)(201 461)(202 462)(203 463)(204 464)(205 465)(206 466)(207 467)(208 468)(209 469)(210 470)(211 471)(212 472)(213 355)(214 356)(215 357)(216 358)(217 359)(218 360)(219 361)(220 362)(221 363)(222 364)(223 365)(224 366)(225 367)(226 368)(227 369)(228 370)(229 371)(230 372)(231 373)(232 374)(233 375)(234 376)(235 377)(236 378)
(1 196)(2 197)(3 198)(4 199)(5 200)(6 201)(7 202)(8 203)(9 204)(10 205)(11 206)(12 207)(13 208)(14 209)(15 210)(16 211)(17 212)(18 213)(19 214)(20 215)(21 216)(22 217)(23 218)(24 219)(25 220)(26 221)(27 222)(28 223)(29 224)(30 225)(31 226)(32 227)(33 228)(34 229)(35 230)(36 231)(37 232)(38 233)(39 234)(40 235)(41 236)(42 119)(43 120)(44 121)(45 122)(46 123)(47 124)(48 125)(49 126)(50 127)(51 128)(52 129)(53 130)(54 131)(55 132)(56 133)(57 134)(58 135)(59 136)(60 137)(61 138)(62 139)(63 140)(64 141)(65 142)(66 143)(67 144)(68 145)(69 146)(70 147)(71 148)(72 149)(73 150)(74 151)(75 152)(76 153)(77 154)(78 155)(79 156)(80 157)(81 158)(82 159)(83 160)(84 161)(85 162)(86 163)(87 164)(88 165)(89 166)(90 167)(91 168)(92 169)(93 170)(94 171)(95 172)(96 173)(97 174)(98 175)(99 176)(100 177)(101 178)(102 179)(103 180)(104 181)(105 182)(106 183)(107 184)(108 185)(109 186)(110 187)(111 188)(112 189)(113 190)(114 191)(115 192)(116 193)(117 194)(118 195)(237 458)(238 459)(239 460)(240 461)(241 462)(242 463)(243 464)(244 465)(245 466)(246 467)(247 468)(248 469)(249 470)(250 471)(251 472)(252 355)(253 356)(254 357)(255 358)(256 359)(257 360)(258 361)(259 362)(260 363)(261 364)(262 365)(263 366)(264 367)(265 368)(266 369)(267 370)(268 371)(269 372)(270 373)(271 374)(272 375)(273 376)(274 377)(275 378)(276 379)(277 380)(278 381)(279 382)(280 383)(281 384)(282 385)(283 386)(284 387)(285 388)(286 389)(287 390)(288 391)(289 392)(290 393)(291 394)(292 395)(293 396)(294 397)(295 398)(296 399)(297 400)(298 401)(299 402)(300 403)(301 404)(302 405)(303 406)(304 407)(305 408)(306 409)(307 410)(308 411)(309 412)(310 413)(311 414)(312 415)(313 416)(314 417)(315 418)(316 419)(317 420)(318 421)(319 422)(320 423)(321 424)(322 425)(323 426)(324 427)(325 428)(326 429)(327 430)(328 431)(329 432)(330 433)(331 434)(332 435)(333 436)(334 437)(335 438)(336 439)(337 440)(338 441)(339 442)(340 443)(341 444)(342 445)(343 446)(344 447)(345 448)(346 449)(347 450)(348 451)(349 452)(350 453)(351 454)(352 455)(353 456)(354 457)
(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)(355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472)

G:=sub<Sym(472)| (1,353)(2,354)(3,237)(4,238)(5,239)(6,240)(7,241)(8,242)(9,243)(10,244)(11,245)(12,246)(13,247)(14,248)(15,249)(16,250)(17,251)(18,252)(19,253)(20,254)(21,255)(22,256)(23,257)(24,258)(25,259)(26,260)(27,261)(28,262)(29,263)(30,264)(31,265)(32,266)(33,267)(34,268)(35,269)(36,270)(37,271)(38,272)(39,273)(40,274)(41,275)(42,276)(43,277)(44,278)(45,279)(46,280)(47,281)(48,282)(49,283)(50,284)(51,285)(52,286)(53,287)(54,288)(55,289)(56,290)(57,291)(58,292)(59,293)(60,294)(61,295)(62,296)(63,297)(64,298)(65,299)(66,300)(67,301)(68,302)(69,303)(70,304)(71,305)(72,306)(73,307)(74,308)(75,309)(76,310)(77,311)(78,312)(79,313)(80,314)(81,315)(82,316)(83,317)(84,318)(85,319)(86,320)(87,321)(88,322)(89,323)(90,324)(91,325)(92,326)(93,327)(94,328)(95,329)(96,330)(97,331)(98,332)(99,333)(100,334)(101,335)(102,336)(103,337)(104,338)(105,339)(106,340)(107,341)(108,342)(109,343)(110,344)(111,345)(112,346)(113,347)(114,348)(115,349)(116,350)(117,351)(118,352)(119,379)(120,380)(121,381)(122,382)(123,383)(124,384)(125,385)(126,386)(127,387)(128,388)(129,389)(130,390)(131,391)(132,392)(133,393)(134,394)(135,395)(136,396)(137,397)(138,398)(139,399)(140,400)(141,401)(142,402)(143,403)(144,404)(145,405)(146,406)(147,407)(148,408)(149,409)(150,410)(151,411)(152,412)(153,413)(154,414)(155,415)(156,416)(157,417)(158,418)(159,419)(160,420)(161,421)(162,422)(163,423)(164,424)(165,425)(166,426)(167,427)(168,428)(169,429)(170,430)(171,431)(172,432)(173,433)(174,434)(175,435)(176,436)(177,437)(178,438)(179,439)(180,440)(181,441)(182,442)(183,443)(184,444)(185,445)(186,446)(187,447)(188,448)(189,449)(190,450)(191,451)(192,452)(193,453)(194,454)(195,455)(196,456)(197,457)(198,458)(199,459)(200,460)(201,461)(202,462)(203,463)(204,464)(205,465)(206,466)(207,467)(208,468)(209,469)(210,470)(211,471)(212,472)(213,355)(214,356)(215,357)(216,358)(217,359)(218,360)(219,361)(220,362)(221,363)(222,364)(223,365)(224,366)(225,367)(226,368)(227,369)(228,370)(229,371)(230,372)(231,373)(232,374)(233,375)(234,376)(235,377)(236,378), (1,196)(2,197)(3,198)(4,199)(5,200)(6,201)(7,202)(8,203)(9,204)(10,205)(11,206)(12,207)(13,208)(14,209)(15,210)(16,211)(17,212)(18,213)(19,214)(20,215)(21,216)(22,217)(23,218)(24,219)(25,220)(26,221)(27,222)(28,223)(29,224)(30,225)(31,226)(32,227)(33,228)(34,229)(35,230)(36,231)(37,232)(38,233)(39,234)(40,235)(41,236)(42,119)(43,120)(44,121)(45,122)(46,123)(47,124)(48,125)(49,126)(50,127)(51,128)(52,129)(53,130)(54,131)(55,132)(56,133)(57,134)(58,135)(59,136)(60,137)(61,138)(62,139)(63,140)(64,141)(65,142)(66,143)(67,144)(68,145)(69,146)(70,147)(71,148)(72,149)(73,150)(74,151)(75,152)(76,153)(77,154)(78,155)(79,156)(80,157)(81,158)(82,159)(83,160)(84,161)(85,162)(86,163)(87,164)(88,165)(89,166)(90,167)(91,168)(92,169)(93,170)(94,171)(95,172)(96,173)(97,174)(98,175)(99,176)(100,177)(101,178)(102,179)(103,180)(104,181)(105,182)(106,183)(107,184)(108,185)(109,186)(110,187)(111,188)(112,189)(113,190)(114,191)(115,192)(116,193)(117,194)(118,195)(237,458)(238,459)(239,460)(240,461)(241,462)(242,463)(243,464)(244,465)(245,466)(246,467)(247,468)(248,469)(249,470)(250,471)(251,472)(252,355)(253,356)(254,357)(255,358)(256,359)(257,360)(258,361)(259,362)(260,363)(261,364)(262,365)(263,366)(264,367)(265,368)(266,369)(267,370)(268,371)(269,372)(270,373)(271,374)(272,375)(273,376)(274,377)(275,378)(276,379)(277,380)(278,381)(279,382)(280,383)(281,384)(282,385)(283,386)(284,387)(285,388)(286,389)(287,390)(288,391)(289,392)(290,393)(291,394)(292,395)(293,396)(294,397)(295,398)(296,399)(297,400)(298,401)(299,402)(300,403)(301,404)(302,405)(303,406)(304,407)(305,408)(306,409)(307,410)(308,411)(309,412)(310,413)(311,414)(312,415)(313,416)(314,417)(315,418)(316,419)(317,420)(318,421)(319,422)(320,423)(321,424)(322,425)(323,426)(324,427)(325,428)(326,429)(327,430)(328,431)(329,432)(330,433)(331,434)(332,435)(333,436)(334,437)(335,438)(336,439)(337,440)(338,441)(339,442)(340,443)(341,444)(342,445)(343,446)(344,447)(345,448)(346,449)(347,450)(348,451)(349,452)(350,453)(351,454)(352,455)(353,456)(354,457), (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)(355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472)>;

G:=Group( (1,353)(2,354)(3,237)(4,238)(5,239)(6,240)(7,241)(8,242)(9,243)(10,244)(11,245)(12,246)(13,247)(14,248)(15,249)(16,250)(17,251)(18,252)(19,253)(20,254)(21,255)(22,256)(23,257)(24,258)(25,259)(26,260)(27,261)(28,262)(29,263)(30,264)(31,265)(32,266)(33,267)(34,268)(35,269)(36,270)(37,271)(38,272)(39,273)(40,274)(41,275)(42,276)(43,277)(44,278)(45,279)(46,280)(47,281)(48,282)(49,283)(50,284)(51,285)(52,286)(53,287)(54,288)(55,289)(56,290)(57,291)(58,292)(59,293)(60,294)(61,295)(62,296)(63,297)(64,298)(65,299)(66,300)(67,301)(68,302)(69,303)(70,304)(71,305)(72,306)(73,307)(74,308)(75,309)(76,310)(77,311)(78,312)(79,313)(80,314)(81,315)(82,316)(83,317)(84,318)(85,319)(86,320)(87,321)(88,322)(89,323)(90,324)(91,325)(92,326)(93,327)(94,328)(95,329)(96,330)(97,331)(98,332)(99,333)(100,334)(101,335)(102,336)(103,337)(104,338)(105,339)(106,340)(107,341)(108,342)(109,343)(110,344)(111,345)(112,346)(113,347)(114,348)(115,349)(116,350)(117,351)(118,352)(119,379)(120,380)(121,381)(122,382)(123,383)(124,384)(125,385)(126,386)(127,387)(128,388)(129,389)(130,390)(131,391)(132,392)(133,393)(134,394)(135,395)(136,396)(137,397)(138,398)(139,399)(140,400)(141,401)(142,402)(143,403)(144,404)(145,405)(146,406)(147,407)(148,408)(149,409)(150,410)(151,411)(152,412)(153,413)(154,414)(155,415)(156,416)(157,417)(158,418)(159,419)(160,420)(161,421)(162,422)(163,423)(164,424)(165,425)(166,426)(167,427)(168,428)(169,429)(170,430)(171,431)(172,432)(173,433)(174,434)(175,435)(176,436)(177,437)(178,438)(179,439)(180,440)(181,441)(182,442)(183,443)(184,444)(185,445)(186,446)(187,447)(188,448)(189,449)(190,450)(191,451)(192,452)(193,453)(194,454)(195,455)(196,456)(197,457)(198,458)(199,459)(200,460)(201,461)(202,462)(203,463)(204,464)(205,465)(206,466)(207,467)(208,468)(209,469)(210,470)(211,471)(212,472)(213,355)(214,356)(215,357)(216,358)(217,359)(218,360)(219,361)(220,362)(221,363)(222,364)(223,365)(224,366)(225,367)(226,368)(227,369)(228,370)(229,371)(230,372)(231,373)(232,374)(233,375)(234,376)(235,377)(236,378), (1,196)(2,197)(3,198)(4,199)(5,200)(6,201)(7,202)(8,203)(9,204)(10,205)(11,206)(12,207)(13,208)(14,209)(15,210)(16,211)(17,212)(18,213)(19,214)(20,215)(21,216)(22,217)(23,218)(24,219)(25,220)(26,221)(27,222)(28,223)(29,224)(30,225)(31,226)(32,227)(33,228)(34,229)(35,230)(36,231)(37,232)(38,233)(39,234)(40,235)(41,236)(42,119)(43,120)(44,121)(45,122)(46,123)(47,124)(48,125)(49,126)(50,127)(51,128)(52,129)(53,130)(54,131)(55,132)(56,133)(57,134)(58,135)(59,136)(60,137)(61,138)(62,139)(63,140)(64,141)(65,142)(66,143)(67,144)(68,145)(69,146)(70,147)(71,148)(72,149)(73,150)(74,151)(75,152)(76,153)(77,154)(78,155)(79,156)(80,157)(81,158)(82,159)(83,160)(84,161)(85,162)(86,163)(87,164)(88,165)(89,166)(90,167)(91,168)(92,169)(93,170)(94,171)(95,172)(96,173)(97,174)(98,175)(99,176)(100,177)(101,178)(102,179)(103,180)(104,181)(105,182)(106,183)(107,184)(108,185)(109,186)(110,187)(111,188)(112,189)(113,190)(114,191)(115,192)(116,193)(117,194)(118,195)(237,458)(238,459)(239,460)(240,461)(241,462)(242,463)(243,464)(244,465)(245,466)(246,467)(247,468)(248,469)(249,470)(250,471)(251,472)(252,355)(253,356)(254,357)(255,358)(256,359)(257,360)(258,361)(259,362)(260,363)(261,364)(262,365)(263,366)(264,367)(265,368)(266,369)(267,370)(268,371)(269,372)(270,373)(271,374)(272,375)(273,376)(274,377)(275,378)(276,379)(277,380)(278,381)(279,382)(280,383)(281,384)(282,385)(283,386)(284,387)(285,388)(286,389)(287,390)(288,391)(289,392)(290,393)(291,394)(292,395)(293,396)(294,397)(295,398)(296,399)(297,400)(298,401)(299,402)(300,403)(301,404)(302,405)(303,406)(304,407)(305,408)(306,409)(307,410)(308,411)(309,412)(310,413)(311,414)(312,415)(313,416)(314,417)(315,418)(316,419)(317,420)(318,421)(319,422)(320,423)(321,424)(322,425)(323,426)(324,427)(325,428)(326,429)(327,430)(328,431)(329,432)(330,433)(331,434)(332,435)(333,436)(334,437)(335,438)(336,439)(337,440)(338,441)(339,442)(340,443)(341,444)(342,445)(343,446)(344,447)(345,448)(346,449)(347,450)(348,451)(349,452)(350,453)(351,454)(352,455)(353,456)(354,457), (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)(355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472) );

G=PermutationGroup([(1,353),(2,354),(3,237),(4,238),(5,239),(6,240),(7,241),(8,242),(9,243),(10,244),(11,245),(12,246),(13,247),(14,248),(15,249),(16,250),(17,251),(18,252),(19,253),(20,254),(21,255),(22,256),(23,257),(24,258),(25,259),(26,260),(27,261),(28,262),(29,263),(30,264),(31,265),(32,266),(33,267),(34,268),(35,269),(36,270),(37,271),(38,272),(39,273),(40,274),(41,275),(42,276),(43,277),(44,278),(45,279),(46,280),(47,281),(48,282),(49,283),(50,284),(51,285),(52,286),(53,287),(54,288),(55,289),(56,290),(57,291),(58,292),(59,293),(60,294),(61,295),(62,296),(63,297),(64,298),(65,299),(66,300),(67,301),(68,302),(69,303),(70,304),(71,305),(72,306),(73,307),(74,308),(75,309),(76,310),(77,311),(78,312),(79,313),(80,314),(81,315),(82,316),(83,317),(84,318),(85,319),(86,320),(87,321),(88,322),(89,323),(90,324),(91,325),(92,326),(93,327),(94,328),(95,329),(96,330),(97,331),(98,332),(99,333),(100,334),(101,335),(102,336),(103,337),(104,338),(105,339),(106,340),(107,341),(108,342),(109,343),(110,344),(111,345),(112,346),(113,347),(114,348),(115,349),(116,350),(117,351),(118,352),(119,379),(120,380),(121,381),(122,382),(123,383),(124,384),(125,385),(126,386),(127,387),(128,388),(129,389),(130,390),(131,391),(132,392),(133,393),(134,394),(135,395),(136,396),(137,397),(138,398),(139,399),(140,400),(141,401),(142,402),(143,403),(144,404),(145,405),(146,406),(147,407),(148,408),(149,409),(150,410),(151,411),(152,412),(153,413),(154,414),(155,415),(156,416),(157,417),(158,418),(159,419),(160,420),(161,421),(162,422),(163,423),(164,424),(165,425),(166,426),(167,427),(168,428),(169,429),(170,430),(171,431),(172,432),(173,433),(174,434),(175,435),(176,436),(177,437),(178,438),(179,439),(180,440),(181,441),(182,442),(183,443),(184,444),(185,445),(186,446),(187,447),(188,448),(189,449),(190,450),(191,451),(192,452),(193,453),(194,454),(195,455),(196,456),(197,457),(198,458),(199,459),(200,460),(201,461),(202,462),(203,463),(204,464),(205,465),(206,466),(207,467),(208,468),(209,469),(210,470),(211,471),(212,472),(213,355),(214,356),(215,357),(216,358),(217,359),(218,360),(219,361),(220,362),(221,363),(222,364),(223,365),(224,366),(225,367),(226,368),(227,369),(228,370),(229,371),(230,372),(231,373),(232,374),(233,375),(234,376),(235,377),(236,378)], [(1,196),(2,197),(3,198),(4,199),(5,200),(6,201),(7,202),(8,203),(9,204),(10,205),(11,206),(12,207),(13,208),(14,209),(15,210),(16,211),(17,212),(18,213),(19,214),(20,215),(21,216),(22,217),(23,218),(24,219),(25,220),(26,221),(27,222),(28,223),(29,224),(30,225),(31,226),(32,227),(33,228),(34,229),(35,230),(36,231),(37,232),(38,233),(39,234),(40,235),(41,236),(42,119),(43,120),(44,121),(45,122),(46,123),(47,124),(48,125),(49,126),(50,127),(51,128),(52,129),(53,130),(54,131),(55,132),(56,133),(57,134),(58,135),(59,136),(60,137),(61,138),(62,139),(63,140),(64,141),(65,142),(66,143),(67,144),(68,145),(69,146),(70,147),(71,148),(72,149),(73,150),(74,151),(75,152),(76,153),(77,154),(78,155),(79,156),(80,157),(81,158),(82,159),(83,160),(84,161),(85,162),(86,163),(87,164),(88,165),(89,166),(90,167),(91,168),(92,169),(93,170),(94,171),(95,172),(96,173),(97,174),(98,175),(99,176),(100,177),(101,178),(102,179),(103,180),(104,181),(105,182),(106,183),(107,184),(108,185),(109,186),(110,187),(111,188),(112,189),(113,190),(114,191),(115,192),(116,193),(117,194),(118,195),(237,458),(238,459),(239,460),(240,461),(241,462),(242,463),(243,464),(244,465),(245,466),(246,467),(247,468),(248,469),(249,470),(250,471),(251,472),(252,355),(253,356),(254,357),(255,358),(256,359),(257,360),(258,361),(259,362),(260,363),(261,364),(262,365),(263,366),(264,367),(265,368),(266,369),(267,370),(268,371),(269,372),(270,373),(271,374),(272,375),(273,376),(274,377),(275,378),(276,379),(277,380),(278,381),(279,382),(280,383),(281,384),(282,385),(283,386),(284,387),(285,388),(286,389),(287,390),(288,391),(289,392),(290,393),(291,394),(292,395),(293,396),(294,397),(295,398),(296,399),(297,400),(298,401),(299,402),(300,403),(301,404),(302,405),(303,406),(304,407),(305,408),(306,409),(307,410),(308,411),(309,412),(310,413),(311,414),(312,415),(313,416),(314,417),(315,418),(316,419),(317,420),(318,421),(319,422),(320,423),(321,424),(322,425),(323,426),(324,427),(325,428),(326,429),(327,430),(328,431),(329,432),(330,433),(331,434),(332,435),(333,436),(334,437),(335,438),(336,439),(337,440),(338,441),(339,442),(340,443),(341,444),(342,445),(343,446),(344,447),(345,448),(346,449),(347,450),(348,451),(349,452),(350,453),(351,454),(352,455),(353,456),(354,457)], [(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),(355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472)])

472 conjugacy classes

class 1 2A···2G59A···59BF118A···118OP
order12···259···59118···118
size11···11···11···1

472 irreducible representations

dim1111
type++
imageC1C2C59C118
kernelC22×C118C2×C118C23C22
# reps1758406

Matrix representation of C22×C118 in GL3(𝔽709) generated by

70800
07080
00708
,
100
07080
001
,
4400
06650
00627
G:=sub<GL(3,GF(709))| [708,0,0,0,708,0,0,0,708],[1,0,0,0,708,0,0,0,1],[44,0,0,0,665,0,0,0,627] >;

C22×C118 in GAP, Magma, Sage, TeX

C_2^2\times C_{118}
% in TeX

G:=Group("C2^2xC118");
// GroupNames label

G:=SmallGroup(472,12);
// by ID

G=gap.SmallGroup(472,12);
# by ID

G:=PCGroup([4,-2,-2,-2,-59]);
// Polycyclic

G:=Group<a,b,c|a^2=b^2=c^118=1,a*b=b*a,a*c=c*a,b*c=c*b>;
// generators/relations

Export

Subgroup lattice of C22×C118 in TeX

׿
×
𝔽