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G = C22×C122order 488 = 23·61

Abelian group of type [2,2,122]

direct product, abelian, monomial, 2-elementary

Aliases: C22×C122, SmallGroup(488,14)

Series: Derived Chief Lower central Upper central

C1 — C22×C122
C1C61C122C2×C122 — C22×C122
C1 — C22×C122
C1 — C22×C122

Generators and relations for C22×C122
 G = < a,b,c | a2=b2=c122=1, ab=ba, ac=ca, bc=cb >


Smallest permutation representation of C22×C122
Regular action on 488 points
Generators in S488
(1 344)(2 345)(3 346)(4 347)(5 348)(6 349)(7 350)(8 351)(9 352)(10 353)(11 354)(12 355)(13 356)(14 357)(15 358)(16 359)(17 360)(18 361)(19 362)(20 363)(21 364)(22 365)(23 366)(24 245)(25 246)(26 247)(27 248)(28 249)(29 250)(30 251)(31 252)(32 253)(33 254)(34 255)(35 256)(36 257)(37 258)(38 259)(39 260)(40 261)(41 262)(42 263)(43 264)(44 265)(45 266)(46 267)(47 268)(48 269)(49 270)(50 271)(51 272)(52 273)(53 274)(54 275)(55 276)(56 277)(57 278)(58 279)(59 280)(60 281)(61 282)(62 283)(63 284)(64 285)(65 286)(66 287)(67 288)(68 289)(69 290)(70 291)(71 292)(72 293)(73 294)(74 295)(75 296)(76 297)(77 298)(78 299)(79 300)(80 301)(81 302)(82 303)(83 304)(84 305)(85 306)(86 307)(87 308)(88 309)(89 310)(90 311)(91 312)(92 313)(93 314)(94 315)(95 316)(96 317)(97 318)(98 319)(99 320)(100 321)(101 322)(102 323)(103 324)(104 325)(105 326)(106 327)(107 328)(108 329)(109 330)(110 331)(111 332)(112 333)(113 334)(114 335)(115 336)(116 337)(117 338)(118 339)(119 340)(120 341)(121 342)(122 343)(123 376)(124 377)(125 378)(126 379)(127 380)(128 381)(129 382)(130 383)(131 384)(132 385)(133 386)(134 387)(135 388)(136 389)(137 390)(138 391)(139 392)(140 393)(141 394)(142 395)(143 396)(144 397)(145 398)(146 399)(147 400)(148 401)(149 402)(150 403)(151 404)(152 405)(153 406)(154 407)(155 408)(156 409)(157 410)(158 411)(159 412)(160 413)(161 414)(162 415)(163 416)(164 417)(165 418)(166 419)(167 420)(168 421)(169 422)(170 423)(171 424)(172 425)(173 426)(174 427)(175 428)(176 429)(177 430)(178 431)(179 432)(180 433)(181 434)(182 435)(183 436)(184 437)(185 438)(186 439)(187 440)(188 441)(189 442)(190 443)(191 444)(192 445)(193 446)(194 447)(195 448)(196 449)(197 450)(198 451)(199 452)(200 453)(201 454)(202 455)(203 456)(204 457)(205 458)(206 459)(207 460)(208 461)(209 462)(210 463)(211 464)(212 465)(213 466)(214 467)(215 468)(216 469)(217 470)(218 471)(219 472)(220 473)(221 474)(222 475)(223 476)(224 477)(225 478)(226 479)(227 480)(228 481)(229 482)(230 483)(231 484)(232 485)(233 486)(234 487)(235 488)(236 367)(237 368)(238 369)(239 370)(240 371)(241 372)(242 373)(243 374)(244 375)
(1 208)(2 209)(3 210)(4 211)(5 212)(6 213)(7 214)(8 215)(9 216)(10 217)(11 218)(12 219)(13 220)(14 221)(15 222)(16 223)(17 224)(18 225)(19 226)(20 227)(21 228)(22 229)(23 230)(24 231)(25 232)(26 233)(27 234)(28 235)(29 236)(30 237)(31 238)(32 239)(33 240)(34 241)(35 242)(36 243)(37 244)(38 123)(39 124)(40 125)(41 126)(42 127)(43 128)(44 129)(45 130)(46 131)(47 132)(48 133)(49 134)(50 135)(51 136)(52 137)(53 138)(54 139)(55 140)(56 141)(57 142)(58 143)(59 144)(60 145)(61 146)(62 147)(63 148)(64 149)(65 150)(66 151)(67 152)(68 153)(69 154)(70 155)(71 156)(72 157)(73 158)(74 159)(75 160)(76 161)(77 162)(78 163)(79 164)(80 165)(81 166)(82 167)(83 168)(84 169)(85 170)(86 171)(87 172)(88 173)(89 174)(90 175)(91 176)(92 177)(93 178)(94 179)(95 180)(96 181)(97 182)(98 183)(99 184)(100 185)(101 186)(102 187)(103 188)(104 189)(105 190)(106 191)(107 192)(108 193)(109 194)(110 195)(111 196)(112 197)(113 198)(114 199)(115 200)(116 201)(117 202)(118 203)(119 204)(120 205)(121 206)(122 207)(245 484)(246 485)(247 486)(248 487)(249 488)(250 367)(251 368)(252 369)(253 370)(254 371)(255 372)(256 373)(257 374)(258 375)(259 376)(260 377)(261 378)(262 379)(263 380)(264 381)(265 382)(266 383)(267 384)(268 385)(269 386)(270 387)(271 388)(272 389)(273 390)(274 391)(275 392)(276 393)(277 394)(278 395)(279 396)(280 397)(281 398)(282 399)(283 400)(284 401)(285 402)(286 403)(287 404)(288 405)(289 406)(290 407)(291 408)(292 409)(293 410)(294 411)(295 412)(296 413)(297 414)(298 415)(299 416)(300 417)(301 418)(302 419)(303 420)(304 421)(305 422)(306 423)(307 424)(308 425)(309 426)(310 427)(311 428)(312 429)(313 430)(314 431)(315 432)(316 433)(317 434)(318 435)(319 436)(320 437)(321 438)(322 439)(323 440)(324 441)(325 442)(326 443)(327 444)(328 445)(329 446)(330 447)(331 448)(332 449)(333 450)(334 451)(335 452)(336 453)(337 454)(338 455)(339 456)(340 457)(341 458)(342 459)(343 460)(344 461)(345 462)(346 463)(347 464)(348 465)(349 466)(350 467)(351 468)(352 469)(353 470)(354 471)(355 472)(356 473)(357 474)(358 475)(359 476)(360 477)(361 478)(362 479)(363 480)(364 481)(365 482)(366 483)
(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)(367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488)

G:=sub<Sym(488)| (1,344)(2,345)(3,346)(4,347)(5,348)(6,349)(7,350)(8,351)(9,352)(10,353)(11,354)(12,355)(13,356)(14,357)(15,358)(16,359)(17,360)(18,361)(19,362)(20,363)(21,364)(22,365)(23,366)(24,245)(25,246)(26,247)(27,248)(28,249)(29,250)(30,251)(31,252)(32,253)(33,254)(34,255)(35,256)(36,257)(37,258)(38,259)(39,260)(40,261)(41,262)(42,263)(43,264)(44,265)(45,266)(46,267)(47,268)(48,269)(49,270)(50,271)(51,272)(52,273)(53,274)(54,275)(55,276)(56,277)(57,278)(58,279)(59,280)(60,281)(61,282)(62,283)(63,284)(64,285)(65,286)(66,287)(67,288)(68,289)(69,290)(70,291)(71,292)(72,293)(73,294)(74,295)(75,296)(76,297)(77,298)(78,299)(79,300)(80,301)(81,302)(82,303)(83,304)(84,305)(85,306)(86,307)(87,308)(88,309)(89,310)(90,311)(91,312)(92,313)(93,314)(94,315)(95,316)(96,317)(97,318)(98,319)(99,320)(100,321)(101,322)(102,323)(103,324)(104,325)(105,326)(106,327)(107,328)(108,329)(109,330)(110,331)(111,332)(112,333)(113,334)(114,335)(115,336)(116,337)(117,338)(118,339)(119,340)(120,341)(121,342)(122,343)(123,376)(124,377)(125,378)(126,379)(127,380)(128,381)(129,382)(130,383)(131,384)(132,385)(133,386)(134,387)(135,388)(136,389)(137,390)(138,391)(139,392)(140,393)(141,394)(142,395)(143,396)(144,397)(145,398)(146,399)(147,400)(148,401)(149,402)(150,403)(151,404)(152,405)(153,406)(154,407)(155,408)(156,409)(157,410)(158,411)(159,412)(160,413)(161,414)(162,415)(163,416)(164,417)(165,418)(166,419)(167,420)(168,421)(169,422)(170,423)(171,424)(172,425)(173,426)(174,427)(175,428)(176,429)(177,430)(178,431)(179,432)(180,433)(181,434)(182,435)(183,436)(184,437)(185,438)(186,439)(187,440)(188,441)(189,442)(190,443)(191,444)(192,445)(193,446)(194,447)(195,448)(196,449)(197,450)(198,451)(199,452)(200,453)(201,454)(202,455)(203,456)(204,457)(205,458)(206,459)(207,460)(208,461)(209,462)(210,463)(211,464)(212,465)(213,466)(214,467)(215,468)(216,469)(217,470)(218,471)(219,472)(220,473)(221,474)(222,475)(223,476)(224,477)(225,478)(226,479)(227,480)(228,481)(229,482)(230,483)(231,484)(232,485)(233,486)(234,487)(235,488)(236,367)(237,368)(238,369)(239,370)(240,371)(241,372)(242,373)(243,374)(244,375), (1,208)(2,209)(3,210)(4,211)(5,212)(6,213)(7,214)(8,215)(9,216)(10,217)(11,218)(12,219)(13,220)(14,221)(15,222)(16,223)(17,224)(18,225)(19,226)(20,227)(21,228)(22,229)(23,230)(24,231)(25,232)(26,233)(27,234)(28,235)(29,236)(30,237)(31,238)(32,239)(33,240)(34,241)(35,242)(36,243)(37,244)(38,123)(39,124)(40,125)(41,126)(42,127)(43,128)(44,129)(45,130)(46,131)(47,132)(48,133)(49,134)(50,135)(51,136)(52,137)(53,138)(54,139)(55,140)(56,141)(57,142)(58,143)(59,144)(60,145)(61,146)(62,147)(63,148)(64,149)(65,150)(66,151)(67,152)(68,153)(69,154)(70,155)(71,156)(72,157)(73,158)(74,159)(75,160)(76,161)(77,162)(78,163)(79,164)(80,165)(81,166)(82,167)(83,168)(84,169)(85,170)(86,171)(87,172)(88,173)(89,174)(90,175)(91,176)(92,177)(93,178)(94,179)(95,180)(96,181)(97,182)(98,183)(99,184)(100,185)(101,186)(102,187)(103,188)(104,189)(105,190)(106,191)(107,192)(108,193)(109,194)(110,195)(111,196)(112,197)(113,198)(114,199)(115,200)(116,201)(117,202)(118,203)(119,204)(120,205)(121,206)(122,207)(245,484)(246,485)(247,486)(248,487)(249,488)(250,367)(251,368)(252,369)(253,370)(254,371)(255,372)(256,373)(257,374)(258,375)(259,376)(260,377)(261,378)(262,379)(263,380)(264,381)(265,382)(266,383)(267,384)(268,385)(269,386)(270,387)(271,388)(272,389)(273,390)(274,391)(275,392)(276,393)(277,394)(278,395)(279,396)(280,397)(281,398)(282,399)(283,400)(284,401)(285,402)(286,403)(287,404)(288,405)(289,406)(290,407)(291,408)(292,409)(293,410)(294,411)(295,412)(296,413)(297,414)(298,415)(299,416)(300,417)(301,418)(302,419)(303,420)(304,421)(305,422)(306,423)(307,424)(308,425)(309,426)(310,427)(311,428)(312,429)(313,430)(314,431)(315,432)(316,433)(317,434)(318,435)(319,436)(320,437)(321,438)(322,439)(323,440)(324,441)(325,442)(326,443)(327,444)(328,445)(329,446)(330,447)(331,448)(332,449)(333,450)(334,451)(335,452)(336,453)(337,454)(338,455)(339,456)(340,457)(341,458)(342,459)(343,460)(344,461)(345,462)(346,463)(347,464)(348,465)(349,466)(350,467)(351,468)(352,469)(353,470)(354,471)(355,472)(356,473)(357,474)(358,475)(359,476)(360,477)(361,478)(362,479)(363,480)(364,481)(365,482)(366,483), (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)(367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488)>;

G:=Group( (1,344)(2,345)(3,346)(4,347)(5,348)(6,349)(7,350)(8,351)(9,352)(10,353)(11,354)(12,355)(13,356)(14,357)(15,358)(16,359)(17,360)(18,361)(19,362)(20,363)(21,364)(22,365)(23,366)(24,245)(25,246)(26,247)(27,248)(28,249)(29,250)(30,251)(31,252)(32,253)(33,254)(34,255)(35,256)(36,257)(37,258)(38,259)(39,260)(40,261)(41,262)(42,263)(43,264)(44,265)(45,266)(46,267)(47,268)(48,269)(49,270)(50,271)(51,272)(52,273)(53,274)(54,275)(55,276)(56,277)(57,278)(58,279)(59,280)(60,281)(61,282)(62,283)(63,284)(64,285)(65,286)(66,287)(67,288)(68,289)(69,290)(70,291)(71,292)(72,293)(73,294)(74,295)(75,296)(76,297)(77,298)(78,299)(79,300)(80,301)(81,302)(82,303)(83,304)(84,305)(85,306)(86,307)(87,308)(88,309)(89,310)(90,311)(91,312)(92,313)(93,314)(94,315)(95,316)(96,317)(97,318)(98,319)(99,320)(100,321)(101,322)(102,323)(103,324)(104,325)(105,326)(106,327)(107,328)(108,329)(109,330)(110,331)(111,332)(112,333)(113,334)(114,335)(115,336)(116,337)(117,338)(118,339)(119,340)(120,341)(121,342)(122,343)(123,376)(124,377)(125,378)(126,379)(127,380)(128,381)(129,382)(130,383)(131,384)(132,385)(133,386)(134,387)(135,388)(136,389)(137,390)(138,391)(139,392)(140,393)(141,394)(142,395)(143,396)(144,397)(145,398)(146,399)(147,400)(148,401)(149,402)(150,403)(151,404)(152,405)(153,406)(154,407)(155,408)(156,409)(157,410)(158,411)(159,412)(160,413)(161,414)(162,415)(163,416)(164,417)(165,418)(166,419)(167,420)(168,421)(169,422)(170,423)(171,424)(172,425)(173,426)(174,427)(175,428)(176,429)(177,430)(178,431)(179,432)(180,433)(181,434)(182,435)(183,436)(184,437)(185,438)(186,439)(187,440)(188,441)(189,442)(190,443)(191,444)(192,445)(193,446)(194,447)(195,448)(196,449)(197,450)(198,451)(199,452)(200,453)(201,454)(202,455)(203,456)(204,457)(205,458)(206,459)(207,460)(208,461)(209,462)(210,463)(211,464)(212,465)(213,466)(214,467)(215,468)(216,469)(217,470)(218,471)(219,472)(220,473)(221,474)(222,475)(223,476)(224,477)(225,478)(226,479)(227,480)(228,481)(229,482)(230,483)(231,484)(232,485)(233,486)(234,487)(235,488)(236,367)(237,368)(238,369)(239,370)(240,371)(241,372)(242,373)(243,374)(244,375), (1,208)(2,209)(3,210)(4,211)(5,212)(6,213)(7,214)(8,215)(9,216)(10,217)(11,218)(12,219)(13,220)(14,221)(15,222)(16,223)(17,224)(18,225)(19,226)(20,227)(21,228)(22,229)(23,230)(24,231)(25,232)(26,233)(27,234)(28,235)(29,236)(30,237)(31,238)(32,239)(33,240)(34,241)(35,242)(36,243)(37,244)(38,123)(39,124)(40,125)(41,126)(42,127)(43,128)(44,129)(45,130)(46,131)(47,132)(48,133)(49,134)(50,135)(51,136)(52,137)(53,138)(54,139)(55,140)(56,141)(57,142)(58,143)(59,144)(60,145)(61,146)(62,147)(63,148)(64,149)(65,150)(66,151)(67,152)(68,153)(69,154)(70,155)(71,156)(72,157)(73,158)(74,159)(75,160)(76,161)(77,162)(78,163)(79,164)(80,165)(81,166)(82,167)(83,168)(84,169)(85,170)(86,171)(87,172)(88,173)(89,174)(90,175)(91,176)(92,177)(93,178)(94,179)(95,180)(96,181)(97,182)(98,183)(99,184)(100,185)(101,186)(102,187)(103,188)(104,189)(105,190)(106,191)(107,192)(108,193)(109,194)(110,195)(111,196)(112,197)(113,198)(114,199)(115,200)(116,201)(117,202)(118,203)(119,204)(120,205)(121,206)(122,207)(245,484)(246,485)(247,486)(248,487)(249,488)(250,367)(251,368)(252,369)(253,370)(254,371)(255,372)(256,373)(257,374)(258,375)(259,376)(260,377)(261,378)(262,379)(263,380)(264,381)(265,382)(266,383)(267,384)(268,385)(269,386)(270,387)(271,388)(272,389)(273,390)(274,391)(275,392)(276,393)(277,394)(278,395)(279,396)(280,397)(281,398)(282,399)(283,400)(284,401)(285,402)(286,403)(287,404)(288,405)(289,406)(290,407)(291,408)(292,409)(293,410)(294,411)(295,412)(296,413)(297,414)(298,415)(299,416)(300,417)(301,418)(302,419)(303,420)(304,421)(305,422)(306,423)(307,424)(308,425)(309,426)(310,427)(311,428)(312,429)(313,430)(314,431)(315,432)(316,433)(317,434)(318,435)(319,436)(320,437)(321,438)(322,439)(323,440)(324,441)(325,442)(326,443)(327,444)(328,445)(329,446)(330,447)(331,448)(332,449)(333,450)(334,451)(335,452)(336,453)(337,454)(338,455)(339,456)(340,457)(341,458)(342,459)(343,460)(344,461)(345,462)(346,463)(347,464)(348,465)(349,466)(350,467)(351,468)(352,469)(353,470)(354,471)(355,472)(356,473)(357,474)(358,475)(359,476)(360,477)(361,478)(362,479)(363,480)(364,481)(365,482)(366,483), (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)(367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488) );

G=PermutationGroup([(1,344),(2,345),(3,346),(4,347),(5,348),(6,349),(7,350),(8,351),(9,352),(10,353),(11,354),(12,355),(13,356),(14,357),(15,358),(16,359),(17,360),(18,361),(19,362),(20,363),(21,364),(22,365),(23,366),(24,245),(25,246),(26,247),(27,248),(28,249),(29,250),(30,251),(31,252),(32,253),(33,254),(34,255),(35,256),(36,257),(37,258),(38,259),(39,260),(40,261),(41,262),(42,263),(43,264),(44,265),(45,266),(46,267),(47,268),(48,269),(49,270),(50,271),(51,272),(52,273),(53,274),(54,275),(55,276),(56,277),(57,278),(58,279),(59,280),(60,281),(61,282),(62,283),(63,284),(64,285),(65,286),(66,287),(67,288),(68,289),(69,290),(70,291),(71,292),(72,293),(73,294),(74,295),(75,296),(76,297),(77,298),(78,299),(79,300),(80,301),(81,302),(82,303),(83,304),(84,305),(85,306),(86,307),(87,308),(88,309),(89,310),(90,311),(91,312),(92,313),(93,314),(94,315),(95,316),(96,317),(97,318),(98,319),(99,320),(100,321),(101,322),(102,323),(103,324),(104,325),(105,326),(106,327),(107,328),(108,329),(109,330),(110,331),(111,332),(112,333),(113,334),(114,335),(115,336),(116,337),(117,338),(118,339),(119,340),(120,341),(121,342),(122,343),(123,376),(124,377),(125,378),(126,379),(127,380),(128,381),(129,382),(130,383),(131,384),(132,385),(133,386),(134,387),(135,388),(136,389),(137,390),(138,391),(139,392),(140,393),(141,394),(142,395),(143,396),(144,397),(145,398),(146,399),(147,400),(148,401),(149,402),(150,403),(151,404),(152,405),(153,406),(154,407),(155,408),(156,409),(157,410),(158,411),(159,412),(160,413),(161,414),(162,415),(163,416),(164,417),(165,418),(166,419),(167,420),(168,421),(169,422),(170,423),(171,424),(172,425),(173,426),(174,427),(175,428),(176,429),(177,430),(178,431),(179,432),(180,433),(181,434),(182,435),(183,436),(184,437),(185,438),(186,439),(187,440),(188,441),(189,442),(190,443),(191,444),(192,445),(193,446),(194,447),(195,448),(196,449),(197,450),(198,451),(199,452),(200,453),(201,454),(202,455),(203,456),(204,457),(205,458),(206,459),(207,460),(208,461),(209,462),(210,463),(211,464),(212,465),(213,466),(214,467),(215,468),(216,469),(217,470),(218,471),(219,472),(220,473),(221,474),(222,475),(223,476),(224,477),(225,478),(226,479),(227,480),(228,481),(229,482),(230,483),(231,484),(232,485),(233,486),(234,487),(235,488),(236,367),(237,368),(238,369),(239,370),(240,371),(241,372),(242,373),(243,374),(244,375)], [(1,208),(2,209),(3,210),(4,211),(5,212),(6,213),(7,214),(8,215),(9,216),(10,217),(11,218),(12,219),(13,220),(14,221),(15,222),(16,223),(17,224),(18,225),(19,226),(20,227),(21,228),(22,229),(23,230),(24,231),(25,232),(26,233),(27,234),(28,235),(29,236),(30,237),(31,238),(32,239),(33,240),(34,241),(35,242),(36,243),(37,244),(38,123),(39,124),(40,125),(41,126),(42,127),(43,128),(44,129),(45,130),(46,131),(47,132),(48,133),(49,134),(50,135),(51,136),(52,137),(53,138),(54,139),(55,140),(56,141),(57,142),(58,143),(59,144),(60,145),(61,146),(62,147),(63,148),(64,149),(65,150),(66,151),(67,152),(68,153),(69,154),(70,155),(71,156),(72,157),(73,158),(74,159),(75,160),(76,161),(77,162),(78,163),(79,164),(80,165),(81,166),(82,167),(83,168),(84,169),(85,170),(86,171),(87,172),(88,173),(89,174),(90,175),(91,176),(92,177),(93,178),(94,179),(95,180),(96,181),(97,182),(98,183),(99,184),(100,185),(101,186),(102,187),(103,188),(104,189),(105,190),(106,191),(107,192),(108,193),(109,194),(110,195),(111,196),(112,197),(113,198),(114,199),(115,200),(116,201),(117,202),(118,203),(119,204),(120,205),(121,206),(122,207),(245,484),(246,485),(247,486),(248,487),(249,488),(250,367),(251,368),(252,369),(253,370),(254,371),(255,372),(256,373),(257,374),(258,375),(259,376),(260,377),(261,378),(262,379),(263,380),(264,381),(265,382),(266,383),(267,384),(268,385),(269,386),(270,387),(271,388),(272,389),(273,390),(274,391),(275,392),(276,393),(277,394),(278,395),(279,396),(280,397),(281,398),(282,399),(283,400),(284,401),(285,402),(286,403),(287,404),(288,405),(289,406),(290,407),(291,408),(292,409),(293,410),(294,411),(295,412),(296,413),(297,414),(298,415),(299,416),(300,417),(301,418),(302,419),(303,420),(304,421),(305,422),(306,423),(307,424),(308,425),(309,426),(310,427),(311,428),(312,429),(313,430),(314,431),(315,432),(316,433),(317,434),(318,435),(319,436),(320,437),(321,438),(322,439),(323,440),(324,441),(325,442),(326,443),(327,444),(328,445),(329,446),(330,447),(331,448),(332,449),(333,450),(334,451),(335,452),(336,453),(337,454),(338,455),(339,456),(340,457),(341,458),(342,459),(343,460),(344,461),(345,462),(346,463),(347,464),(348,465),(349,466),(350,467),(351,468),(352,469),(353,470),(354,471),(355,472),(356,473),(357,474),(358,475),(359,476),(360,477),(361,478),(362,479),(363,480),(364,481),(365,482),(366,483)], [(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),(367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488)])

488 conjugacy classes

class 1 2A···2G61A···61BH122A···122PD
order12···261···61122···122
size11···11···11···1

488 irreducible representations

dim1111
type++
imageC1C2C61C122
kernelC22×C122C2×C122C23C22
# reps1760420

Matrix representation of C22×C122 in GL3(𝔽367) generated by

100
03660
00366
,
36600
010
001
,
26000
03400
0045
G:=sub<GL(3,GF(367))| [1,0,0,0,366,0,0,0,366],[366,0,0,0,1,0,0,0,1],[260,0,0,0,340,0,0,0,45] >;

C22×C122 in GAP, Magma, Sage, TeX

C_2^2\times C_{122}
% in TeX

G:=Group("C2^2xC122");
// GroupNames label

G:=SmallGroup(488,14);
// by ID

G=gap.SmallGroup(488,14);
# by ID

G:=PCGroup([4,-2,-2,-2,-61]);
// Polycyclic

G:=Group<a,b,c|a^2=b^2=c^122=1,a*b=b*a,a*c=c*a,b*c=c*b>;
// generators/relations

Export

Subgroup lattice of C22×C122 in TeX

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