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G = C23×C62order 496 = 24·31

Abelian group of type [2,2,2,62]

direct product, abelian, monomial, 2-elementary

Aliases: C23×C62, SmallGroup(496,42)

Series: Derived Chief Lower central Upper central

C1 — C23×C62
C1C31C62C2×C62C22×C62 — 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 [×15], C22 [×35], C23 [×15], C24, C31, C62 [×15], C2×C62 [×35], C22×C62 [×15], C23×C62
Quotients: C1, C2 [×15], C22 [×35], C23 [×15], C24, C31, C62 [×15], C2×C62 [×35], C22×C62 [×15], C23×C62

Smallest permutation representation of C23×C62
Regular action on 496 points
Generators in S496
(1 286)(2 287)(3 288)(4 289)(5 290)(6 291)(7 292)(8 293)(9 294)(10 295)(11 296)(12 297)(13 298)(14 299)(15 300)(16 301)(17 302)(18 303)(19 304)(20 305)(21 306)(22 307)(23 308)(24 309)(25 310)(26 249)(27 250)(28 251)(29 252)(30 253)(31 254)(32 255)(33 256)(34 257)(35 258)(36 259)(37 260)(38 261)(39 262)(40 263)(41 264)(42 265)(43 266)(44 267)(45 268)(46 269)(47 270)(48 271)(49 272)(50 273)(51 274)(52 275)(53 276)(54 277)(55 278)(56 279)(57 280)(58 281)(59 282)(60 283)(61 284)(62 285)(63 313)(64 314)(65 315)(66 316)(67 317)(68 318)(69 319)(70 320)(71 321)(72 322)(73 323)(74 324)(75 325)(76 326)(77 327)(78 328)(79 329)(80 330)(81 331)(82 332)(83 333)(84 334)(85 335)(86 336)(87 337)(88 338)(89 339)(90 340)(91 341)(92 342)(93 343)(94 344)(95 345)(96 346)(97 347)(98 348)(99 349)(100 350)(101 351)(102 352)(103 353)(104 354)(105 355)(106 356)(107 357)(108 358)(109 359)(110 360)(111 361)(112 362)(113 363)(114 364)(115 365)(116 366)(117 367)(118 368)(119 369)(120 370)(121 371)(122 372)(123 311)(124 312)(125 414)(126 415)(127 416)(128 417)(129 418)(130 419)(131 420)(132 421)(133 422)(134 423)(135 424)(136 425)(137 426)(138 427)(139 428)(140 429)(141 430)(142 431)(143 432)(144 433)(145 434)(146 373)(147 374)(148 375)(149 376)(150 377)(151 378)(152 379)(153 380)(154 381)(155 382)(156 383)(157 384)(158 385)(159 386)(160 387)(161 388)(162 389)(163 390)(164 391)(165 392)(166 393)(167 394)(168 395)(169 396)(170 397)(171 398)(172 399)(173 400)(174 401)(175 402)(176 403)(177 404)(178 405)(179 406)(180 407)(181 408)(182 409)(183 410)(184 411)(185 412)(186 413)(187 495)(188 496)(189 435)(190 436)(191 437)(192 438)(193 439)(194 440)(195 441)(196 442)(197 443)(198 444)(199 445)(200 446)(201 447)(202 448)(203 449)(204 450)(205 451)(206 452)(207 453)(208 454)(209 455)(210 456)(211 457)(212 458)(213 459)(214 460)(215 461)(216 462)(217 463)(218 464)(219 465)(220 466)(221 467)(222 468)(223 469)(224 470)(225 471)(226 472)(227 473)(228 474)(229 475)(230 476)(231 477)(232 478)(233 479)(234 480)(235 481)(236 482)(237 483)(238 484)(239 485)(240 486)(241 487)(242 488)(243 489)(244 490)(245 491)(246 492)(247 493)(248 494)
(1 181)(2 182)(3 183)(4 184)(5 185)(6 186)(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)(63 198)(64 199)(65 200)(66 201)(67 202)(68 203)(69 204)(70 205)(71 206)(72 207)(73 208)(74 209)(75 210)(76 211)(77 212)(78 213)(79 214)(80 215)(81 216)(82 217)(83 218)(84 219)(85 220)(86 221)(87 222)(88 223)(89 224)(90 225)(91 226)(92 227)(93 228)(94 229)(95 230)(96 231)(97 232)(98 233)(99 234)(100 235)(101 236)(102 237)(103 238)(104 239)(105 240)(106 241)(107 242)(108 243)(109 244)(110 245)(111 246)(112 247)(113 248)(114 187)(115 188)(116 189)(117 190)(118 191)(119 192)(120 193)(121 194)(122 195)(123 196)(124 197)(249 433)(250 434)(251 373)(252 374)(253 375)(254 376)(255 377)(256 378)(257 379)(258 380)(259 381)(260 382)(261 383)(262 384)(263 385)(264 386)(265 387)(266 388)(267 389)(268 390)(269 391)(270 392)(271 393)(272 394)(273 395)(274 396)(275 397)(276 398)(277 399)(278 400)(279 401)(280 402)(281 403)(282 404)(283 405)(284 406)(285 407)(286 408)(287 409)(288 410)(289 411)(290 412)(291 413)(292 414)(293 415)(294 416)(295 417)(296 418)(297 419)(298 420)(299 421)(300 422)(301 423)(302 424)(303 425)(304 426)(305 427)(306 428)(307 429)(308 430)(309 431)(310 432)(311 442)(312 443)(313 444)(314 445)(315 446)(316 447)(317 448)(318 449)(319 450)(320 451)(321 452)(322 453)(323 454)(324 455)(325 456)(326 457)(327 458)(328 459)(329 460)(330 461)(331 462)(332 463)(333 464)(334 465)(335 466)(336 467)(337 468)(338 469)(339 470)(340 471)(341 472)(342 473)(343 474)(344 475)(345 476)(346 477)(347 478)(348 479)(349 480)(350 481)(351 482)(352 483)(353 484)(354 485)(355 486)(356 487)(357 488)(358 489)(359 490)(360 491)(361 492)(362 493)(363 494)(364 495)(365 496)(366 435)(367 436)(368 437)(369 438)(370 439)(371 440)(372 441)
(1 103)(2 104)(3 105)(4 106)(5 107)(6 108)(7 109)(8 110)(9 111)(10 112)(11 113)(12 114)(13 115)(14 116)(15 117)(16 118)(17 119)(18 120)(19 121)(20 122)(21 123)(22 124)(23 63)(24 64)(25 65)(26 66)(27 67)(28 68)(29 69)(30 70)(31 71)(32 72)(33 73)(34 74)(35 75)(36 76)(37 77)(38 78)(39 79)(40 80)(41 81)(42 82)(43 83)(44 84)(45 85)(46 86)(47 87)(48 88)(49 89)(50 90)(51 91)(52 92)(53 93)(54 94)(55 95)(56 96)(57 97)(58 98)(59 99)(60 100)(61 101)(62 102)(125 244)(126 245)(127 246)(128 247)(129 248)(130 187)(131 188)(132 189)(133 190)(134 191)(135 192)(136 193)(137 194)(138 195)(139 196)(140 197)(141 198)(142 199)(143 200)(144 201)(145 202)(146 203)(147 204)(148 205)(149 206)(150 207)(151 208)(152 209)(153 210)(154 211)(155 212)(156 213)(157 214)(158 215)(159 216)(160 217)(161 218)(162 219)(163 220)(164 221)(165 222)(166 223)(167 224)(168 225)(169 226)(170 227)(171 228)(172 229)(173 230)(174 231)(175 232)(176 233)(177 234)(178 235)(179 236)(180 237)(181 238)(182 239)(183 240)(184 241)(185 242)(186 243)(249 316)(250 317)(251 318)(252 319)(253 320)(254 321)(255 322)(256 323)(257 324)(258 325)(259 326)(260 327)(261 328)(262 329)(263 330)(264 331)(265 332)(266 333)(267 334)(268 335)(269 336)(270 337)(271 338)(272 339)(273 340)(274 341)(275 342)(276 343)(277 344)(278 345)(279 346)(280 347)(281 348)(282 349)(283 350)(284 351)(285 352)(286 353)(287 354)(288 355)(289 356)(290 357)(291 358)(292 359)(293 360)(294 361)(295 362)(296 363)(297 364)(298 365)(299 366)(300 367)(301 368)(302 369)(303 370)(304 371)(305 372)(306 311)(307 312)(308 313)(309 314)(310 315)(373 449)(374 450)(375 451)(376 452)(377 453)(378 454)(379 455)(380 456)(381 457)(382 458)(383 459)(384 460)(385 461)(386 462)(387 463)(388 464)(389 465)(390 466)(391 467)(392 468)(393 469)(394 470)(395 471)(396 472)(397 473)(398 474)(399 475)(400 476)(401 477)(402 478)(403 479)(404 480)(405 481)(406 482)(407 483)(408 484)(409 485)(410 486)(411 487)(412 488)(413 489)(414 490)(415 491)(416 492)(417 493)(418 494)(419 495)(420 496)(421 435)(422 436)(423 437)(424 438)(425 439)(426 440)(427 441)(428 442)(429 443)(430 444)(431 445)(432 446)(433 447)(434 448)
(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)| (1,286)(2,287)(3,288)(4,289)(5,290)(6,291)(7,292)(8,293)(9,294)(10,295)(11,296)(12,297)(13,298)(14,299)(15,300)(16,301)(17,302)(18,303)(19,304)(20,305)(21,306)(22,307)(23,308)(24,309)(25,310)(26,249)(27,250)(28,251)(29,252)(30,253)(31,254)(32,255)(33,256)(34,257)(35,258)(36,259)(37,260)(38,261)(39,262)(40,263)(41,264)(42,265)(43,266)(44,267)(45,268)(46,269)(47,270)(48,271)(49,272)(50,273)(51,274)(52,275)(53,276)(54,277)(55,278)(56,279)(57,280)(58,281)(59,282)(60,283)(61,284)(62,285)(63,313)(64,314)(65,315)(66,316)(67,317)(68,318)(69,319)(70,320)(71,321)(72,322)(73,323)(74,324)(75,325)(76,326)(77,327)(78,328)(79,329)(80,330)(81,331)(82,332)(83,333)(84,334)(85,335)(86,336)(87,337)(88,338)(89,339)(90,340)(91,341)(92,342)(93,343)(94,344)(95,345)(96,346)(97,347)(98,348)(99,349)(100,350)(101,351)(102,352)(103,353)(104,354)(105,355)(106,356)(107,357)(108,358)(109,359)(110,360)(111,361)(112,362)(113,363)(114,364)(115,365)(116,366)(117,367)(118,368)(119,369)(120,370)(121,371)(122,372)(123,311)(124,312)(125,414)(126,415)(127,416)(128,417)(129,418)(130,419)(131,420)(132,421)(133,422)(134,423)(135,424)(136,425)(137,426)(138,427)(139,428)(140,429)(141,430)(142,431)(143,432)(144,433)(145,434)(146,373)(147,374)(148,375)(149,376)(150,377)(151,378)(152,379)(153,380)(154,381)(155,382)(156,383)(157,384)(158,385)(159,386)(160,387)(161,388)(162,389)(163,390)(164,391)(165,392)(166,393)(167,394)(168,395)(169,396)(170,397)(171,398)(172,399)(173,400)(174,401)(175,402)(176,403)(177,404)(178,405)(179,406)(180,407)(181,408)(182,409)(183,410)(184,411)(185,412)(186,413)(187,495)(188,496)(189,435)(190,436)(191,437)(192,438)(193,439)(194,440)(195,441)(196,442)(197,443)(198,444)(199,445)(200,446)(201,447)(202,448)(203,449)(204,450)(205,451)(206,452)(207,453)(208,454)(209,455)(210,456)(211,457)(212,458)(213,459)(214,460)(215,461)(216,462)(217,463)(218,464)(219,465)(220,466)(221,467)(222,468)(223,469)(224,470)(225,471)(226,472)(227,473)(228,474)(229,475)(230,476)(231,477)(232,478)(233,479)(234,480)(235,481)(236,482)(237,483)(238,484)(239,485)(240,486)(241,487)(242,488)(243,489)(244,490)(245,491)(246,492)(247,493)(248,494), (1,181)(2,182)(3,183)(4,184)(5,185)(6,186)(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)(63,198)(64,199)(65,200)(66,201)(67,202)(68,203)(69,204)(70,205)(71,206)(72,207)(73,208)(74,209)(75,210)(76,211)(77,212)(78,213)(79,214)(80,215)(81,216)(82,217)(83,218)(84,219)(85,220)(86,221)(87,222)(88,223)(89,224)(90,225)(91,226)(92,227)(93,228)(94,229)(95,230)(96,231)(97,232)(98,233)(99,234)(100,235)(101,236)(102,237)(103,238)(104,239)(105,240)(106,241)(107,242)(108,243)(109,244)(110,245)(111,246)(112,247)(113,248)(114,187)(115,188)(116,189)(117,190)(118,191)(119,192)(120,193)(121,194)(122,195)(123,196)(124,197)(249,433)(250,434)(251,373)(252,374)(253,375)(254,376)(255,377)(256,378)(257,379)(258,380)(259,381)(260,382)(261,383)(262,384)(263,385)(264,386)(265,387)(266,388)(267,389)(268,390)(269,391)(270,392)(271,393)(272,394)(273,395)(274,396)(275,397)(276,398)(277,399)(278,400)(279,401)(280,402)(281,403)(282,404)(283,405)(284,406)(285,407)(286,408)(287,409)(288,410)(289,411)(290,412)(291,413)(292,414)(293,415)(294,416)(295,417)(296,418)(297,419)(298,420)(299,421)(300,422)(301,423)(302,424)(303,425)(304,426)(305,427)(306,428)(307,429)(308,430)(309,431)(310,432)(311,442)(312,443)(313,444)(314,445)(315,446)(316,447)(317,448)(318,449)(319,450)(320,451)(321,452)(322,453)(323,454)(324,455)(325,456)(326,457)(327,458)(328,459)(329,460)(330,461)(331,462)(332,463)(333,464)(334,465)(335,466)(336,467)(337,468)(338,469)(339,470)(340,471)(341,472)(342,473)(343,474)(344,475)(345,476)(346,477)(347,478)(348,479)(349,480)(350,481)(351,482)(352,483)(353,484)(354,485)(355,486)(356,487)(357,488)(358,489)(359,490)(360,491)(361,492)(362,493)(363,494)(364,495)(365,496)(366,435)(367,436)(368,437)(369,438)(370,439)(371,440)(372,441), (1,103)(2,104)(3,105)(4,106)(5,107)(6,108)(7,109)(8,110)(9,111)(10,112)(11,113)(12,114)(13,115)(14,116)(15,117)(16,118)(17,119)(18,120)(19,121)(20,122)(21,123)(22,124)(23,63)(24,64)(25,65)(26,66)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)(33,73)(34,74)(35,75)(36,76)(37,77)(38,78)(39,79)(40,80)(41,81)(42,82)(43,83)(44,84)(45,85)(46,86)(47,87)(48,88)(49,89)(50,90)(51,91)(52,92)(53,93)(54,94)(55,95)(56,96)(57,97)(58,98)(59,99)(60,100)(61,101)(62,102)(125,244)(126,245)(127,246)(128,247)(129,248)(130,187)(131,188)(132,189)(133,190)(134,191)(135,192)(136,193)(137,194)(138,195)(139,196)(140,197)(141,198)(142,199)(143,200)(144,201)(145,202)(146,203)(147,204)(148,205)(149,206)(150,207)(151,208)(152,209)(153,210)(154,211)(155,212)(156,213)(157,214)(158,215)(159,216)(160,217)(161,218)(162,219)(163,220)(164,221)(165,222)(166,223)(167,224)(168,225)(169,226)(170,227)(171,228)(172,229)(173,230)(174,231)(175,232)(176,233)(177,234)(178,235)(179,236)(180,237)(181,238)(182,239)(183,240)(184,241)(185,242)(186,243)(249,316)(250,317)(251,318)(252,319)(253,320)(254,321)(255,322)(256,323)(257,324)(258,325)(259,326)(260,327)(261,328)(262,329)(263,330)(264,331)(265,332)(266,333)(267,334)(268,335)(269,336)(270,337)(271,338)(272,339)(273,340)(274,341)(275,342)(276,343)(277,344)(278,345)(279,346)(280,347)(281,348)(282,349)(283,350)(284,351)(285,352)(286,353)(287,354)(288,355)(289,356)(290,357)(291,358)(292,359)(293,360)(294,361)(295,362)(296,363)(297,364)(298,365)(299,366)(300,367)(301,368)(302,369)(303,370)(304,371)(305,372)(306,311)(307,312)(308,313)(309,314)(310,315)(373,449)(374,450)(375,451)(376,452)(377,453)(378,454)(379,455)(380,456)(381,457)(382,458)(383,459)(384,460)(385,461)(386,462)(387,463)(388,464)(389,465)(390,466)(391,467)(392,468)(393,469)(394,470)(395,471)(396,472)(397,473)(398,474)(399,475)(400,476)(401,477)(402,478)(403,479)(404,480)(405,481)(406,482)(407,483)(408,484)(409,485)(410,486)(411,487)(412,488)(413,489)(414,490)(415,491)(416,492)(417,493)(418,494)(419,495)(420,496)(421,435)(422,436)(423,437)(424,438)(425,439)(426,440)(427,441)(428,442)(429,443)(430,444)(431,445)(432,446)(433,447)(434,448), (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( (1,286)(2,287)(3,288)(4,289)(5,290)(6,291)(7,292)(8,293)(9,294)(10,295)(11,296)(12,297)(13,298)(14,299)(15,300)(16,301)(17,302)(18,303)(19,304)(20,305)(21,306)(22,307)(23,308)(24,309)(25,310)(26,249)(27,250)(28,251)(29,252)(30,253)(31,254)(32,255)(33,256)(34,257)(35,258)(36,259)(37,260)(38,261)(39,262)(40,263)(41,264)(42,265)(43,266)(44,267)(45,268)(46,269)(47,270)(48,271)(49,272)(50,273)(51,274)(52,275)(53,276)(54,277)(55,278)(56,279)(57,280)(58,281)(59,282)(60,283)(61,284)(62,285)(63,313)(64,314)(65,315)(66,316)(67,317)(68,318)(69,319)(70,320)(71,321)(72,322)(73,323)(74,324)(75,325)(76,326)(77,327)(78,328)(79,329)(80,330)(81,331)(82,332)(83,333)(84,334)(85,335)(86,336)(87,337)(88,338)(89,339)(90,340)(91,341)(92,342)(93,343)(94,344)(95,345)(96,346)(97,347)(98,348)(99,349)(100,350)(101,351)(102,352)(103,353)(104,354)(105,355)(106,356)(107,357)(108,358)(109,359)(110,360)(111,361)(112,362)(113,363)(114,364)(115,365)(116,366)(117,367)(118,368)(119,369)(120,370)(121,371)(122,372)(123,311)(124,312)(125,414)(126,415)(127,416)(128,417)(129,418)(130,419)(131,420)(132,421)(133,422)(134,423)(135,424)(136,425)(137,426)(138,427)(139,428)(140,429)(141,430)(142,431)(143,432)(144,433)(145,434)(146,373)(147,374)(148,375)(149,376)(150,377)(151,378)(152,379)(153,380)(154,381)(155,382)(156,383)(157,384)(158,385)(159,386)(160,387)(161,388)(162,389)(163,390)(164,391)(165,392)(166,393)(167,394)(168,395)(169,396)(170,397)(171,398)(172,399)(173,400)(174,401)(175,402)(176,403)(177,404)(178,405)(179,406)(180,407)(181,408)(182,409)(183,410)(184,411)(185,412)(186,413)(187,495)(188,496)(189,435)(190,436)(191,437)(192,438)(193,439)(194,440)(195,441)(196,442)(197,443)(198,444)(199,445)(200,446)(201,447)(202,448)(203,449)(204,450)(205,451)(206,452)(207,453)(208,454)(209,455)(210,456)(211,457)(212,458)(213,459)(214,460)(215,461)(216,462)(217,463)(218,464)(219,465)(220,466)(221,467)(222,468)(223,469)(224,470)(225,471)(226,472)(227,473)(228,474)(229,475)(230,476)(231,477)(232,478)(233,479)(234,480)(235,481)(236,482)(237,483)(238,484)(239,485)(240,486)(241,487)(242,488)(243,489)(244,490)(245,491)(246,492)(247,493)(248,494), (1,181)(2,182)(3,183)(4,184)(5,185)(6,186)(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)(63,198)(64,199)(65,200)(66,201)(67,202)(68,203)(69,204)(70,205)(71,206)(72,207)(73,208)(74,209)(75,210)(76,211)(77,212)(78,213)(79,214)(80,215)(81,216)(82,217)(83,218)(84,219)(85,220)(86,221)(87,222)(88,223)(89,224)(90,225)(91,226)(92,227)(93,228)(94,229)(95,230)(96,231)(97,232)(98,233)(99,234)(100,235)(101,236)(102,237)(103,238)(104,239)(105,240)(106,241)(107,242)(108,243)(109,244)(110,245)(111,246)(112,247)(113,248)(114,187)(115,188)(116,189)(117,190)(118,191)(119,192)(120,193)(121,194)(122,195)(123,196)(124,197)(249,433)(250,434)(251,373)(252,374)(253,375)(254,376)(255,377)(256,378)(257,379)(258,380)(259,381)(260,382)(261,383)(262,384)(263,385)(264,386)(265,387)(266,388)(267,389)(268,390)(269,391)(270,392)(271,393)(272,394)(273,395)(274,396)(275,397)(276,398)(277,399)(278,400)(279,401)(280,402)(281,403)(282,404)(283,405)(284,406)(285,407)(286,408)(287,409)(288,410)(289,411)(290,412)(291,413)(292,414)(293,415)(294,416)(295,417)(296,418)(297,419)(298,420)(299,421)(300,422)(301,423)(302,424)(303,425)(304,426)(305,427)(306,428)(307,429)(308,430)(309,431)(310,432)(311,442)(312,443)(313,444)(314,445)(315,446)(316,447)(317,448)(318,449)(319,450)(320,451)(321,452)(322,453)(323,454)(324,455)(325,456)(326,457)(327,458)(328,459)(329,460)(330,461)(331,462)(332,463)(333,464)(334,465)(335,466)(336,467)(337,468)(338,469)(339,470)(340,471)(341,472)(342,473)(343,474)(344,475)(345,476)(346,477)(347,478)(348,479)(349,480)(350,481)(351,482)(352,483)(353,484)(354,485)(355,486)(356,487)(357,488)(358,489)(359,490)(360,491)(361,492)(362,493)(363,494)(364,495)(365,496)(366,435)(367,436)(368,437)(369,438)(370,439)(371,440)(372,441), (1,103)(2,104)(3,105)(4,106)(5,107)(6,108)(7,109)(8,110)(9,111)(10,112)(11,113)(12,114)(13,115)(14,116)(15,117)(16,118)(17,119)(18,120)(19,121)(20,122)(21,123)(22,124)(23,63)(24,64)(25,65)(26,66)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)(33,73)(34,74)(35,75)(36,76)(37,77)(38,78)(39,79)(40,80)(41,81)(42,82)(43,83)(44,84)(45,85)(46,86)(47,87)(48,88)(49,89)(50,90)(51,91)(52,92)(53,93)(54,94)(55,95)(56,96)(57,97)(58,98)(59,99)(60,100)(61,101)(62,102)(125,244)(126,245)(127,246)(128,247)(129,248)(130,187)(131,188)(132,189)(133,190)(134,191)(135,192)(136,193)(137,194)(138,195)(139,196)(140,197)(141,198)(142,199)(143,200)(144,201)(145,202)(146,203)(147,204)(148,205)(149,206)(150,207)(151,208)(152,209)(153,210)(154,211)(155,212)(156,213)(157,214)(158,215)(159,216)(160,217)(161,218)(162,219)(163,220)(164,221)(165,222)(166,223)(167,224)(168,225)(169,226)(170,227)(171,228)(172,229)(173,230)(174,231)(175,232)(176,233)(177,234)(178,235)(179,236)(180,237)(181,238)(182,239)(183,240)(184,241)(185,242)(186,243)(249,316)(250,317)(251,318)(252,319)(253,320)(254,321)(255,322)(256,323)(257,324)(258,325)(259,326)(260,327)(261,328)(262,329)(263,330)(264,331)(265,332)(266,333)(267,334)(268,335)(269,336)(270,337)(271,338)(272,339)(273,340)(274,341)(275,342)(276,343)(277,344)(278,345)(279,346)(280,347)(281,348)(282,349)(283,350)(284,351)(285,352)(286,353)(287,354)(288,355)(289,356)(290,357)(291,358)(292,359)(293,360)(294,361)(295,362)(296,363)(297,364)(298,365)(299,366)(300,367)(301,368)(302,369)(303,370)(304,371)(305,372)(306,311)(307,312)(308,313)(309,314)(310,315)(373,449)(374,450)(375,451)(376,452)(377,453)(378,454)(379,455)(380,456)(381,457)(382,458)(383,459)(384,460)(385,461)(386,462)(387,463)(388,464)(389,465)(390,466)(391,467)(392,468)(393,469)(394,470)(395,471)(396,472)(397,473)(398,474)(399,475)(400,476)(401,477)(402,478)(403,479)(404,480)(405,481)(406,482)(407,483)(408,484)(409,485)(410,486)(411,487)(412,488)(413,489)(414,490)(415,491)(416,492)(417,493)(418,494)(419,495)(420,496)(421,435)(422,436)(423,437)(424,438)(425,439)(426,440)(427,441)(428,442)(429,443)(430,444)(431,445)(432,446)(433,447)(434,448), (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([(1,286),(2,287),(3,288),(4,289),(5,290),(6,291),(7,292),(8,293),(9,294),(10,295),(11,296),(12,297),(13,298),(14,299),(15,300),(16,301),(17,302),(18,303),(19,304),(20,305),(21,306),(22,307),(23,308),(24,309),(25,310),(26,249),(27,250),(28,251),(29,252),(30,253),(31,254),(32,255),(33,256),(34,257),(35,258),(36,259),(37,260),(38,261),(39,262),(40,263),(41,264),(42,265),(43,266),(44,267),(45,268),(46,269),(47,270),(48,271),(49,272),(50,273),(51,274),(52,275),(53,276),(54,277),(55,278),(56,279),(57,280),(58,281),(59,282),(60,283),(61,284),(62,285),(63,313),(64,314),(65,315),(66,316),(67,317),(68,318),(69,319),(70,320),(71,321),(72,322),(73,323),(74,324),(75,325),(76,326),(77,327),(78,328),(79,329),(80,330),(81,331),(82,332),(83,333),(84,334),(85,335),(86,336),(87,337),(88,338),(89,339),(90,340),(91,341),(92,342),(93,343),(94,344),(95,345),(96,346),(97,347),(98,348),(99,349),(100,350),(101,351),(102,352),(103,353),(104,354),(105,355),(106,356),(107,357),(108,358),(109,359),(110,360),(111,361),(112,362),(113,363),(114,364),(115,365),(116,366),(117,367),(118,368),(119,369),(120,370),(121,371),(122,372),(123,311),(124,312),(125,414),(126,415),(127,416),(128,417),(129,418),(130,419),(131,420),(132,421),(133,422),(134,423),(135,424),(136,425),(137,426),(138,427),(139,428),(140,429),(141,430),(142,431),(143,432),(144,433),(145,434),(146,373),(147,374),(148,375),(149,376),(150,377),(151,378),(152,379),(153,380),(154,381),(155,382),(156,383),(157,384),(158,385),(159,386),(160,387),(161,388),(162,389),(163,390),(164,391),(165,392),(166,393),(167,394),(168,395),(169,396),(170,397),(171,398),(172,399),(173,400),(174,401),(175,402),(176,403),(177,404),(178,405),(179,406),(180,407),(181,408),(182,409),(183,410),(184,411),(185,412),(186,413),(187,495),(188,496),(189,435),(190,436),(191,437),(192,438),(193,439),(194,440),(195,441),(196,442),(197,443),(198,444),(199,445),(200,446),(201,447),(202,448),(203,449),(204,450),(205,451),(206,452),(207,453),(208,454),(209,455),(210,456),(211,457),(212,458),(213,459),(214,460),(215,461),(216,462),(217,463),(218,464),(219,465),(220,466),(221,467),(222,468),(223,469),(224,470),(225,471),(226,472),(227,473),(228,474),(229,475),(230,476),(231,477),(232,478),(233,479),(234,480),(235,481),(236,482),(237,483),(238,484),(239,485),(240,486),(241,487),(242,488),(243,489),(244,490),(245,491),(246,492),(247,493),(248,494)], [(1,181),(2,182),(3,183),(4,184),(5,185),(6,186),(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),(63,198),(64,199),(65,200),(66,201),(67,202),(68,203),(69,204),(70,205),(71,206),(72,207),(73,208),(74,209),(75,210),(76,211),(77,212),(78,213),(79,214),(80,215),(81,216),(82,217),(83,218),(84,219),(85,220),(86,221),(87,222),(88,223),(89,224),(90,225),(91,226),(92,227),(93,228),(94,229),(95,230),(96,231),(97,232),(98,233),(99,234),(100,235),(101,236),(102,237),(103,238),(104,239),(105,240),(106,241),(107,242),(108,243),(109,244),(110,245),(111,246),(112,247),(113,248),(114,187),(115,188),(116,189),(117,190),(118,191),(119,192),(120,193),(121,194),(122,195),(123,196),(124,197),(249,433),(250,434),(251,373),(252,374),(253,375),(254,376),(255,377),(256,378),(257,379),(258,380),(259,381),(260,382),(261,383),(262,384),(263,385),(264,386),(265,387),(266,388),(267,389),(268,390),(269,391),(270,392),(271,393),(272,394),(273,395),(274,396),(275,397),(276,398),(277,399),(278,400),(279,401),(280,402),(281,403),(282,404),(283,405),(284,406),(285,407),(286,408),(287,409),(288,410),(289,411),(290,412),(291,413),(292,414),(293,415),(294,416),(295,417),(296,418),(297,419),(298,420),(299,421),(300,422),(301,423),(302,424),(303,425),(304,426),(305,427),(306,428),(307,429),(308,430),(309,431),(310,432),(311,442),(312,443),(313,444),(314,445),(315,446),(316,447),(317,448),(318,449),(319,450),(320,451),(321,452),(322,453),(323,454),(324,455),(325,456),(326,457),(327,458),(328,459),(329,460),(330,461),(331,462),(332,463),(333,464),(334,465),(335,466),(336,467),(337,468),(338,469),(339,470),(340,471),(341,472),(342,473),(343,474),(344,475),(345,476),(346,477),(347,478),(348,479),(349,480),(350,481),(351,482),(352,483),(353,484),(354,485),(355,486),(356,487),(357,488),(358,489),(359,490),(360,491),(361,492),(362,493),(363,494),(364,495),(365,496),(366,435),(367,436),(368,437),(369,438),(370,439),(371,440),(372,441)], [(1,103),(2,104),(3,105),(4,106),(5,107),(6,108),(7,109),(8,110),(9,111),(10,112),(11,113),(12,114),(13,115),(14,116),(15,117),(16,118),(17,119),(18,120),(19,121),(20,122),(21,123),(22,124),(23,63),(24,64),(25,65),(26,66),(27,67),(28,68),(29,69),(30,70),(31,71),(32,72),(33,73),(34,74),(35,75),(36,76),(37,77),(38,78),(39,79),(40,80),(41,81),(42,82),(43,83),(44,84),(45,85),(46,86),(47,87),(48,88),(49,89),(50,90),(51,91),(52,92),(53,93),(54,94),(55,95),(56,96),(57,97),(58,98),(59,99),(60,100),(61,101),(62,102),(125,244),(126,245),(127,246),(128,247),(129,248),(130,187),(131,188),(132,189),(133,190),(134,191),(135,192),(136,193),(137,194),(138,195),(139,196),(140,197),(141,198),(142,199),(143,200),(144,201),(145,202),(146,203),(147,204),(148,205),(149,206),(150,207),(151,208),(152,209),(153,210),(154,211),(155,212),(156,213),(157,214),(158,215),(159,216),(160,217),(161,218),(162,219),(163,220),(164,221),(165,222),(166,223),(167,224),(168,225),(169,226),(170,227),(171,228),(172,229),(173,230),(174,231),(175,232),(176,233),(177,234),(178,235),(179,236),(180,237),(181,238),(182,239),(183,240),(184,241),(185,242),(186,243),(249,316),(250,317),(251,318),(252,319),(253,320),(254,321),(255,322),(256,323),(257,324),(258,325),(259,326),(260,327),(261,328),(262,329),(263,330),(264,331),(265,332),(266,333),(267,334),(268,335),(269,336),(270,337),(271,338),(272,339),(273,340),(274,341),(275,342),(276,343),(277,344),(278,345),(279,346),(280,347),(281,348),(282,349),(283,350),(284,351),(285,352),(286,353),(287,354),(288,355),(289,356),(290,357),(291,358),(292,359),(293,360),(294,361),(295,362),(296,363),(297,364),(298,365),(299,366),(300,367),(301,368),(302,369),(303,370),(304,371),(305,372),(306,311),(307,312),(308,313),(309,314),(310,315),(373,449),(374,450),(375,451),(376,452),(377,453),(378,454),(379,455),(380,456),(381,457),(382,458),(383,459),(384,460),(385,461),(386,462),(387,463),(388,464),(389,465),(390,466),(391,467),(392,468),(393,469),(394,470),(395,471),(396,472),(397,473),(398,474),(399,475),(400,476),(401,477),(402,478),(403,479),(404,480),(405,481),(406,482),(407,483),(408,484),(409,485),(410,486),(411,487),(412,488),(413,489),(414,490),(415,491),(416,492),(417,493),(418,494),(419,495),(420,496),(421,435),(422,436),(423,437),(424,438),(425,439),(426,440),(427,441),(428,442),(429,443),(430,444),(431,445),(432,446),(433,447),(434,448)], [(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···2O31A···31AD62A···62QH
order12···231···3162···62
size11···11···11···1

496 irreducible representations

dim1111
type++
imageC1C2C31C62
kernelC23×C62C22×C62C24C23
# reps11530450

Matrix representation of C23×C62 in GL4(𝔽311) generated by

1000
031000
003100
000310
,
1000
0100
003100
0001
,
310000
0100
003100
000310
,
142000
01800
00410
00020
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

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