direct product, abelian, monomial, 2-elementary
Aliases: C23×C62, SmallGroup(496,42)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C23×C62 |
| C1 — C23×C62 |
| C1 — C23×C62 |
Generators and relations for C23×C62
G = < a,b,c,d | a2=b2=c2=d62=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, cd=dc >
Subgroups: 134, all normal (4 characteristic)
C1, C2, C22, C23, C24, C31, C62, C2×C62, C22×C62, C23×C62
Quotients: C1, C2, C22, C23, C24, C31, C62, C2×C62, C22×C62, C23×C62
►Regular action on 496 points
Generators in S496
(1 307)(2 308)(3 309)(4 310)(5 249)(6 250)(7 251)(8 252)(9 253)(10 254)(11 255)(12 256)(13 257)(14 258)(15 259)(16 260)(17 261)(18 262)(19 263)(20 264)(21 265)(22 266)(23 267)(24 268)(25 269)(26 270)(27 271)(28 272)(29 273)(30 274)(31 275)(32 276)(33 277)(34 278)(35 279)(36 280)(37 281)(38 282)(39 283)(40 284)(41 285)(42 286)(43 287)(44 288)(45 289)(46 290)(47 291)(48 292)(49 293)(50 294)(51 295)(52 296)(53 297)(54 298)(55 299)(56 300)(57 301)(58 302)(59 303)(60 304)(61 305)(62 306)(63 358)(64 359)(65 360)(66 361)(67 362)(68 363)(69 364)(70 365)(71 366)(72 367)(73 368)(74 369)(75 370)(76 371)(77 372)(78 311)(79 312)(80 313)(81 314)(82 315)(83 316)(84 317)(85 318)(86 319)(87 320)(88 321)(89 322)(90 323)(91 324)(92 325)(93 326)(94 327)(95 328)(96 329)(97 330)(98 331)(99 332)(100 333)(101 334)(102 335)(103 336)(104 337)(105 338)(106 339)(107 340)(108 341)(109 342)(110 343)(111 344)(112 345)(113 346)(114 347)(115 348)(116 349)(117 350)(118 351)(119 352)(120 353)(121 354)(122 355)(123 356)(124 357)(125 425)(126 426)(127 427)(128 428)(129 429)(130 430)(131 431)(132 432)(133 433)(134 434)(135 373)(136 374)(137 375)(138 376)(139 377)(140 378)(141 379)(142 380)(143 381)(144 382)(145 383)(146 384)(147 385)(148 386)(149 387)(150 388)(151 389)(152 390)(153 391)(154 392)(155 393)(156 394)(157 395)(158 396)(159 397)(160 398)(161 399)(162 400)(163 401)(164 402)(165 403)(166 404)(167 405)(168 406)(169 407)(170 408)(171 409)(172 410)(173 411)(174 412)(175 413)(176 414)(177 415)(178 416)(179 417)(180 418)(181 419)(182 420)(183 421)(184 422)(185 423)(186 424)(187 453)(188 454)(189 455)(190 456)(191 457)(192 458)(193 459)(194 460)(195 461)(196 462)(197 463)(198 464)(199 465)(200 466)(201 467)(202 468)(203 469)(204 470)(205 471)(206 472)(207 473)(208 474)(209 475)(210 476)(211 477)(212 478)(213 479)(214 480)(215 481)(216 482)(217 483)(218 484)(219 485)(220 486)(221 487)(222 488)(223 489)(224 490)(225 491)(226 492)(227 493)(228 494)(229 495)(230 496)(231 435)(232 436)(233 437)(234 438)(235 439)(236 440)(237 441)(238 442)(239 443)(240 444)(241 445)(242 446)(243 447)(244 448)(245 449)(246 450)(247 451)(248 452)
(1 174)(2 175)(3 176)(4 177)(5 178)(6 179)(7 180)(8 181)(9 182)(10 183)(11 184)(12 185)(13 186)(14 125)(15 126)(16 127)(17 128)(18 129)(19 130)(20 131)(21 132)(22 133)(23 134)(24 135)(25 136)(26 137)(27 138)(28 139)(29 140)(30 141)(31 142)(32 143)(33 144)(34 145)(35 146)(36 147)(37 148)(38 149)(39 150)(40 151)(41 152)(42 153)(43 154)(44 155)(45 156)(46 157)(47 158)(48 159)(49 160)(50 161)(51 162)(52 163)(53 164)(54 165)(55 166)(56 167)(57 168)(58 169)(59 170)(60 171)(61 172)(62 173)(63 226)(64 227)(65 228)(66 229)(67 230)(68 231)(69 232)(70 233)(71 234)(72 235)(73 236)(74 237)(75 238)(76 239)(77 240)(78 241)(79 242)(80 243)(81 244)(82 245)(83 246)(84 247)(85 248)(86 187)(87 188)(88 189)(89 190)(90 191)(91 192)(92 193)(93 194)(94 195)(95 196)(96 197)(97 198)(98 199)(99 200)(100 201)(101 202)(102 203)(103 204)(104 205)(105 206)(106 207)(107 208)(108 209)(109 210)(110 211)(111 212)(112 213)(113 214)(114 215)(115 216)(116 217)(117 218)(118 219)(119 220)(120 221)(121 222)(122 223)(123 224)(124 225)(249 416)(250 417)(251 418)(252 419)(253 420)(254 421)(255 422)(256 423)(257 424)(258 425)(259 426)(260 427)(261 428)(262 429)(263 430)(264 431)(265 432)(266 433)(267 434)(268 373)(269 374)(270 375)(271 376)(272 377)(273 378)(274 379)(275 380)(276 381)(277 382)(278 383)(279 384)(280 385)(281 386)(282 387)(283 388)(284 389)(285 390)(286 391)(287 392)(288 393)(289 394)(290 395)(291 396)(292 397)(293 398)(294 399)(295 400)(296 401)(297 402)(298 403)(299 404)(300 405)(301 406)(302 407)(303 408)(304 409)(305 410)(306 411)(307 412)(308 413)(309 414)(310 415)(311 445)(312 446)(313 447)(314 448)(315 449)(316 450)(317 451)(318 452)(319 453)(320 454)(321 455)(322 456)(323 457)(324 458)(325 459)(326 460)(327 461)(328 462)(329 463)(330 464)(331 465)(332 466)(333 467)(334 468)(335 469)(336 470)(337 471)(338 472)(339 473)(340 474)(341 475)(342 476)(343 477)(344 478)(345 479)(346 480)(347 481)(348 482)(349 483)(350 484)(351 485)(352 486)(353 487)(354 488)(355 489)(356 490)(357 491)(358 492)(359 493)(360 494)(361 495)(362 496)(363 435)(364 436)(365 437)(366 438)(367 439)(368 440)(369 441)(370 442)(371 443)(372 444)
(1 118)(2 119)(3 120)(4 121)(5 122)(6 123)(7 124)(8 63)(9 64)(10 65)(11 66)(12 67)(13 68)(14 69)(15 70)(16 71)(17 72)(18 73)(19 74)(20 75)(21 76)(22 77)(23 78)(24 79)(25 80)(26 81)(27 82)(28 83)(29 84)(30 85)(31 86)(32 87)(33 88)(34 89)(35 90)(36 91)(37 92)(38 93)(39 94)(40 95)(41 96)(42 97)(43 98)(44 99)(45 100)(46 101)(47 102)(48 103)(49 104)(50 105)(51 106)(52 107)(53 108)(54 109)(55 110)(56 111)(57 112)(58 113)(59 114)(60 115)(61 116)(62 117)(125 232)(126 233)(127 234)(128 235)(129 236)(130 237)(131 238)(132 239)(133 240)(134 241)(135 242)(136 243)(137 244)(138 245)(139 246)(140 247)(141 248)(142 187)(143 188)(144 189)(145 190)(146 191)(147 192)(148 193)(149 194)(150 195)(151 196)(152 197)(153 198)(154 199)(155 200)(156 201)(157 202)(158 203)(159 204)(160 205)(161 206)(162 207)(163 208)(164 209)(165 210)(166 211)(167 212)(168 213)(169 214)(170 215)(171 216)(172 217)(173 218)(174 219)(175 220)(176 221)(177 222)(178 223)(179 224)(180 225)(181 226)(182 227)(183 228)(184 229)(185 230)(186 231)(249 355)(250 356)(251 357)(252 358)(253 359)(254 360)(255 361)(256 362)(257 363)(258 364)(259 365)(260 366)(261 367)(262 368)(263 369)(264 370)(265 371)(266 372)(267 311)(268 312)(269 313)(270 314)(271 315)(272 316)(273 317)(274 318)(275 319)(276 320)(277 321)(278 322)(279 323)(280 324)(281 325)(282 326)(283 327)(284 328)(285 329)(286 330)(287 331)(288 332)(289 333)(290 334)(291 335)(292 336)(293 337)(294 338)(295 339)(296 340)(297 341)(298 342)(299 343)(300 344)(301 345)(302 346)(303 347)(304 348)(305 349)(306 350)(307 351)(308 352)(309 353)(310 354)(373 446)(374 447)(375 448)(376 449)(377 450)(378 451)(379 452)(380 453)(381 454)(382 455)(383 456)(384 457)(385 458)(386 459)(387 460)(388 461)(389 462)(390 463)(391 464)(392 465)(393 466)(394 467)(395 468)(396 469)(397 470)(398 471)(399 472)(400 473)(401 474)(402 475)(403 476)(404 477)(405 478)(406 479)(407 480)(408 481)(409 482)(410 483)(411 484)(412 485)(413 486)(414 487)(415 488)(416 489)(417 490)(418 491)(419 492)(420 493)(421 494)(422 495)(423 496)(424 435)(425 436)(426 437)(427 438)(428 439)(429 440)(430 441)(431 442)(432 443)(433 444)(434 445)
(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)(435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496)
G:=sub<Sym(496)| (1,307)(2,308)(3,309)(4,310)(5,249)(6,250)(7,251)(8,252)(9,253)(10,254)(11,255)(12,256)(13,257)(14,258)(15,259)(16,260)(17,261)(18,262)(19,263)(20,264)(21,265)(22,266)(23,267)(24,268)(25,269)(26,270)(27,271)(28,272)(29,273)(30,274)(31,275)(32,276)(33,277)(34,278)(35,279)(36,280)(37,281)(38,282)(39,283)(40,284)(41,285)(42,286)(43,287)(44,288)(45,289)(46,290)(47,291)(48,292)(49,293)(50,294)(51,295)(52,296)(53,297)(54,298)(55,299)(56,300)(57,301)(58,302)(59,303)(60,304)(61,305)(62,306)(63,358)(64,359)(65,360)(66,361)(67,362)(68,363)(69,364)(70,365)(71,366)(72,367)(73,368)(74,369)(75,370)(76,371)(77,372)(78,311)(79,312)(80,313)(81,314)(82,315)(83,316)(84,317)(85,318)(86,319)(87,320)(88,321)(89,322)(90,323)(91,324)(92,325)(93,326)(94,327)(95,328)(96,329)(97,330)(98,331)(99,332)(100,333)(101,334)(102,335)(103,336)(104,337)(105,338)(106,339)(107,340)(108,341)(109,342)(110,343)(111,344)(112,345)(113,346)(114,347)(115,348)(116,349)(117,350)(118,351)(119,352)(120,353)(121,354)(122,355)(123,356)(124,357)(125,425)(126,426)(127,427)(128,428)(129,429)(130,430)(131,431)(132,432)(133,433)(134,434)(135,373)(136,374)(137,375)(138,376)(139,377)(140,378)(141,379)(142,380)(143,381)(144,382)(145,383)(146,384)(147,385)(148,386)(149,387)(150,388)(151,389)(152,390)(153,391)(154,392)(155,393)(156,394)(157,395)(158,396)(159,397)(160,398)(161,399)(162,400)(163,401)(164,402)(165,403)(166,404)(167,405)(168,406)(169,407)(170,408)(171,409)(172,410)(173,411)(174,412)(175,413)(176,414)(177,415)(178,416)(179,417)(180,418)(181,419)(182,420)(183,421)(184,422)(185,423)(186,424)(187,453)(188,454)(189,455)(190,456)(191,457)(192,458)(193,459)(194,460)(195,461)(196,462)(197,463)(198,464)(199,465)(200,466)(201,467)(202,468)(203,469)(204,470)(205,471)(206,472)(207,473)(208,474)(209,475)(210,476)(211,477)(212,478)(213,479)(214,480)(215,481)(216,482)(217,483)(218,484)(219,485)(220,486)(221,487)(222,488)(223,489)(224,490)(225,491)(226,492)(227,493)(228,494)(229,495)(230,496)(231,435)(232,436)(233,437)(234,438)(235,439)(236,440)(237,441)(238,442)(239,443)(240,444)(241,445)(242,446)(243,447)(244,448)(245,449)(246,450)(247,451)(248,452), (1,174)(2,175)(3,176)(4,177)(5,178)(6,179)(7,180)(8,181)(9,182)(10,183)(11,184)(12,185)(13,186)(14,125)(15,126)(16,127)(17,128)(18,129)(19,130)(20,131)(21,132)(22,133)(23,134)(24,135)(25,136)(26,137)(27,138)(28,139)(29,140)(30,141)(31,142)(32,143)(33,144)(34,145)(35,146)(36,147)(37,148)(38,149)(39,150)(40,151)(41,152)(42,153)(43,154)(44,155)(45,156)(46,157)(47,158)(48,159)(49,160)(50,161)(51,162)(52,163)(53,164)(54,165)(55,166)(56,167)(57,168)(58,169)(59,170)(60,171)(61,172)(62,173)(63,226)(64,227)(65,228)(66,229)(67,230)(68,231)(69,232)(70,233)(71,234)(72,235)(73,236)(74,237)(75,238)(76,239)(77,240)(78,241)(79,242)(80,243)(81,244)(82,245)(83,246)(84,247)(85,248)(86,187)(87,188)(88,189)(89,190)(90,191)(91,192)(92,193)(93,194)(94,195)(95,196)(96,197)(97,198)(98,199)(99,200)(100,201)(101,202)(102,203)(103,204)(104,205)(105,206)(106,207)(107,208)(108,209)(109,210)(110,211)(111,212)(112,213)(113,214)(114,215)(115,216)(116,217)(117,218)(118,219)(119,220)(120,221)(121,222)(122,223)(123,224)(124,225)(249,416)(250,417)(251,418)(252,419)(253,420)(254,421)(255,422)(256,423)(257,424)(258,425)(259,426)(260,427)(261,428)(262,429)(263,430)(264,431)(265,432)(266,433)(267,434)(268,373)(269,374)(270,375)(271,376)(272,377)(273,378)(274,379)(275,380)(276,381)(277,382)(278,383)(279,384)(280,385)(281,386)(282,387)(283,388)(284,389)(285,390)(286,391)(287,392)(288,393)(289,394)(290,395)(291,396)(292,397)(293,398)(294,399)(295,400)(296,401)(297,402)(298,403)(299,404)(300,405)(301,406)(302,407)(303,408)(304,409)(305,410)(306,411)(307,412)(308,413)(309,414)(310,415)(311,445)(312,446)(313,447)(314,448)(315,449)(316,450)(317,451)(318,452)(319,453)(320,454)(321,455)(322,456)(323,457)(324,458)(325,459)(326,460)(327,461)(328,462)(329,463)(330,464)(331,465)(332,466)(333,467)(334,468)(335,469)(336,470)(337,471)(338,472)(339,473)(340,474)(341,475)(342,476)(343,477)(344,478)(345,479)(346,480)(347,481)(348,482)(349,483)(350,484)(351,485)(352,486)(353,487)(354,488)(355,489)(356,490)(357,491)(358,492)(359,493)(360,494)(361,495)(362,496)(363,435)(364,436)(365,437)(366,438)(367,439)(368,440)(369,441)(370,442)(371,443)(372,444), (1,118)(2,119)(3,120)(4,121)(5,122)(6,123)(7,124)(8,63)(9,64)(10,65)(11,66)(12,67)(13,68)(14,69)(15,70)(16,71)(17,72)(18,73)(19,74)(20,75)(21,76)(22,77)(23,78)(24,79)(25,80)(26,81)(27,82)(28,83)(29,84)(30,85)(31,86)(32,87)(33,88)(34,89)(35,90)(36,91)(37,92)(38,93)(39,94)(40,95)(41,96)(42,97)(43,98)(44,99)(45,100)(46,101)(47,102)(48,103)(49,104)(50,105)(51,106)(52,107)(53,108)(54,109)(55,110)(56,111)(57,112)(58,113)(59,114)(60,115)(61,116)(62,117)(125,232)(126,233)(127,234)(128,235)(129,236)(130,237)(131,238)(132,239)(133,240)(134,241)(135,242)(136,243)(137,244)(138,245)(139,246)(140,247)(141,248)(142,187)(143,188)(144,189)(145,190)(146,191)(147,192)(148,193)(149,194)(150,195)(151,196)(152,197)(153,198)(154,199)(155,200)(156,201)(157,202)(158,203)(159,204)(160,205)(161,206)(162,207)(163,208)(164,209)(165,210)(166,211)(167,212)(168,213)(169,214)(170,215)(171,216)(172,217)(173,218)(174,219)(175,220)(176,221)(177,222)(178,223)(179,224)(180,225)(181,226)(182,227)(183,228)(184,229)(185,230)(186,231)(249,355)(250,356)(251,357)(252,358)(253,359)(254,360)(255,361)(256,362)(257,363)(258,364)(259,365)(260,366)(261,367)(262,368)(263,369)(264,370)(265,371)(266,372)(267,311)(268,312)(269,313)(270,314)(271,315)(272,316)(273,317)(274,318)(275,319)(276,320)(277,321)(278,322)(279,323)(280,324)(281,325)(282,326)(283,327)(284,328)(285,329)(286,330)(287,331)(288,332)(289,333)(290,334)(291,335)(292,336)(293,337)(294,338)(295,339)(296,340)(297,341)(298,342)(299,343)(300,344)(301,345)(302,346)(303,347)(304,348)(305,349)(306,350)(307,351)(308,352)(309,353)(310,354)(373,446)(374,447)(375,448)(376,449)(377,450)(378,451)(379,452)(380,453)(381,454)(382,455)(383,456)(384,457)(385,458)(386,459)(387,460)(388,461)(389,462)(390,463)(391,464)(392,465)(393,466)(394,467)(395,468)(396,469)(397,470)(398,471)(399,472)(400,473)(401,474)(402,475)(403,476)(404,477)(405,478)(406,479)(407,480)(408,481)(409,482)(410,483)(411,484)(412,485)(413,486)(414,487)(415,488)(416,489)(417,490)(418,491)(419,492)(420,493)(421,494)(422,495)(423,496)(424,435)(425,436)(426,437)(427,438)(428,439)(429,440)(430,441)(431,442)(432,443)(433,444)(434,445), (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)(435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496)>;
G:=Group( (1,307)(2,308)(3,309)(4,310)(5,249)(6,250)(7,251)(8,252)(9,253)(10,254)(11,255)(12,256)(13,257)(14,258)(15,259)(16,260)(17,261)(18,262)(19,263)(20,264)(21,265)(22,266)(23,267)(24,268)(25,269)(26,270)(27,271)(28,272)(29,273)(30,274)(31,275)(32,276)(33,277)(34,278)(35,279)(36,280)(37,281)(38,282)(39,283)(40,284)(41,285)(42,286)(43,287)(44,288)(45,289)(46,290)(47,291)(48,292)(49,293)(50,294)(51,295)(52,296)(53,297)(54,298)(55,299)(56,300)(57,301)(58,302)(59,303)(60,304)(61,305)(62,306)(63,358)(64,359)(65,360)(66,361)(67,362)(68,363)(69,364)(70,365)(71,366)(72,367)(73,368)(74,369)(75,370)(76,371)(77,372)(78,311)(79,312)(80,313)(81,314)(82,315)(83,316)(84,317)(85,318)(86,319)(87,320)(88,321)(89,322)(90,323)(91,324)(92,325)(93,326)(94,327)(95,328)(96,329)(97,330)(98,331)(99,332)(100,333)(101,334)(102,335)(103,336)(104,337)(105,338)(106,339)(107,340)(108,341)(109,342)(110,343)(111,344)(112,345)(113,346)(114,347)(115,348)(116,349)(117,350)(118,351)(119,352)(120,353)(121,354)(122,355)(123,356)(124,357)(125,425)(126,426)(127,427)(128,428)(129,429)(130,430)(131,431)(132,432)(133,433)(134,434)(135,373)(136,374)(137,375)(138,376)(139,377)(140,378)(141,379)(142,380)(143,381)(144,382)(145,383)(146,384)(147,385)(148,386)(149,387)(150,388)(151,389)(152,390)(153,391)(154,392)(155,393)(156,394)(157,395)(158,396)(159,397)(160,398)(161,399)(162,400)(163,401)(164,402)(165,403)(166,404)(167,405)(168,406)(169,407)(170,408)(171,409)(172,410)(173,411)(174,412)(175,413)(176,414)(177,415)(178,416)(179,417)(180,418)(181,419)(182,420)(183,421)(184,422)(185,423)(186,424)(187,453)(188,454)(189,455)(190,456)(191,457)(192,458)(193,459)(194,460)(195,461)(196,462)(197,463)(198,464)(199,465)(200,466)(201,467)(202,468)(203,469)(204,470)(205,471)(206,472)(207,473)(208,474)(209,475)(210,476)(211,477)(212,478)(213,479)(214,480)(215,481)(216,482)(217,483)(218,484)(219,485)(220,486)(221,487)(222,488)(223,489)(224,490)(225,491)(226,492)(227,493)(228,494)(229,495)(230,496)(231,435)(232,436)(233,437)(234,438)(235,439)(236,440)(237,441)(238,442)(239,443)(240,444)(241,445)(242,446)(243,447)(244,448)(245,449)(246,450)(247,451)(248,452), (1,174)(2,175)(3,176)(4,177)(5,178)(6,179)(7,180)(8,181)(9,182)(10,183)(11,184)(12,185)(13,186)(14,125)(15,126)(16,127)(17,128)(18,129)(19,130)(20,131)(21,132)(22,133)(23,134)(24,135)(25,136)(26,137)(27,138)(28,139)(29,140)(30,141)(31,142)(32,143)(33,144)(34,145)(35,146)(36,147)(37,148)(38,149)(39,150)(40,151)(41,152)(42,153)(43,154)(44,155)(45,156)(46,157)(47,158)(48,159)(49,160)(50,161)(51,162)(52,163)(53,164)(54,165)(55,166)(56,167)(57,168)(58,169)(59,170)(60,171)(61,172)(62,173)(63,226)(64,227)(65,228)(66,229)(67,230)(68,231)(69,232)(70,233)(71,234)(72,235)(73,236)(74,237)(75,238)(76,239)(77,240)(78,241)(79,242)(80,243)(81,244)(82,245)(83,246)(84,247)(85,248)(86,187)(87,188)(88,189)(89,190)(90,191)(91,192)(92,193)(93,194)(94,195)(95,196)(96,197)(97,198)(98,199)(99,200)(100,201)(101,202)(102,203)(103,204)(104,205)(105,206)(106,207)(107,208)(108,209)(109,210)(110,211)(111,212)(112,213)(113,214)(114,215)(115,216)(116,217)(117,218)(118,219)(119,220)(120,221)(121,222)(122,223)(123,224)(124,225)(249,416)(250,417)(251,418)(252,419)(253,420)(254,421)(255,422)(256,423)(257,424)(258,425)(259,426)(260,427)(261,428)(262,429)(263,430)(264,431)(265,432)(266,433)(267,434)(268,373)(269,374)(270,375)(271,376)(272,377)(273,378)(274,379)(275,380)(276,381)(277,382)(278,383)(279,384)(280,385)(281,386)(282,387)(283,388)(284,389)(285,390)(286,391)(287,392)(288,393)(289,394)(290,395)(291,396)(292,397)(293,398)(294,399)(295,400)(296,401)(297,402)(298,403)(299,404)(300,405)(301,406)(302,407)(303,408)(304,409)(305,410)(306,411)(307,412)(308,413)(309,414)(310,415)(311,445)(312,446)(313,447)(314,448)(315,449)(316,450)(317,451)(318,452)(319,453)(320,454)(321,455)(322,456)(323,457)(324,458)(325,459)(326,460)(327,461)(328,462)(329,463)(330,464)(331,465)(332,466)(333,467)(334,468)(335,469)(336,470)(337,471)(338,472)(339,473)(340,474)(341,475)(342,476)(343,477)(344,478)(345,479)(346,480)(347,481)(348,482)(349,483)(350,484)(351,485)(352,486)(353,487)(354,488)(355,489)(356,490)(357,491)(358,492)(359,493)(360,494)(361,495)(362,496)(363,435)(364,436)(365,437)(366,438)(367,439)(368,440)(369,441)(370,442)(371,443)(372,444), (1,118)(2,119)(3,120)(4,121)(5,122)(6,123)(7,124)(8,63)(9,64)(10,65)(11,66)(12,67)(13,68)(14,69)(15,70)(16,71)(17,72)(18,73)(19,74)(20,75)(21,76)(22,77)(23,78)(24,79)(25,80)(26,81)(27,82)(28,83)(29,84)(30,85)(31,86)(32,87)(33,88)(34,89)(35,90)(36,91)(37,92)(38,93)(39,94)(40,95)(41,96)(42,97)(43,98)(44,99)(45,100)(46,101)(47,102)(48,103)(49,104)(50,105)(51,106)(52,107)(53,108)(54,109)(55,110)(56,111)(57,112)(58,113)(59,114)(60,115)(61,116)(62,117)(125,232)(126,233)(127,234)(128,235)(129,236)(130,237)(131,238)(132,239)(133,240)(134,241)(135,242)(136,243)(137,244)(138,245)(139,246)(140,247)(141,248)(142,187)(143,188)(144,189)(145,190)(146,191)(147,192)(148,193)(149,194)(150,195)(151,196)(152,197)(153,198)(154,199)(155,200)(156,201)(157,202)(158,203)(159,204)(160,205)(161,206)(162,207)(163,208)(164,209)(165,210)(166,211)(167,212)(168,213)(169,214)(170,215)(171,216)(172,217)(173,218)(174,219)(175,220)(176,221)(177,222)(178,223)(179,224)(180,225)(181,226)(182,227)(183,228)(184,229)(185,230)(186,231)(249,355)(250,356)(251,357)(252,358)(253,359)(254,360)(255,361)(256,362)(257,363)(258,364)(259,365)(260,366)(261,367)(262,368)(263,369)(264,370)(265,371)(266,372)(267,311)(268,312)(269,313)(270,314)(271,315)(272,316)(273,317)(274,318)(275,319)(276,320)(277,321)(278,322)(279,323)(280,324)(281,325)(282,326)(283,327)(284,328)(285,329)(286,330)(287,331)(288,332)(289,333)(290,334)(291,335)(292,336)(293,337)(294,338)(295,339)(296,340)(297,341)(298,342)(299,343)(300,344)(301,345)(302,346)(303,347)(304,348)(305,349)(306,350)(307,351)(308,352)(309,353)(310,354)(373,446)(374,447)(375,448)(376,449)(377,450)(378,451)(379,452)(380,453)(381,454)(382,455)(383,456)(384,457)(385,458)(386,459)(387,460)(388,461)(389,462)(390,463)(391,464)(392,465)(393,466)(394,467)(395,468)(396,469)(397,470)(398,471)(399,472)(400,473)(401,474)(402,475)(403,476)(404,477)(405,478)(406,479)(407,480)(408,481)(409,482)(410,483)(411,484)(412,485)(413,486)(414,487)(415,488)(416,489)(417,490)(418,491)(419,492)(420,493)(421,494)(422,495)(423,496)(424,435)(425,436)(426,437)(427,438)(428,439)(429,440)(430,441)(431,442)(432,443)(433,444)(434,445), (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)(435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496) );
G=PermutationGroup([[(1,307),(2,308),(3,309),(4,310),(5,249),(6,250),(7,251),(8,252),(9,253),(10,254),(11,255),(12,256),(13,257),(14,258),(15,259),(16,260),(17,261),(18,262),(19,263),(20,264),(21,265),(22,266),(23,267),(24,268),(25,269),(26,270),(27,271),(28,272),(29,273),(30,274),(31,275),(32,276),(33,277),(34,278),(35,279),(36,280),(37,281),(38,282),(39,283),(40,284),(41,285),(42,286),(43,287),(44,288),(45,289),(46,290),(47,291),(48,292),(49,293),(50,294),(51,295),(52,296),(53,297),(54,298),(55,299),(56,300),(57,301),(58,302),(59,303),(60,304),(61,305),(62,306),(63,358),(64,359),(65,360),(66,361),(67,362),(68,363),(69,364),(70,365),(71,366),(72,367),(73,368),(74,369),(75,370),(76,371),(77,372),(78,311),(79,312),(80,313),(81,314),(82,315),(83,316),(84,317),(85,318),(86,319),(87,320),(88,321),(89,322),(90,323),(91,324),(92,325),(93,326),(94,327),(95,328),(96,329),(97,330),(98,331),(99,332),(100,333),(101,334),(102,335),(103,336),(104,337),(105,338),(106,339),(107,340),(108,341),(109,342),(110,343),(111,344),(112,345),(113,346),(114,347),(115,348),(116,349),(117,350),(118,351),(119,352),(120,353),(121,354),(122,355),(123,356),(124,357),(125,425),(126,426),(127,427),(128,428),(129,429),(130,430),(131,431),(132,432),(133,433),(134,434),(135,373),(136,374),(137,375),(138,376),(139,377),(140,378),(141,379),(142,380),(143,381),(144,382),(145,383),(146,384),(147,385),(148,386),(149,387),(150,388),(151,389),(152,390),(153,391),(154,392),(155,393),(156,394),(157,395),(158,396),(159,397),(160,398),(161,399),(162,400),(163,401),(164,402),(165,403),(166,404),(167,405),(168,406),(169,407),(170,408),(171,409),(172,410),(173,411),(174,412),(175,413),(176,414),(177,415),(178,416),(179,417),(180,418),(181,419),(182,420),(183,421),(184,422),(185,423),(186,424),(187,453),(188,454),(189,455),(190,456),(191,457),(192,458),(193,459),(194,460),(195,461),(196,462),(197,463),(198,464),(199,465),(200,466),(201,467),(202,468),(203,469),(204,470),(205,471),(206,472),(207,473),(208,474),(209,475),(210,476),(211,477),(212,478),(213,479),(214,480),(215,481),(216,482),(217,483),(218,484),(219,485),(220,486),(221,487),(222,488),(223,489),(224,490),(225,491),(226,492),(227,493),(228,494),(229,495),(230,496),(231,435),(232,436),(233,437),(234,438),(235,439),(236,440),(237,441),(238,442),(239,443),(240,444),(241,445),(242,446),(243,447),(244,448),(245,449),(246,450),(247,451),(248,452)], [(1,174),(2,175),(3,176),(4,177),(5,178),(6,179),(7,180),(8,181),(9,182),(10,183),(11,184),(12,185),(13,186),(14,125),(15,126),(16,127),(17,128),(18,129),(19,130),(20,131),(21,132),(22,133),(23,134),(24,135),(25,136),(26,137),(27,138),(28,139),(29,140),(30,141),(31,142),(32,143),(33,144),(34,145),(35,146),(36,147),(37,148),(38,149),(39,150),(40,151),(41,152),(42,153),(43,154),(44,155),(45,156),(46,157),(47,158),(48,159),(49,160),(50,161),(51,162),(52,163),(53,164),(54,165),(55,166),(56,167),(57,168),(58,169),(59,170),(60,171),(61,172),(62,173),(63,226),(64,227),(65,228),(66,229),(67,230),(68,231),(69,232),(70,233),(71,234),(72,235),(73,236),(74,237),(75,238),(76,239),(77,240),(78,241),(79,242),(80,243),(81,244),(82,245),(83,246),(84,247),(85,248),(86,187),(87,188),(88,189),(89,190),(90,191),(91,192),(92,193),(93,194),(94,195),(95,196),(96,197),(97,198),(98,199),(99,200),(100,201),(101,202),(102,203),(103,204),(104,205),(105,206),(106,207),(107,208),(108,209),(109,210),(110,211),(111,212),(112,213),(113,214),(114,215),(115,216),(116,217),(117,218),(118,219),(119,220),(120,221),(121,222),(122,223),(123,224),(124,225),(249,416),(250,417),(251,418),(252,419),(253,420),(254,421),(255,422),(256,423),(257,424),(258,425),(259,426),(260,427),(261,428),(262,429),(263,430),(264,431),(265,432),(266,433),(267,434),(268,373),(269,374),(270,375),(271,376),(272,377),(273,378),(274,379),(275,380),(276,381),(277,382),(278,383),(279,384),(280,385),(281,386),(282,387),(283,388),(284,389),(285,390),(286,391),(287,392),(288,393),(289,394),(290,395),(291,396),(292,397),(293,398),(294,399),(295,400),(296,401),(297,402),(298,403),(299,404),(300,405),(301,406),(302,407),(303,408),(304,409),(305,410),(306,411),(307,412),(308,413),(309,414),(310,415),(311,445),(312,446),(313,447),(314,448),(315,449),(316,450),(317,451),(318,452),(319,453),(320,454),(321,455),(322,456),(323,457),(324,458),(325,459),(326,460),(327,461),(328,462),(329,463),(330,464),(331,465),(332,466),(333,467),(334,468),(335,469),(336,470),(337,471),(338,472),(339,473),(340,474),(341,475),(342,476),(343,477),(344,478),(345,479),(346,480),(347,481),(348,482),(349,483),(350,484),(351,485),(352,486),(353,487),(354,488),(355,489),(356,490),(357,491),(358,492),(359,493),(360,494),(361,495),(362,496),(363,435),(364,436),(365,437),(366,438),(367,439),(368,440),(369,441),(370,442),(371,443),(372,444)], [(1,118),(2,119),(3,120),(4,121),(5,122),(6,123),(7,124),(8,63),(9,64),(10,65),(11,66),(12,67),(13,68),(14,69),(15,70),(16,71),(17,72),(18,73),(19,74),(20,75),(21,76),(22,77),(23,78),(24,79),(25,80),(26,81),(27,82),(28,83),(29,84),(30,85),(31,86),(32,87),(33,88),(34,89),(35,90),(36,91),(37,92),(38,93),(39,94),(40,95),(41,96),(42,97),(43,98),(44,99),(45,100),(46,101),(47,102),(48,103),(49,104),(50,105),(51,106),(52,107),(53,108),(54,109),(55,110),(56,111),(57,112),(58,113),(59,114),(60,115),(61,116),(62,117),(125,232),(126,233),(127,234),(128,235),(129,236),(130,237),(131,238),(132,239),(133,240),(134,241),(135,242),(136,243),(137,244),(138,245),(139,246),(140,247),(141,248),(142,187),(143,188),(144,189),(145,190),(146,191),(147,192),(148,193),(149,194),(150,195),(151,196),(152,197),(153,198),(154,199),(155,200),(156,201),(157,202),(158,203),(159,204),(160,205),(161,206),(162,207),(163,208),(164,209),(165,210),(166,211),(167,212),(168,213),(169,214),(170,215),(171,216),(172,217),(173,218),(174,219),(175,220),(176,221),(177,222),(178,223),(179,224),(180,225),(181,226),(182,227),(183,228),(184,229),(185,230),(186,231),(249,355),(250,356),(251,357),(252,358),(253,359),(254,360),(255,361),(256,362),(257,363),(258,364),(259,365),(260,366),(261,367),(262,368),(263,369),(264,370),(265,371),(266,372),(267,311),(268,312),(269,313),(270,314),(271,315),(272,316),(273,317),(274,318),(275,319),(276,320),(277,321),(278,322),(279,323),(280,324),(281,325),(282,326),(283,327),(284,328),(285,329),(286,330),(287,331),(288,332),(289,333),(290,334),(291,335),(292,336),(293,337),(294,338),(295,339),(296,340),(297,341),(298,342),(299,343),(300,344),(301,345),(302,346),(303,347),(304,348),(305,349),(306,350),(307,351),(308,352),(309,353),(310,354),(373,446),(374,447),(375,448),(376,449),(377,450),(378,451),(379,452),(380,453),(381,454),(382,455),(383,456),(384,457),(385,458),(386,459),(387,460),(388,461),(389,462),(390,463),(391,464),(392,465),(393,466),(394,467),(395,468),(396,469),(397,470),(398,471),(399,472),(400,473),(401,474),(402,475),(403,476),(404,477),(405,478),(406,479),(407,480),(408,481),(409,482),(410,483),(411,484),(412,485),(413,486),(414,487),(415,488),(416,489),(417,490),(418,491),(419,492),(420,493),(421,494),(422,495),(423,496),(424,435),(425,436),(426,437),(427,438),(428,439),(429,440),(430,441),(431,442),(432,443),(433,444),(434,445)], [(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),(435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496)]])
496 conjugacy classes
| class | 1 | 2A | ··· | 2O | 31A | ··· | 31AD | 62A | ··· | 62QH |
| order | 1 | 2 | ··· | 2 | 31 | ··· | 31 | 62 | ··· | 62 |
| size | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
496 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | + | ||
| image | C1 | C2 | C31 | C62 |
| kernel | C23×C62 | C22×C62 | C24 | C23 |
| # reps | 1 | 15 | 30 | 450 |
Matrix representation of C23×C62 ►in GL4(𝔽311) generated by
| 1 | 0 | 0 | 0 |
| 0 | 310 | 0 | 0 |
| 0 | 0 | 310 | 0 |
| 0 | 0 | 0 | 310 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 310 | 0 |
| 0 | 0 | 0 | 1 |
| 310 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 310 | 0 |
| 0 | 0 | 0 | 310 |
| 142 | 0 | 0 | 0 |
| 0 | 18 | 0 | 0 |
| 0 | 0 | 41 | 0 |
| 0 | 0 | 0 | 20 |
G:=sub<GL(4,GF(311))| [1,0,0,0,0,310,0,0,0,0,310,0,0,0,0,310],[1,0,0,0,0,1,0,0,0,0,310,0,0,0,0,1],[310,0,0,0,0,1,0,0,0,0,310,0,0,0,0,310],[142,0,0,0,0,18,0,0,0,0,41,0,0,0,0,20] >;
C23×C62 in GAP, Magma, Sage, TeX
C_2^3\times C_{62} % in TeX
G:=Group("C2^3xC62"); // GroupNames label
G:=SmallGroup(496,42);
// by ID
G=gap.SmallGroup(496,42);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-31]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^2=c^2=d^62=1,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,c*d=d*c>;
// generators/relations