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G = C23×C58order 464 = 24·29

Abelian group of type [2,2,2,58]

direct product, abelian, monomial, 2-elementary

Aliases: C23×C58, SmallGroup(464,51)

Series: Derived Chief Lower central Upper central

C1 — C23×C58
C1C29C58C2×C58C22×C58 — 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 [×15], C22 [×35], C23 [×15], C24, C29, C58 [×15], C2×C58 [×35], C22×C58 [×15], C23×C58
Quotients: C1, C2 [×15], C22 [×35], C23 [×15], C24, C29, C58 [×15], C2×C58 [×35], C22×C58 [×15], C23×C58

Smallest permutation representation of C23×C58
Regular action on 464 points
Generators in S464
(1 271)(2 272)(3 273)(4 274)(5 275)(6 276)(7 277)(8 278)(9 279)(10 280)(11 281)(12 282)(13 283)(14 284)(15 285)(16 286)(17 287)(18 288)(19 289)(20 290)(21 233)(22 234)(23 235)(24 236)(25 237)(26 238)(27 239)(28 240)(29 241)(30 242)(31 243)(32 244)(33 245)(34 246)(35 247)(36 248)(37 249)(38 250)(39 251)(40 252)(41 253)(42 254)(43 255)(44 256)(45 257)(46 258)(47 259)(48 260)(49 261)(50 262)(51 263)(52 264)(53 265)(54 266)(55 267)(56 268)(57 269)(58 270)(59 298)(60 299)(61 300)(62 301)(63 302)(64 303)(65 304)(66 305)(67 306)(68 307)(69 308)(70 309)(71 310)(72 311)(73 312)(74 313)(75 314)(76 315)(77 316)(78 317)(79 318)(80 319)(81 320)(82 321)(83 322)(84 323)(85 324)(86 325)(87 326)(88 327)(89 328)(90 329)(91 330)(92 331)(93 332)(94 333)(95 334)(96 335)(97 336)(98 337)(99 338)(100 339)(101 340)(102 341)(103 342)(104 343)(105 344)(106 345)(107 346)(108 347)(109 348)(110 291)(111 292)(112 293)(113 294)(114 295)(115 296)(116 297)(117 359)(118 360)(119 361)(120 362)(121 363)(122 364)(123 365)(124 366)(125 367)(126 368)(127 369)(128 370)(129 371)(130 372)(131 373)(132 374)(133 375)(134 376)(135 377)(136 378)(137 379)(138 380)(139 381)(140 382)(141 383)(142 384)(143 385)(144 386)(145 387)(146 388)(147 389)(148 390)(149 391)(150 392)(151 393)(152 394)(153 395)(154 396)(155 397)(156 398)(157 399)(158 400)(159 401)(160 402)(161 403)(162 404)(163 405)(164 406)(165 349)(166 350)(167 351)(168 352)(169 353)(170 354)(171 355)(172 356)(173 357)(174 358)(175 423)(176 424)(177 425)(178 426)(179 427)(180 428)(181 429)(182 430)(183 431)(184 432)(185 433)(186 434)(187 435)(188 436)(189 437)(190 438)(191 439)(192 440)(193 441)(194 442)(195 443)(196 444)(197 445)(198 446)(199 447)(200 448)(201 449)(202 450)(203 451)(204 452)(205 453)(206 454)(207 455)(208 456)(209 457)(210 458)(211 459)(212 460)(213 461)(214 462)(215 463)(216 464)(217 407)(218 408)(219 409)(220 410)(221 411)(222 412)(223 413)(224 414)(225 415)(226 416)(227 417)(228 418)(229 419)(230 420)(231 421)(232 422)
(1 147)(2 148)(3 149)(4 150)(5 151)(6 152)(7 153)(8 154)(9 155)(10 156)(11 157)(12 158)(13 159)(14 160)(15 161)(16 162)(17 163)(18 164)(19 165)(20 166)(21 167)(22 168)(23 169)(24 170)(25 171)(26 172)(27 173)(28 174)(29 117)(30 118)(31 119)(32 120)(33 121)(34 122)(35 123)(36 124)(37 125)(38 126)(39 127)(40 128)(41 129)(42 130)(43 131)(44 132)(45 133)(46 134)(47 135)(48 136)(49 137)(50 138)(51 139)(52 140)(53 141)(54 142)(55 143)(56 144)(57 145)(58 146)(59 183)(60 184)(61 185)(62 186)(63 187)(64 188)(65 189)(66 190)(67 191)(68 192)(69 193)(70 194)(71 195)(72 196)(73 197)(74 198)(75 199)(76 200)(77 201)(78 202)(79 203)(80 204)(81 205)(82 206)(83 207)(84 208)(85 209)(86 210)(87 211)(88 212)(89 213)(90 214)(91 215)(92 216)(93 217)(94 218)(95 219)(96 220)(97 221)(98 222)(99 223)(100 224)(101 225)(102 226)(103 227)(104 228)(105 229)(106 230)(107 231)(108 232)(109 175)(110 176)(111 177)(112 178)(113 179)(114 180)(115 181)(116 182)(233 351)(234 352)(235 353)(236 354)(237 355)(238 356)(239 357)(240 358)(241 359)(242 360)(243 361)(244 362)(245 363)(246 364)(247 365)(248 366)(249 367)(250 368)(251 369)(252 370)(253 371)(254 372)(255 373)(256 374)(257 375)(258 376)(259 377)(260 378)(261 379)(262 380)(263 381)(264 382)(265 383)(266 384)(267 385)(268 386)(269 387)(270 388)(271 389)(272 390)(273 391)(274 392)(275 393)(276 394)(277 395)(278 396)(279 397)(280 398)(281 399)(282 400)(283 401)(284 402)(285 403)(286 404)(287 405)(288 406)(289 349)(290 350)(291 424)(292 425)(293 426)(294 427)(295 428)(296 429)(297 430)(298 431)(299 432)(300 433)(301 434)(302 435)(303 436)(304 437)(305 438)(306 439)(307 440)(308 441)(309 442)(310 443)(311 444)(312 445)(313 446)(314 447)(315 448)(316 449)(317 450)(318 451)(319 452)(320 453)(321 454)(322 455)(323 456)(324 457)(325 458)(326 459)(327 460)(328 461)(329 462)(330 463)(331 464)(332 407)(333 408)(334 409)(335 410)(336 411)(337 412)(338 413)(339 414)(340 415)(341 416)(342 417)(343 418)(344 419)(345 420)(346 421)(347 422)(348 423)
(1 92)(2 93)(3 94)(4 95)(5 96)(6 97)(7 98)(8 99)(9 100)(10 101)(11 102)(12 103)(13 104)(14 105)(15 106)(16 107)(17 108)(18 109)(19 110)(20 111)(21 112)(22 113)(23 114)(24 115)(25 116)(26 59)(27 60)(28 61)(29 62)(30 63)(31 64)(32 65)(33 66)(34 67)(35 68)(36 69)(37 70)(38 71)(39 72)(40 73)(41 74)(42 75)(43 76)(44 77)(45 78)(46 79)(47 80)(48 81)(49 82)(50 83)(51 84)(52 85)(53 86)(54 87)(55 88)(56 89)(57 90)(58 91)(117 186)(118 187)(119 188)(120 189)(121 190)(122 191)(123 192)(124 193)(125 194)(126 195)(127 196)(128 197)(129 198)(130 199)(131 200)(132 201)(133 202)(134 203)(135 204)(136 205)(137 206)(138 207)(139 208)(140 209)(141 210)(142 211)(143 212)(144 213)(145 214)(146 215)(147 216)(148 217)(149 218)(150 219)(151 220)(152 221)(153 222)(154 223)(155 224)(156 225)(157 226)(158 227)(159 228)(160 229)(161 230)(162 231)(163 232)(164 175)(165 176)(166 177)(167 178)(168 179)(169 180)(170 181)(171 182)(172 183)(173 184)(174 185)(233 293)(234 294)(235 295)(236 296)(237 297)(238 298)(239 299)(240 300)(241 301)(242 302)(243 303)(244 304)(245 305)(246 306)(247 307)(248 308)(249 309)(250 310)(251 311)(252 312)(253 313)(254 314)(255 315)(256 316)(257 317)(258 318)(259 319)(260 320)(261 321)(262 322)(263 323)(264 324)(265 325)(266 326)(267 327)(268 328)(269 329)(270 330)(271 331)(272 332)(273 333)(274 334)(275 335)(276 336)(277 337)(278 338)(279 339)(280 340)(281 341)(282 342)(283 343)(284 344)(285 345)(286 346)(287 347)(288 348)(289 291)(290 292)(349 424)(350 425)(351 426)(352 427)(353 428)(354 429)(355 430)(356 431)(357 432)(358 433)(359 434)(360 435)(361 436)(362 437)(363 438)(364 439)(365 440)(366 441)(367 442)(368 443)(369 444)(370 445)(371 446)(372 447)(373 448)(374 449)(375 450)(376 451)(377 452)(378 453)(379 454)(380 455)(381 456)(382 457)(383 458)(384 459)(385 460)(386 461)(387 462)(388 463)(389 464)(390 407)(391 408)(392 409)(393 410)(394 411)(395 412)(396 413)(397 414)(398 415)(399 416)(400 417)(401 418)(402 419)(403 420)(404 421)(405 422)(406 423)
(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)| (1,271)(2,272)(3,273)(4,274)(5,275)(6,276)(7,277)(8,278)(9,279)(10,280)(11,281)(12,282)(13,283)(14,284)(15,285)(16,286)(17,287)(18,288)(19,289)(20,290)(21,233)(22,234)(23,235)(24,236)(25,237)(26,238)(27,239)(28,240)(29,241)(30,242)(31,243)(32,244)(33,245)(34,246)(35,247)(36,248)(37,249)(38,250)(39,251)(40,252)(41,253)(42,254)(43,255)(44,256)(45,257)(46,258)(47,259)(48,260)(49,261)(50,262)(51,263)(52,264)(53,265)(54,266)(55,267)(56,268)(57,269)(58,270)(59,298)(60,299)(61,300)(62,301)(63,302)(64,303)(65,304)(66,305)(67,306)(68,307)(69,308)(70,309)(71,310)(72,311)(73,312)(74,313)(75,314)(76,315)(77,316)(78,317)(79,318)(80,319)(81,320)(82,321)(83,322)(84,323)(85,324)(86,325)(87,326)(88,327)(89,328)(90,329)(91,330)(92,331)(93,332)(94,333)(95,334)(96,335)(97,336)(98,337)(99,338)(100,339)(101,340)(102,341)(103,342)(104,343)(105,344)(106,345)(107,346)(108,347)(109,348)(110,291)(111,292)(112,293)(113,294)(114,295)(115,296)(116,297)(117,359)(118,360)(119,361)(120,362)(121,363)(122,364)(123,365)(124,366)(125,367)(126,368)(127,369)(128,370)(129,371)(130,372)(131,373)(132,374)(133,375)(134,376)(135,377)(136,378)(137,379)(138,380)(139,381)(140,382)(141,383)(142,384)(143,385)(144,386)(145,387)(146,388)(147,389)(148,390)(149,391)(150,392)(151,393)(152,394)(153,395)(154,396)(155,397)(156,398)(157,399)(158,400)(159,401)(160,402)(161,403)(162,404)(163,405)(164,406)(165,349)(166,350)(167,351)(168,352)(169,353)(170,354)(171,355)(172,356)(173,357)(174,358)(175,423)(176,424)(177,425)(178,426)(179,427)(180,428)(181,429)(182,430)(183,431)(184,432)(185,433)(186,434)(187,435)(188,436)(189,437)(190,438)(191,439)(192,440)(193,441)(194,442)(195,443)(196,444)(197,445)(198,446)(199,447)(200,448)(201,449)(202,450)(203,451)(204,452)(205,453)(206,454)(207,455)(208,456)(209,457)(210,458)(211,459)(212,460)(213,461)(214,462)(215,463)(216,464)(217,407)(218,408)(219,409)(220,410)(221,411)(222,412)(223,413)(224,414)(225,415)(226,416)(227,417)(228,418)(229,419)(230,420)(231,421)(232,422), (1,147)(2,148)(3,149)(4,150)(5,151)(6,152)(7,153)(8,154)(9,155)(10,156)(11,157)(12,158)(13,159)(14,160)(15,161)(16,162)(17,163)(18,164)(19,165)(20,166)(21,167)(22,168)(23,169)(24,170)(25,171)(26,172)(27,173)(28,174)(29,117)(30,118)(31,119)(32,120)(33,121)(34,122)(35,123)(36,124)(37,125)(38,126)(39,127)(40,128)(41,129)(42,130)(43,131)(44,132)(45,133)(46,134)(47,135)(48,136)(49,137)(50,138)(51,139)(52,140)(53,141)(54,142)(55,143)(56,144)(57,145)(58,146)(59,183)(60,184)(61,185)(62,186)(63,187)(64,188)(65,189)(66,190)(67,191)(68,192)(69,193)(70,194)(71,195)(72,196)(73,197)(74,198)(75,199)(76,200)(77,201)(78,202)(79,203)(80,204)(81,205)(82,206)(83,207)(84,208)(85,209)(86,210)(87,211)(88,212)(89,213)(90,214)(91,215)(92,216)(93,217)(94,218)(95,219)(96,220)(97,221)(98,222)(99,223)(100,224)(101,225)(102,226)(103,227)(104,228)(105,229)(106,230)(107,231)(108,232)(109,175)(110,176)(111,177)(112,178)(113,179)(114,180)(115,181)(116,182)(233,351)(234,352)(235,353)(236,354)(237,355)(238,356)(239,357)(240,358)(241,359)(242,360)(243,361)(244,362)(245,363)(246,364)(247,365)(248,366)(249,367)(250,368)(251,369)(252,370)(253,371)(254,372)(255,373)(256,374)(257,375)(258,376)(259,377)(260,378)(261,379)(262,380)(263,381)(264,382)(265,383)(266,384)(267,385)(268,386)(269,387)(270,388)(271,389)(272,390)(273,391)(274,392)(275,393)(276,394)(277,395)(278,396)(279,397)(280,398)(281,399)(282,400)(283,401)(284,402)(285,403)(286,404)(287,405)(288,406)(289,349)(290,350)(291,424)(292,425)(293,426)(294,427)(295,428)(296,429)(297,430)(298,431)(299,432)(300,433)(301,434)(302,435)(303,436)(304,437)(305,438)(306,439)(307,440)(308,441)(309,442)(310,443)(311,444)(312,445)(313,446)(314,447)(315,448)(316,449)(317,450)(318,451)(319,452)(320,453)(321,454)(322,455)(323,456)(324,457)(325,458)(326,459)(327,460)(328,461)(329,462)(330,463)(331,464)(332,407)(333,408)(334,409)(335,410)(336,411)(337,412)(338,413)(339,414)(340,415)(341,416)(342,417)(343,418)(344,419)(345,420)(346,421)(347,422)(348,423), (1,92)(2,93)(3,94)(4,95)(5,96)(6,97)(7,98)(8,99)(9,100)(10,101)(11,102)(12,103)(13,104)(14,105)(15,106)(16,107)(17,108)(18,109)(19,110)(20,111)(21,112)(22,113)(23,114)(24,115)(25,116)(26,59)(27,60)(28,61)(29,62)(30,63)(31,64)(32,65)(33,66)(34,67)(35,68)(36,69)(37,70)(38,71)(39,72)(40,73)(41,74)(42,75)(43,76)(44,77)(45,78)(46,79)(47,80)(48,81)(49,82)(50,83)(51,84)(52,85)(53,86)(54,87)(55,88)(56,89)(57,90)(58,91)(117,186)(118,187)(119,188)(120,189)(121,190)(122,191)(123,192)(124,193)(125,194)(126,195)(127,196)(128,197)(129,198)(130,199)(131,200)(132,201)(133,202)(134,203)(135,204)(136,205)(137,206)(138,207)(139,208)(140,209)(141,210)(142,211)(143,212)(144,213)(145,214)(146,215)(147,216)(148,217)(149,218)(150,219)(151,220)(152,221)(153,222)(154,223)(155,224)(156,225)(157,226)(158,227)(159,228)(160,229)(161,230)(162,231)(163,232)(164,175)(165,176)(166,177)(167,178)(168,179)(169,180)(170,181)(171,182)(172,183)(173,184)(174,185)(233,293)(234,294)(235,295)(236,296)(237,297)(238,298)(239,299)(240,300)(241,301)(242,302)(243,303)(244,304)(245,305)(246,306)(247,307)(248,308)(249,309)(250,310)(251,311)(252,312)(253,313)(254,314)(255,315)(256,316)(257,317)(258,318)(259,319)(260,320)(261,321)(262,322)(263,323)(264,324)(265,325)(266,326)(267,327)(268,328)(269,329)(270,330)(271,331)(272,332)(273,333)(274,334)(275,335)(276,336)(277,337)(278,338)(279,339)(280,340)(281,341)(282,342)(283,343)(284,344)(285,345)(286,346)(287,347)(288,348)(289,291)(290,292)(349,424)(350,425)(351,426)(352,427)(353,428)(354,429)(355,430)(356,431)(357,432)(358,433)(359,434)(360,435)(361,436)(362,437)(363,438)(364,439)(365,440)(366,441)(367,442)(368,443)(369,444)(370,445)(371,446)(372,447)(373,448)(374,449)(375,450)(376,451)(377,452)(378,453)(379,454)(380,455)(381,456)(382,457)(383,458)(384,459)(385,460)(386,461)(387,462)(388,463)(389,464)(390,407)(391,408)(392,409)(393,410)(394,411)(395,412)(396,413)(397,414)(398,415)(399,416)(400,417)(401,418)(402,419)(403,420)(404,421)(405,422)(406,423), (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( (1,271)(2,272)(3,273)(4,274)(5,275)(6,276)(7,277)(8,278)(9,279)(10,280)(11,281)(12,282)(13,283)(14,284)(15,285)(16,286)(17,287)(18,288)(19,289)(20,290)(21,233)(22,234)(23,235)(24,236)(25,237)(26,238)(27,239)(28,240)(29,241)(30,242)(31,243)(32,244)(33,245)(34,246)(35,247)(36,248)(37,249)(38,250)(39,251)(40,252)(41,253)(42,254)(43,255)(44,256)(45,257)(46,258)(47,259)(48,260)(49,261)(50,262)(51,263)(52,264)(53,265)(54,266)(55,267)(56,268)(57,269)(58,270)(59,298)(60,299)(61,300)(62,301)(63,302)(64,303)(65,304)(66,305)(67,306)(68,307)(69,308)(70,309)(71,310)(72,311)(73,312)(74,313)(75,314)(76,315)(77,316)(78,317)(79,318)(80,319)(81,320)(82,321)(83,322)(84,323)(85,324)(86,325)(87,326)(88,327)(89,328)(90,329)(91,330)(92,331)(93,332)(94,333)(95,334)(96,335)(97,336)(98,337)(99,338)(100,339)(101,340)(102,341)(103,342)(104,343)(105,344)(106,345)(107,346)(108,347)(109,348)(110,291)(111,292)(112,293)(113,294)(114,295)(115,296)(116,297)(117,359)(118,360)(119,361)(120,362)(121,363)(122,364)(123,365)(124,366)(125,367)(126,368)(127,369)(128,370)(129,371)(130,372)(131,373)(132,374)(133,375)(134,376)(135,377)(136,378)(137,379)(138,380)(139,381)(140,382)(141,383)(142,384)(143,385)(144,386)(145,387)(146,388)(147,389)(148,390)(149,391)(150,392)(151,393)(152,394)(153,395)(154,396)(155,397)(156,398)(157,399)(158,400)(159,401)(160,402)(161,403)(162,404)(163,405)(164,406)(165,349)(166,350)(167,351)(168,352)(169,353)(170,354)(171,355)(172,356)(173,357)(174,358)(175,423)(176,424)(177,425)(178,426)(179,427)(180,428)(181,429)(182,430)(183,431)(184,432)(185,433)(186,434)(187,435)(188,436)(189,437)(190,438)(191,439)(192,440)(193,441)(194,442)(195,443)(196,444)(197,445)(198,446)(199,447)(200,448)(201,449)(202,450)(203,451)(204,452)(205,453)(206,454)(207,455)(208,456)(209,457)(210,458)(211,459)(212,460)(213,461)(214,462)(215,463)(216,464)(217,407)(218,408)(219,409)(220,410)(221,411)(222,412)(223,413)(224,414)(225,415)(226,416)(227,417)(228,418)(229,419)(230,420)(231,421)(232,422), (1,147)(2,148)(3,149)(4,150)(5,151)(6,152)(7,153)(8,154)(9,155)(10,156)(11,157)(12,158)(13,159)(14,160)(15,161)(16,162)(17,163)(18,164)(19,165)(20,166)(21,167)(22,168)(23,169)(24,170)(25,171)(26,172)(27,173)(28,174)(29,117)(30,118)(31,119)(32,120)(33,121)(34,122)(35,123)(36,124)(37,125)(38,126)(39,127)(40,128)(41,129)(42,130)(43,131)(44,132)(45,133)(46,134)(47,135)(48,136)(49,137)(50,138)(51,139)(52,140)(53,141)(54,142)(55,143)(56,144)(57,145)(58,146)(59,183)(60,184)(61,185)(62,186)(63,187)(64,188)(65,189)(66,190)(67,191)(68,192)(69,193)(70,194)(71,195)(72,196)(73,197)(74,198)(75,199)(76,200)(77,201)(78,202)(79,203)(80,204)(81,205)(82,206)(83,207)(84,208)(85,209)(86,210)(87,211)(88,212)(89,213)(90,214)(91,215)(92,216)(93,217)(94,218)(95,219)(96,220)(97,221)(98,222)(99,223)(100,224)(101,225)(102,226)(103,227)(104,228)(105,229)(106,230)(107,231)(108,232)(109,175)(110,176)(111,177)(112,178)(113,179)(114,180)(115,181)(116,182)(233,351)(234,352)(235,353)(236,354)(237,355)(238,356)(239,357)(240,358)(241,359)(242,360)(243,361)(244,362)(245,363)(246,364)(247,365)(248,366)(249,367)(250,368)(251,369)(252,370)(253,371)(254,372)(255,373)(256,374)(257,375)(258,376)(259,377)(260,378)(261,379)(262,380)(263,381)(264,382)(265,383)(266,384)(267,385)(268,386)(269,387)(270,388)(271,389)(272,390)(273,391)(274,392)(275,393)(276,394)(277,395)(278,396)(279,397)(280,398)(281,399)(282,400)(283,401)(284,402)(285,403)(286,404)(287,405)(288,406)(289,349)(290,350)(291,424)(292,425)(293,426)(294,427)(295,428)(296,429)(297,430)(298,431)(299,432)(300,433)(301,434)(302,435)(303,436)(304,437)(305,438)(306,439)(307,440)(308,441)(309,442)(310,443)(311,444)(312,445)(313,446)(314,447)(315,448)(316,449)(317,450)(318,451)(319,452)(320,453)(321,454)(322,455)(323,456)(324,457)(325,458)(326,459)(327,460)(328,461)(329,462)(330,463)(331,464)(332,407)(333,408)(334,409)(335,410)(336,411)(337,412)(338,413)(339,414)(340,415)(341,416)(342,417)(343,418)(344,419)(345,420)(346,421)(347,422)(348,423), (1,92)(2,93)(3,94)(4,95)(5,96)(6,97)(7,98)(8,99)(9,100)(10,101)(11,102)(12,103)(13,104)(14,105)(15,106)(16,107)(17,108)(18,109)(19,110)(20,111)(21,112)(22,113)(23,114)(24,115)(25,116)(26,59)(27,60)(28,61)(29,62)(30,63)(31,64)(32,65)(33,66)(34,67)(35,68)(36,69)(37,70)(38,71)(39,72)(40,73)(41,74)(42,75)(43,76)(44,77)(45,78)(46,79)(47,80)(48,81)(49,82)(50,83)(51,84)(52,85)(53,86)(54,87)(55,88)(56,89)(57,90)(58,91)(117,186)(118,187)(119,188)(120,189)(121,190)(122,191)(123,192)(124,193)(125,194)(126,195)(127,196)(128,197)(129,198)(130,199)(131,200)(132,201)(133,202)(134,203)(135,204)(136,205)(137,206)(138,207)(139,208)(140,209)(141,210)(142,211)(143,212)(144,213)(145,214)(146,215)(147,216)(148,217)(149,218)(150,219)(151,220)(152,221)(153,222)(154,223)(155,224)(156,225)(157,226)(158,227)(159,228)(160,229)(161,230)(162,231)(163,232)(164,175)(165,176)(166,177)(167,178)(168,179)(169,180)(170,181)(171,182)(172,183)(173,184)(174,185)(233,293)(234,294)(235,295)(236,296)(237,297)(238,298)(239,299)(240,300)(241,301)(242,302)(243,303)(244,304)(245,305)(246,306)(247,307)(248,308)(249,309)(250,310)(251,311)(252,312)(253,313)(254,314)(255,315)(256,316)(257,317)(258,318)(259,319)(260,320)(261,321)(262,322)(263,323)(264,324)(265,325)(266,326)(267,327)(268,328)(269,329)(270,330)(271,331)(272,332)(273,333)(274,334)(275,335)(276,336)(277,337)(278,338)(279,339)(280,340)(281,341)(282,342)(283,343)(284,344)(285,345)(286,346)(287,347)(288,348)(289,291)(290,292)(349,424)(350,425)(351,426)(352,427)(353,428)(354,429)(355,430)(356,431)(357,432)(358,433)(359,434)(360,435)(361,436)(362,437)(363,438)(364,439)(365,440)(366,441)(367,442)(368,443)(369,444)(370,445)(371,446)(372,447)(373,448)(374,449)(375,450)(376,451)(377,452)(378,453)(379,454)(380,455)(381,456)(382,457)(383,458)(384,459)(385,460)(386,461)(387,462)(388,463)(389,464)(390,407)(391,408)(392,409)(393,410)(394,411)(395,412)(396,413)(397,414)(398,415)(399,416)(400,417)(401,418)(402,419)(403,420)(404,421)(405,422)(406,423), (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([(1,271),(2,272),(3,273),(4,274),(5,275),(6,276),(7,277),(8,278),(9,279),(10,280),(11,281),(12,282),(13,283),(14,284),(15,285),(16,286),(17,287),(18,288),(19,289),(20,290),(21,233),(22,234),(23,235),(24,236),(25,237),(26,238),(27,239),(28,240),(29,241),(30,242),(31,243),(32,244),(33,245),(34,246),(35,247),(36,248),(37,249),(38,250),(39,251),(40,252),(41,253),(42,254),(43,255),(44,256),(45,257),(46,258),(47,259),(48,260),(49,261),(50,262),(51,263),(52,264),(53,265),(54,266),(55,267),(56,268),(57,269),(58,270),(59,298),(60,299),(61,300),(62,301),(63,302),(64,303),(65,304),(66,305),(67,306),(68,307),(69,308),(70,309),(71,310),(72,311),(73,312),(74,313),(75,314),(76,315),(77,316),(78,317),(79,318),(80,319),(81,320),(82,321),(83,322),(84,323),(85,324),(86,325),(87,326),(88,327),(89,328),(90,329),(91,330),(92,331),(93,332),(94,333),(95,334),(96,335),(97,336),(98,337),(99,338),(100,339),(101,340),(102,341),(103,342),(104,343),(105,344),(106,345),(107,346),(108,347),(109,348),(110,291),(111,292),(112,293),(113,294),(114,295),(115,296),(116,297),(117,359),(118,360),(119,361),(120,362),(121,363),(122,364),(123,365),(124,366),(125,367),(126,368),(127,369),(128,370),(129,371),(130,372),(131,373),(132,374),(133,375),(134,376),(135,377),(136,378),(137,379),(138,380),(139,381),(140,382),(141,383),(142,384),(143,385),(144,386),(145,387),(146,388),(147,389),(148,390),(149,391),(150,392),(151,393),(152,394),(153,395),(154,396),(155,397),(156,398),(157,399),(158,400),(159,401),(160,402),(161,403),(162,404),(163,405),(164,406),(165,349),(166,350),(167,351),(168,352),(169,353),(170,354),(171,355),(172,356),(173,357),(174,358),(175,423),(176,424),(177,425),(178,426),(179,427),(180,428),(181,429),(182,430),(183,431),(184,432),(185,433),(186,434),(187,435),(188,436),(189,437),(190,438),(191,439),(192,440),(193,441),(194,442),(195,443),(196,444),(197,445),(198,446),(199,447),(200,448),(201,449),(202,450),(203,451),(204,452),(205,453),(206,454),(207,455),(208,456),(209,457),(210,458),(211,459),(212,460),(213,461),(214,462),(215,463),(216,464),(217,407),(218,408),(219,409),(220,410),(221,411),(222,412),(223,413),(224,414),(225,415),(226,416),(227,417),(228,418),(229,419),(230,420),(231,421),(232,422)], [(1,147),(2,148),(3,149),(4,150),(5,151),(6,152),(7,153),(8,154),(9,155),(10,156),(11,157),(12,158),(13,159),(14,160),(15,161),(16,162),(17,163),(18,164),(19,165),(20,166),(21,167),(22,168),(23,169),(24,170),(25,171),(26,172),(27,173),(28,174),(29,117),(30,118),(31,119),(32,120),(33,121),(34,122),(35,123),(36,124),(37,125),(38,126),(39,127),(40,128),(41,129),(42,130),(43,131),(44,132),(45,133),(46,134),(47,135),(48,136),(49,137),(50,138),(51,139),(52,140),(53,141),(54,142),(55,143),(56,144),(57,145),(58,146),(59,183),(60,184),(61,185),(62,186),(63,187),(64,188),(65,189),(66,190),(67,191),(68,192),(69,193),(70,194),(71,195),(72,196),(73,197),(74,198),(75,199),(76,200),(77,201),(78,202),(79,203),(80,204),(81,205),(82,206),(83,207),(84,208),(85,209),(86,210),(87,211),(88,212),(89,213),(90,214),(91,215),(92,216),(93,217),(94,218),(95,219),(96,220),(97,221),(98,222),(99,223),(100,224),(101,225),(102,226),(103,227),(104,228),(105,229),(106,230),(107,231),(108,232),(109,175),(110,176),(111,177),(112,178),(113,179),(114,180),(115,181),(116,182),(233,351),(234,352),(235,353),(236,354),(237,355),(238,356),(239,357),(240,358),(241,359),(242,360),(243,361),(244,362),(245,363),(246,364),(247,365),(248,366),(249,367),(250,368),(251,369),(252,370),(253,371),(254,372),(255,373),(256,374),(257,375),(258,376),(259,377),(260,378),(261,379),(262,380),(263,381),(264,382),(265,383),(266,384),(267,385),(268,386),(269,387),(270,388),(271,389),(272,390),(273,391),(274,392),(275,393),(276,394),(277,395),(278,396),(279,397),(280,398),(281,399),(282,400),(283,401),(284,402),(285,403),(286,404),(287,405),(288,406),(289,349),(290,350),(291,424),(292,425),(293,426),(294,427),(295,428),(296,429),(297,430),(298,431),(299,432),(300,433),(301,434),(302,435),(303,436),(304,437),(305,438),(306,439),(307,440),(308,441),(309,442),(310,443),(311,444),(312,445),(313,446),(314,447),(315,448),(316,449),(317,450),(318,451),(319,452),(320,453),(321,454),(322,455),(323,456),(324,457),(325,458),(326,459),(327,460),(328,461),(329,462),(330,463),(331,464),(332,407),(333,408),(334,409),(335,410),(336,411),(337,412),(338,413),(339,414),(340,415),(341,416),(342,417),(343,418),(344,419),(345,420),(346,421),(347,422),(348,423)], [(1,92),(2,93),(3,94),(4,95),(5,96),(6,97),(7,98),(8,99),(9,100),(10,101),(11,102),(12,103),(13,104),(14,105),(15,106),(16,107),(17,108),(18,109),(19,110),(20,111),(21,112),(22,113),(23,114),(24,115),(25,116),(26,59),(27,60),(28,61),(29,62),(30,63),(31,64),(32,65),(33,66),(34,67),(35,68),(36,69),(37,70),(38,71),(39,72),(40,73),(41,74),(42,75),(43,76),(44,77),(45,78),(46,79),(47,80),(48,81),(49,82),(50,83),(51,84),(52,85),(53,86),(54,87),(55,88),(56,89),(57,90),(58,91),(117,186),(118,187),(119,188),(120,189),(121,190),(122,191),(123,192),(124,193),(125,194),(126,195),(127,196),(128,197),(129,198),(130,199),(131,200),(132,201),(133,202),(134,203),(135,204),(136,205),(137,206),(138,207),(139,208),(140,209),(141,210),(142,211),(143,212),(144,213),(145,214),(146,215),(147,216),(148,217),(149,218),(150,219),(151,220),(152,221),(153,222),(154,223),(155,224),(156,225),(157,226),(158,227),(159,228),(160,229),(161,230),(162,231),(163,232),(164,175),(165,176),(166,177),(167,178),(168,179),(169,180),(170,181),(171,182),(172,183),(173,184),(174,185),(233,293),(234,294),(235,295),(236,296),(237,297),(238,298),(239,299),(240,300),(241,301),(242,302),(243,303),(244,304),(245,305),(246,306),(247,307),(248,308),(249,309),(250,310),(251,311),(252,312),(253,313),(254,314),(255,315),(256,316),(257,317),(258,318),(259,319),(260,320),(261,321),(262,322),(263,323),(264,324),(265,325),(266,326),(267,327),(268,328),(269,329),(270,330),(271,331),(272,332),(273,333),(274,334),(275,335),(276,336),(277,337),(278,338),(279,339),(280,340),(281,341),(282,342),(283,343),(284,344),(285,345),(286,346),(287,347),(288,348),(289,291),(290,292),(349,424),(350,425),(351,426),(352,427),(353,428),(354,429),(355,430),(356,431),(357,432),(358,433),(359,434),(360,435),(361,436),(362,437),(363,438),(364,439),(365,440),(366,441),(367,442),(368,443),(369,444),(370,445),(371,446),(372,447),(373,448),(374,449),(375,450),(376,451),(377,452),(378,453),(379,454),(380,455),(381,456),(382,457),(383,458),(384,459),(385,460),(386,461),(387,462),(388,463),(389,464),(390,407),(391,408),(392,409),(393,410),(394,411),(395,412),(396,413),(397,414),(398,415),(399,416),(400,417),(401,418),(402,419),(403,420),(404,421),(405,422),(406,423)], [(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···2O29A···29AB58A···58PD
order12···229···2958···58
size11···11···11···1

464 irreducible representations

dim1111
type++
imageC1C2C29C58
kernelC23×C58C22×C58C24C23
# reps11528420

Matrix representation of C23×C58 in GL4(𝔽59) generated by

1000
0100
0010
00058
,
58000
0100
0010
00058
,
1000
0100
00580
00058
,
16000
02300
00530
0006
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

׿
×
𝔽