direct product, abelian, monomial, 2-elementary
Aliases: C23×C58, SmallGroup(464,51)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C23×C58 |
| C1 — C23×C58 |
| C1 — C23×C58 |
Generators and relations for C23×C58
G = < a,b,c,d | a2=b2=c2=d58=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, cd=dc >
Subgroups: 134, all normal (4 characteristic)
C1, C2, C22, C23, C24, C29, C58, C2×C58, C22×C58, C23×C58
Quotients: C1, C2, C22, C23, C24, C29, C58, C2×C58, C22×C58, C23×C58
►Regular action on 464 points
Generators in S464
(1 269)(2 270)(3 271)(4 272)(5 273)(6 274)(7 275)(8 276)(9 277)(10 278)(11 279)(12 280)(13 281)(14 282)(15 283)(16 284)(17 285)(18 286)(19 287)(20 288)(21 289)(22 290)(23 233)(24 234)(25 235)(26 236)(27 237)(28 238)(29 239)(30 240)(31 241)(32 242)(33 243)(34 244)(35 245)(36 246)(37 247)(38 248)(39 249)(40 250)(41 251)(42 252)(43 253)(44 254)(45 255)(46 256)(47 257)(48 258)(49 259)(50 260)(51 261)(52 262)(53 263)(54 264)(55 265)(56 266)(57 267)(58 268)(59 339)(60 340)(61 341)(62 342)(63 343)(64 344)(65 345)(66 346)(67 347)(68 348)(69 291)(70 292)(71 293)(72 294)(73 295)(74 296)(75 297)(76 298)(77 299)(78 300)(79 301)(80 302)(81 303)(82 304)(83 305)(84 306)(85 307)(86 308)(87 309)(88 310)(89 311)(90 312)(91 313)(92 314)(93 315)(94 316)(95 317)(96 318)(97 319)(98 320)(99 321)(100 322)(101 323)(102 324)(103 325)(104 326)(105 327)(106 328)(107 329)(108 330)(109 331)(110 332)(111 333)(112 334)(113 335)(114 336)(115 337)(116 338)(117 394)(118 395)(119 396)(120 397)(121 398)(122 399)(123 400)(124 401)(125 402)(126 403)(127 404)(128 405)(129 406)(130 349)(131 350)(132 351)(133 352)(134 353)(135 354)(136 355)(137 356)(138 357)(139 358)(140 359)(141 360)(142 361)(143 362)(144 363)(145 364)(146 365)(147 366)(148 367)(149 368)(150 369)(151 370)(152 371)(153 372)(154 373)(155 374)(156 375)(157 376)(158 377)(159 378)(160 379)(161 380)(162 381)(163 382)(164 383)(165 384)(166 385)(167 386)(168 387)(169 388)(170 389)(171 390)(172 391)(173 392)(174 393)(175 421)(176 422)(177 423)(178 424)(179 425)(180 426)(181 427)(182 428)(183 429)(184 430)(185 431)(186 432)(187 433)(188 434)(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)(219 407)(220 408)(221 409)(222 410)(223 411)(224 412)(225 413)(226 414)(227 415)(228 416)(229 417)(230 418)(231 419)(232 420)
(1 171)(2 172)(3 173)(4 174)(5 117)(6 118)(7 119)(8 120)(9 121)(10 122)(11 123)(12 124)(13 125)(14 126)(15 127)(16 128)(17 129)(18 130)(19 131)(20 132)(21 133)(22 134)(23 135)(24 136)(25 137)(26 138)(27 139)(28 140)(29 141)(30 142)(31 143)(32 144)(33 145)(34 146)(35 147)(36 148)(37 149)(38 150)(39 151)(40 152)(41 153)(42 154)(43 155)(44 156)(45 157)(46 158)(47 159)(48 160)(49 161)(50 162)(51 163)(52 164)(53 165)(54 166)(55 167)(56 168)(57 169)(58 170)(59 220)(60 221)(61 222)(62 223)(63 224)(64 225)(65 226)(66 227)(67 228)(68 229)(69 230)(70 231)(71 232)(72 175)(73 176)(74 177)(75 178)(76 179)(77 180)(78 181)(79 182)(80 183)(81 184)(82 185)(83 186)(84 187)(85 188)(86 189)(87 190)(88 191)(89 192)(90 193)(91 194)(92 195)(93 196)(94 197)(95 198)(96 199)(97 200)(98 201)(99 202)(100 203)(101 204)(102 205)(103 206)(104 207)(105 208)(106 209)(107 210)(108 211)(109 212)(110 213)(111 214)(112 215)(113 216)(114 217)(115 218)(116 219)(233 354)(234 355)(235 356)(236 357)(237 358)(238 359)(239 360)(240 361)(241 362)(242 363)(243 364)(244 365)(245 366)(246 367)(247 368)(248 369)(249 370)(250 371)(251 372)(252 373)(253 374)(254 375)(255 376)(256 377)(257 378)(258 379)(259 380)(260 381)(261 382)(262 383)(263 384)(264 385)(265 386)(266 387)(267 388)(268 389)(269 390)(270 391)(271 392)(272 393)(273 394)(274 395)(275 396)(276 397)(277 398)(278 399)(279 400)(280 401)(281 402)(282 403)(283 404)(284 405)(285 406)(286 349)(287 350)(288 351)(289 352)(290 353)(291 418)(292 419)(293 420)(294 421)(295 422)(296 423)(297 424)(298 425)(299 426)(300 427)(301 428)(302 429)(303 430)(304 431)(305 432)(306 433)(307 434)(308 435)(309 436)(310 437)(311 438)(312 439)(313 440)(314 441)(315 442)(316 443)(317 444)(318 445)(319 446)(320 447)(321 448)(322 449)(323 450)(324 451)(325 452)(326 453)(327 454)(328 455)(329 456)(330 457)(331 458)(332 459)(333 460)(334 461)(335 462)(336 463)(337 464)(338 407)(339 408)(340 409)(341 410)(342 411)(343 412)(344 413)(345 414)(346 415)(347 416)(348 417)
(1 113)(2 114)(3 115)(4 116)(5 59)(6 60)(7 61)(8 62)(9 63)(10 64)(11 65)(12 66)(13 67)(14 68)(15 69)(16 70)(17 71)(18 72)(19 73)(20 74)(21 75)(22 76)(23 77)(24 78)(25 79)(26 80)(27 81)(28 82)(29 83)(30 84)(31 85)(32 86)(33 87)(34 88)(35 89)(36 90)(37 91)(38 92)(39 93)(40 94)(41 95)(42 96)(43 97)(44 98)(45 99)(46 100)(47 101)(48 102)(49 103)(50 104)(51 105)(52 106)(53 107)(54 108)(55 109)(56 110)(57 111)(58 112)(117 220)(118 221)(119 222)(120 223)(121 224)(122 225)(123 226)(124 227)(125 228)(126 229)(127 230)(128 231)(129 232)(130 175)(131 176)(132 177)(133 178)(134 179)(135 180)(136 181)(137 182)(138 183)(139 184)(140 185)(141 186)(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)(233 299)(234 300)(235 301)(236 302)(237 303)(238 304)(239 305)(240 306)(241 307)(242 308)(243 309)(244 310)(245 311)(246 312)(247 313)(248 314)(249 315)(250 316)(251 317)(252 318)(253 319)(254 320)(255 321)(256 322)(257 323)(258 324)(259 325)(260 326)(261 327)(262 328)(263 329)(264 330)(265 331)(266 332)(267 333)(268 334)(269 335)(270 336)(271 337)(272 338)(273 339)(274 340)(275 341)(276 342)(277 343)(278 344)(279 345)(280 346)(281 347)(282 348)(283 291)(284 292)(285 293)(286 294)(287 295)(288 296)(289 297)(290 298)(349 421)(350 422)(351 423)(352 424)(353 425)(354 426)(355 427)(356 428)(357 429)(358 430)(359 431)(360 432)(361 433)(362 434)(363 435)(364 436)(365 437)(366 438)(367 439)(368 440)(369 441)(370 442)(371 443)(372 444)(373 445)(374 446)(375 447)(376 448)(377 449)(378 450)(379 451)(380 452)(381 453)(382 454)(383 455)(384 456)(385 457)(386 458)(387 459)(388 460)(389 461)(390 462)(391 463)(392 464)(393 407)(394 408)(395 409)(396 410)(397 411)(398 412)(399 413)(400 414)(401 415)(402 416)(403 417)(404 418)(405 419)(406 420)
(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)
G:=sub<Sym(464)| (1,269)(2,270)(3,271)(4,272)(5,273)(6,274)(7,275)(8,276)(9,277)(10,278)(11,279)(12,280)(13,281)(14,282)(15,283)(16,284)(17,285)(18,286)(19,287)(20,288)(21,289)(22,290)(23,233)(24,234)(25,235)(26,236)(27,237)(28,238)(29,239)(30,240)(31,241)(32,242)(33,243)(34,244)(35,245)(36,246)(37,247)(38,248)(39,249)(40,250)(41,251)(42,252)(43,253)(44,254)(45,255)(46,256)(47,257)(48,258)(49,259)(50,260)(51,261)(52,262)(53,263)(54,264)(55,265)(56,266)(57,267)(58,268)(59,339)(60,340)(61,341)(62,342)(63,343)(64,344)(65,345)(66,346)(67,347)(68,348)(69,291)(70,292)(71,293)(72,294)(73,295)(74,296)(75,297)(76,298)(77,299)(78,300)(79,301)(80,302)(81,303)(82,304)(83,305)(84,306)(85,307)(86,308)(87,309)(88,310)(89,311)(90,312)(91,313)(92,314)(93,315)(94,316)(95,317)(96,318)(97,319)(98,320)(99,321)(100,322)(101,323)(102,324)(103,325)(104,326)(105,327)(106,328)(107,329)(108,330)(109,331)(110,332)(111,333)(112,334)(113,335)(114,336)(115,337)(116,338)(117,394)(118,395)(119,396)(120,397)(121,398)(122,399)(123,400)(124,401)(125,402)(126,403)(127,404)(128,405)(129,406)(130,349)(131,350)(132,351)(133,352)(134,353)(135,354)(136,355)(137,356)(138,357)(139,358)(140,359)(141,360)(142,361)(143,362)(144,363)(145,364)(146,365)(147,366)(148,367)(149,368)(150,369)(151,370)(152,371)(153,372)(154,373)(155,374)(156,375)(157,376)(158,377)(159,378)(160,379)(161,380)(162,381)(163,382)(164,383)(165,384)(166,385)(167,386)(168,387)(169,388)(170,389)(171,390)(172,391)(173,392)(174,393)(175,421)(176,422)(177,423)(178,424)(179,425)(180,426)(181,427)(182,428)(183,429)(184,430)(185,431)(186,432)(187,433)(188,434)(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)(219,407)(220,408)(221,409)(222,410)(223,411)(224,412)(225,413)(226,414)(227,415)(228,416)(229,417)(230,418)(231,419)(232,420), (1,171)(2,172)(3,173)(4,174)(5,117)(6,118)(7,119)(8,120)(9,121)(10,122)(11,123)(12,124)(13,125)(14,126)(15,127)(16,128)(17,129)(18,130)(19,131)(20,132)(21,133)(22,134)(23,135)(24,136)(25,137)(26,138)(27,139)(28,140)(29,141)(30,142)(31,143)(32,144)(33,145)(34,146)(35,147)(36,148)(37,149)(38,150)(39,151)(40,152)(41,153)(42,154)(43,155)(44,156)(45,157)(46,158)(47,159)(48,160)(49,161)(50,162)(51,163)(52,164)(53,165)(54,166)(55,167)(56,168)(57,169)(58,170)(59,220)(60,221)(61,222)(62,223)(63,224)(64,225)(65,226)(66,227)(67,228)(68,229)(69,230)(70,231)(71,232)(72,175)(73,176)(74,177)(75,178)(76,179)(77,180)(78,181)(79,182)(80,183)(81,184)(82,185)(83,186)(84,187)(85,188)(86,189)(87,190)(88,191)(89,192)(90,193)(91,194)(92,195)(93,196)(94,197)(95,198)(96,199)(97,200)(98,201)(99,202)(100,203)(101,204)(102,205)(103,206)(104,207)(105,208)(106,209)(107,210)(108,211)(109,212)(110,213)(111,214)(112,215)(113,216)(114,217)(115,218)(116,219)(233,354)(234,355)(235,356)(236,357)(237,358)(238,359)(239,360)(240,361)(241,362)(242,363)(243,364)(244,365)(245,366)(246,367)(247,368)(248,369)(249,370)(250,371)(251,372)(252,373)(253,374)(254,375)(255,376)(256,377)(257,378)(258,379)(259,380)(260,381)(261,382)(262,383)(263,384)(264,385)(265,386)(266,387)(267,388)(268,389)(269,390)(270,391)(271,392)(272,393)(273,394)(274,395)(275,396)(276,397)(277,398)(278,399)(279,400)(280,401)(281,402)(282,403)(283,404)(284,405)(285,406)(286,349)(287,350)(288,351)(289,352)(290,353)(291,418)(292,419)(293,420)(294,421)(295,422)(296,423)(297,424)(298,425)(299,426)(300,427)(301,428)(302,429)(303,430)(304,431)(305,432)(306,433)(307,434)(308,435)(309,436)(310,437)(311,438)(312,439)(313,440)(314,441)(315,442)(316,443)(317,444)(318,445)(319,446)(320,447)(321,448)(322,449)(323,450)(324,451)(325,452)(326,453)(327,454)(328,455)(329,456)(330,457)(331,458)(332,459)(333,460)(334,461)(335,462)(336,463)(337,464)(338,407)(339,408)(340,409)(341,410)(342,411)(343,412)(344,413)(345,414)(346,415)(347,416)(348,417), (1,113)(2,114)(3,115)(4,116)(5,59)(6,60)(7,61)(8,62)(9,63)(10,64)(11,65)(12,66)(13,67)(14,68)(15,69)(16,70)(17,71)(18,72)(19,73)(20,74)(21,75)(22,76)(23,77)(24,78)(25,79)(26,80)(27,81)(28,82)(29,83)(30,84)(31,85)(32,86)(33,87)(34,88)(35,89)(36,90)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)(43,97)(44,98)(45,99)(46,100)(47,101)(48,102)(49,103)(50,104)(51,105)(52,106)(53,107)(54,108)(55,109)(56,110)(57,111)(58,112)(117,220)(118,221)(119,222)(120,223)(121,224)(122,225)(123,226)(124,227)(125,228)(126,229)(127,230)(128,231)(129,232)(130,175)(131,176)(132,177)(133,178)(134,179)(135,180)(136,181)(137,182)(138,183)(139,184)(140,185)(141,186)(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)(233,299)(234,300)(235,301)(236,302)(237,303)(238,304)(239,305)(240,306)(241,307)(242,308)(243,309)(244,310)(245,311)(246,312)(247,313)(248,314)(249,315)(250,316)(251,317)(252,318)(253,319)(254,320)(255,321)(256,322)(257,323)(258,324)(259,325)(260,326)(261,327)(262,328)(263,329)(264,330)(265,331)(266,332)(267,333)(268,334)(269,335)(270,336)(271,337)(272,338)(273,339)(274,340)(275,341)(276,342)(277,343)(278,344)(279,345)(280,346)(281,347)(282,348)(283,291)(284,292)(285,293)(286,294)(287,295)(288,296)(289,297)(290,298)(349,421)(350,422)(351,423)(352,424)(353,425)(354,426)(355,427)(356,428)(357,429)(358,430)(359,431)(360,432)(361,433)(362,434)(363,435)(364,436)(365,437)(366,438)(367,439)(368,440)(369,441)(370,442)(371,443)(372,444)(373,445)(374,446)(375,447)(376,448)(377,449)(378,450)(379,451)(380,452)(381,453)(382,454)(383,455)(384,456)(385,457)(386,458)(387,459)(388,460)(389,461)(390,462)(391,463)(392,464)(393,407)(394,408)(395,409)(396,410)(397,411)(398,412)(399,413)(400,414)(401,415)(402,416)(403,417)(404,418)(405,419)(406,420), (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)>;
G:=Group( (1,269)(2,270)(3,271)(4,272)(5,273)(6,274)(7,275)(8,276)(9,277)(10,278)(11,279)(12,280)(13,281)(14,282)(15,283)(16,284)(17,285)(18,286)(19,287)(20,288)(21,289)(22,290)(23,233)(24,234)(25,235)(26,236)(27,237)(28,238)(29,239)(30,240)(31,241)(32,242)(33,243)(34,244)(35,245)(36,246)(37,247)(38,248)(39,249)(40,250)(41,251)(42,252)(43,253)(44,254)(45,255)(46,256)(47,257)(48,258)(49,259)(50,260)(51,261)(52,262)(53,263)(54,264)(55,265)(56,266)(57,267)(58,268)(59,339)(60,340)(61,341)(62,342)(63,343)(64,344)(65,345)(66,346)(67,347)(68,348)(69,291)(70,292)(71,293)(72,294)(73,295)(74,296)(75,297)(76,298)(77,299)(78,300)(79,301)(80,302)(81,303)(82,304)(83,305)(84,306)(85,307)(86,308)(87,309)(88,310)(89,311)(90,312)(91,313)(92,314)(93,315)(94,316)(95,317)(96,318)(97,319)(98,320)(99,321)(100,322)(101,323)(102,324)(103,325)(104,326)(105,327)(106,328)(107,329)(108,330)(109,331)(110,332)(111,333)(112,334)(113,335)(114,336)(115,337)(116,338)(117,394)(118,395)(119,396)(120,397)(121,398)(122,399)(123,400)(124,401)(125,402)(126,403)(127,404)(128,405)(129,406)(130,349)(131,350)(132,351)(133,352)(134,353)(135,354)(136,355)(137,356)(138,357)(139,358)(140,359)(141,360)(142,361)(143,362)(144,363)(145,364)(146,365)(147,366)(148,367)(149,368)(150,369)(151,370)(152,371)(153,372)(154,373)(155,374)(156,375)(157,376)(158,377)(159,378)(160,379)(161,380)(162,381)(163,382)(164,383)(165,384)(166,385)(167,386)(168,387)(169,388)(170,389)(171,390)(172,391)(173,392)(174,393)(175,421)(176,422)(177,423)(178,424)(179,425)(180,426)(181,427)(182,428)(183,429)(184,430)(185,431)(186,432)(187,433)(188,434)(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)(219,407)(220,408)(221,409)(222,410)(223,411)(224,412)(225,413)(226,414)(227,415)(228,416)(229,417)(230,418)(231,419)(232,420), (1,171)(2,172)(3,173)(4,174)(5,117)(6,118)(7,119)(8,120)(9,121)(10,122)(11,123)(12,124)(13,125)(14,126)(15,127)(16,128)(17,129)(18,130)(19,131)(20,132)(21,133)(22,134)(23,135)(24,136)(25,137)(26,138)(27,139)(28,140)(29,141)(30,142)(31,143)(32,144)(33,145)(34,146)(35,147)(36,148)(37,149)(38,150)(39,151)(40,152)(41,153)(42,154)(43,155)(44,156)(45,157)(46,158)(47,159)(48,160)(49,161)(50,162)(51,163)(52,164)(53,165)(54,166)(55,167)(56,168)(57,169)(58,170)(59,220)(60,221)(61,222)(62,223)(63,224)(64,225)(65,226)(66,227)(67,228)(68,229)(69,230)(70,231)(71,232)(72,175)(73,176)(74,177)(75,178)(76,179)(77,180)(78,181)(79,182)(80,183)(81,184)(82,185)(83,186)(84,187)(85,188)(86,189)(87,190)(88,191)(89,192)(90,193)(91,194)(92,195)(93,196)(94,197)(95,198)(96,199)(97,200)(98,201)(99,202)(100,203)(101,204)(102,205)(103,206)(104,207)(105,208)(106,209)(107,210)(108,211)(109,212)(110,213)(111,214)(112,215)(113,216)(114,217)(115,218)(116,219)(233,354)(234,355)(235,356)(236,357)(237,358)(238,359)(239,360)(240,361)(241,362)(242,363)(243,364)(244,365)(245,366)(246,367)(247,368)(248,369)(249,370)(250,371)(251,372)(252,373)(253,374)(254,375)(255,376)(256,377)(257,378)(258,379)(259,380)(260,381)(261,382)(262,383)(263,384)(264,385)(265,386)(266,387)(267,388)(268,389)(269,390)(270,391)(271,392)(272,393)(273,394)(274,395)(275,396)(276,397)(277,398)(278,399)(279,400)(280,401)(281,402)(282,403)(283,404)(284,405)(285,406)(286,349)(287,350)(288,351)(289,352)(290,353)(291,418)(292,419)(293,420)(294,421)(295,422)(296,423)(297,424)(298,425)(299,426)(300,427)(301,428)(302,429)(303,430)(304,431)(305,432)(306,433)(307,434)(308,435)(309,436)(310,437)(311,438)(312,439)(313,440)(314,441)(315,442)(316,443)(317,444)(318,445)(319,446)(320,447)(321,448)(322,449)(323,450)(324,451)(325,452)(326,453)(327,454)(328,455)(329,456)(330,457)(331,458)(332,459)(333,460)(334,461)(335,462)(336,463)(337,464)(338,407)(339,408)(340,409)(341,410)(342,411)(343,412)(344,413)(345,414)(346,415)(347,416)(348,417), (1,113)(2,114)(3,115)(4,116)(5,59)(6,60)(7,61)(8,62)(9,63)(10,64)(11,65)(12,66)(13,67)(14,68)(15,69)(16,70)(17,71)(18,72)(19,73)(20,74)(21,75)(22,76)(23,77)(24,78)(25,79)(26,80)(27,81)(28,82)(29,83)(30,84)(31,85)(32,86)(33,87)(34,88)(35,89)(36,90)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)(43,97)(44,98)(45,99)(46,100)(47,101)(48,102)(49,103)(50,104)(51,105)(52,106)(53,107)(54,108)(55,109)(56,110)(57,111)(58,112)(117,220)(118,221)(119,222)(120,223)(121,224)(122,225)(123,226)(124,227)(125,228)(126,229)(127,230)(128,231)(129,232)(130,175)(131,176)(132,177)(133,178)(134,179)(135,180)(136,181)(137,182)(138,183)(139,184)(140,185)(141,186)(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)(233,299)(234,300)(235,301)(236,302)(237,303)(238,304)(239,305)(240,306)(241,307)(242,308)(243,309)(244,310)(245,311)(246,312)(247,313)(248,314)(249,315)(250,316)(251,317)(252,318)(253,319)(254,320)(255,321)(256,322)(257,323)(258,324)(259,325)(260,326)(261,327)(262,328)(263,329)(264,330)(265,331)(266,332)(267,333)(268,334)(269,335)(270,336)(271,337)(272,338)(273,339)(274,340)(275,341)(276,342)(277,343)(278,344)(279,345)(280,346)(281,347)(282,348)(283,291)(284,292)(285,293)(286,294)(287,295)(288,296)(289,297)(290,298)(349,421)(350,422)(351,423)(352,424)(353,425)(354,426)(355,427)(356,428)(357,429)(358,430)(359,431)(360,432)(361,433)(362,434)(363,435)(364,436)(365,437)(366,438)(367,439)(368,440)(369,441)(370,442)(371,443)(372,444)(373,445)(374,446)(375,447)(376,448)(377,449)(378,450)(379,451)(380,452)(381,453)(382,454)(383,455)(384,456)(385,457)(386,458)(387,459)(388,460)(389,461)(390,462)(391,463)(392,464)(393,407)(394,408)(395,409)(396,410)(397,411)(398,412)(399,413)(400,414)(401,415)(402,416)(403,417)(404,418)(405,419)(406,420), (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) );
G=PermutationGroup([[(1,269),(2,270),(3,271),(4,272),(5,273),(6,274),(7,275),(8,276),(9,277),(10,278),(11,279),(12,280),(13,281),(14,282),(15,283),(16,284),(17,285),(18,286),(19,287),(20,288),(21,289),(22,290),(23,233),(24,234),(25,235),(26,236),(27,237),(28,238),(29,239),(30,240),(31,241),(32,242),(33,243),(34,244),(35,245),(36,246),(37,247),(38,248),(39,249),(40,250),(41,251),(42,252),(43,253),(44,254),(45,255),(46,256),(47,257),(48,258),(49,259),(50,260),(51,261),(52,262),(53,263),(54,264),(55,265),(56,266),(57,267),(58,268),(59,339),(60,340),(61,341),(62,342),(63,343),(64,344),(65,345),(66,346),(67,347),(68,348),(69,291),(70,292),(71,293),(72,294),(73,295),(74,296),(75,297),(76,298),(77,299),(78,300),(79,301),(80,302),(81,303),(82,304),(83,305),(84,306),(85,307),(86,308),(87,309),(88,310),(89,311),(90,312),(91,313),(92,314),(93,315),(94,316),(95,317),(96,318),(97,319),(98,320),(99,321),(100,322),(101,323),(102,324),(103,325),(104,326),(105,327),(106,328),(107,329),(108,330),(109,331),(110,332),(111,333),(112,334),(113,335),(114,336),(115,337),(116,338),(117,394),(118,395),(119,396),(120,397),(121,398),(122,399),(123,400),(124,401),(125,402),(126,403),(127,404),(128,405),(129,406),(130,349),(131,350),(132,351),(133,352),(134,353),(135,354),(136,355),(137,356),(138,357),(139,358),(140,359),(141,360),(142,361),(143,362),(144,363),(145,364),(146,365),(147,366),(148,367),(149,368),(150,369),(151,370),(152,371),(153,372),(154,373),(155,374),(156,375),(157,376),(158,377),(159,378),(160,379),(161,380),(162,381),(163,382),(164,383),(165,384),(166,385),(167,386),(168,387),(169,388),(170,389),(171,390),(172,391),(173,392),(174,393),(175,421),(176,422),(177,423),(178,424),(179,425),(180,426),(181,427),(182,428),(183,429),(184,430),(185,431),(186,432),(187,433),(188,434),(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),(219,407),(220,408),(221,409),(222,410),(223,411),(224,412),(225,413),(226,414),(227,415),(228,416),(229,417),(230,418),(231,419),(232,420)], [(1,171),(2,172),(3,173),(4,174),(5,117),(6,118),(7,119),(8,120),(9,121),(10,122),(11,123),(12,124),(13,125),(14,126),(15,127),(16,128),(17,129),(18,130),(19,131),(20,132),(21,133),(22,134),(23,135),(24,136),(25,137),(26,138),(27,139),(28,140),(29,141),(30,142),(31,143),(32,144),(33,145),(34,146),(35,147),(36,148),(37,149),(38,150),(39,151),(40,152),(41,153),(42,154),(43,155),(44,156),(45,157),(46,158),(47,159),(48,160),(49,161),(50,162),(51,163),(52,164),(53,165),(54,166),(55,167),(56,168),(57,169),(58,170),(59,220),(60,221),(61,222),(62,223),(63,224),(64,225),(65,226),(66,227),(67,228),(68,229),(69,230),(70,231),(71,232),(72,175),(73,176),(74,177),(75,178),(76,179),(77,180),(78,181),(79,182),(80,183),(81,184),(82,185),(83,186),(84,187),(85,188),(86,189),(87,190),(88,191),(89,192),(90,193),(91,194),(92,195),(93,196),(94,197),(95,198),(96,199),(97,200),(98,201),(99,202),(100,203),(101,204),(102,205),(103,206),(104,207),(105,208),(106,209),(107,210),(108,211),(109,212),(110,213),(111,214),(112,215),(113,216),(114,217),(115,218),(116,219),(233,354),(234,355),(235,356),(236,357),(237,358),(238,359),(239,360),(240,361),(241,362),(242,363),(243,364),(244,365),(245,366),(246,367),(247,368),(248,369),(249,370),(250,371),(251,372),(252,373),(253,374),(254,375),(255,376),(256,377),(257,378),(258,379),(259,380),(260,381),(261,382),(262,383),(263,384),(264,385),(265,386),(266,387),(267,388),(268,389),(269,390),(270,391),(271,392),(272,393),(273,394),(274,395),(275,396),(276,397),(277,398),(278,399),(279,400),(280,401),(281,402),(282,403),(283,404),(284,405),(285,406),(286,349),(287,350),(288,351),(289,352),(290,353),(291,418),(292,419),(293,420),(294,421),(295,422),(296,423),(297,424),(298,425),(299,426),(300,427),(301,428),(302,429),(303,430),(304,431),(305,432),(306,433),(307,434),(308,435),(309,436),(310,437),(311,438),(312,439),(313,440),(314,441),(315,442),(316,443),(317,444),(318,445),(319,446),(320,447),(321,448),(322,449),(323,450),(324,451),(325,452),(326,453),(327,454),(328,455),(329,456),(330,457),(331,458),(332,459),(333,460),(334,461),(335,462),(336,463),(337,464),(338,407),(339,408),(340,409),(341,410),(342,411),(343,412),(344,413),(345,414),(346,415),(347,416),(348,417)], [(1,113),(2,114),(3,115),(4,116),(5,59),(6,60),(7,61),(8,62),(9,63),(10,64),(11,65),(12,66),(13,67),(14,68),(15,69),(16,70),(17,71),(18,72),(19,73),(20,74),(21,75),(22,76),(23,77),(24,78),(25,79),(26,80),(27,81),(28,82),(29,83),(30,84),(31,85),(32,86),(33,87),(34,88),(35,89),(36,90),(37,91),(38,92),(39,93),(40,94),(41,95),(42,96),(43,97),(44,98),(45,99),(46,100),(47,101),(48,102),(49,103),(50,104),(51,105),(52,106),(53,107),(54,108),(55,109),(56,110),(57,111),(58,112),(117,220),(118,221),(119,222),(120,223),(121,224),(122,225),(123,226),(124,227),(125,228),(126,229),(127,230),(128,231),(129,232),(130,175),(131,176),(132,177),(133,178),(134,179),(135,180),(136,181),(137,182),(138,183),(139,184),(140,185),(141,186),(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),(233,299),(234,300),(235,301),(236,302),(237,303),(238,304),(239,305),(240,306),(241,307),(242,308),(243,309),(244,310),(245,311),(246,312),(247,313),(248,314),(249,315),(250,316),(251,317),(252,318),(253,319),(254,320),(255,321),(256,322),(257,323),(258,324),(259,325),(260,326),(261,327),(262,328),(263,329),(264,330),(265,331),(266,332),(267,333),(268,334),(269,335),(270,336),(271,337),(272,338),(273,339),(274,340),(275,341),(276,342),(277,343),(278,344),(279,345),(280,346),(281,347),(282,348),(283,291),(284,292),(285,293),(286,294),(287,295),(288,296),(289,297),(290,298),(349,421),(350,422),(351,423),(352,424),(353,425),(354,426),(355,427),(356,428),(357,429),(358,430),(359,431),(360,432),(361,433),(362,434),(363,435),(364,436),(365,437),(366,438),(367,439),(368,440),(369,441),(370,442),(371,443),(372,444),(373,445),(374,446),(375,447),(376,448),(377,449),(378,450),(379,451),(380,452),(381,453),(382,454),(383,455),(384,456),(385,457),(386,458),(387,459),(388,460),(389,461),(390,462),(391,463),(392,464),(393,407),(394,408),(395,409),(396,410),(397,411),(398,412),(399,413),(400,414),(401,415),(402,416),(403,417),(404,418),(405,419),(406,420)], [(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)]])
464 conjugacy classes
| class | 1 | 2A | ··· | 2O | 29A | ··· | 29AB | 58A | ··· | 58PD |
| order | 1 | 2 | ··· | 2 | 29 | ··· | 29 | 58 | ··· | 58 |
| size | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
464 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | + | ||
| image | C1 | C2 | C29 | C58 |
| kernel | C23×C58 | C22×C58 | C24 | C23 |
| # reps | 1 | 15 | 28 | 420 |
Matrix representation of C23×C58 ►in GL4(𝔽59) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 58 |
| 58 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 58 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 58 | 0 |
| 0 | 0 | 0 | 58 |
| 16 | 0 | 0 | 0 |
| 0 | 23 | 0 | 0 |
| 0 | 0 | 53 | 0 |
| 0 | 0 | 0 | 6 |
G:=sub<GL(4,GF(59))| [1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,58],[58,0,0,0,0,1,0,0,0,0,1,0,0,0,0,58],[1,0,0,0,0,1,0,0,0,0,58,0,0,0,0,58],[16,0,0,0,0,23,0,0,0,0,53,0,0,0,0,6] >;
C23×C58 in GAP, Magma, Sage, TeX
C_2^3\times C_{58} % in TeX
G:=Group("C2^3xC58"); // GroupNames label
G:=SmallGroup(464,51);
// by ID
G=gap.SmallGroup(464,51);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-29]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^2=c^2=d^58=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