metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C58.5D4, C58.1Q8, Dic29⋊1C4, C2.1Dic58, C22.4D58, C29⋊2(C4⋊C4), C2.4(C4×D29), (C2×C4).1D29, (C2×C116).1C2, C58.11(C2×C4), C2.1(C29⋊D4), (C2×C58).4C22, (C2×Dic29).1C2, SmallGroup(464,12)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C58.D4
G = < a,b,c | a58=b4=1, c2=a29, bab-1=cac-1=a-1, cbc-1=b-1 >
Smallest permutation representation of C58.D4
►Regular action on 464 points
Generators in S464
(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)
(1 456 145 406)(2 455 146 405)(3 454 147 404)(4 453 148 403)(5 452 149 402)(6 451 150 401)(7 450 151 400)(8 449 152 399)(9 448 153 398)(10 447 154 397)(11 446 155 396)(12 445 156 395)(13 444 157 394)(14 443 158 393)(15 442 159 392)(16 441 160 391)(17 440 161 390)(18 439 162 389)(19 438 163 388)(20 437 164 387)(21 436 165 386)(22 435 166 385)(23 434 167 384)(24 433 168 383)(25 432 169 382)(26 431 170 381)(27 430 171 380)(28 429 172 379)(29 428 173 378)(30 427 174 377)(31 426 117 376)(32 425 118 375)(33 424 119 374)(34 423 120 373)(35 422 121 372)(36 421 122 371)(37 420 123 370)(38 419 124 369)(39 418 125 368)(40 417 126 367)(41 416 127 366)(42 415 128 365)(43 414 129 364)(44 413 130 363)(45 412 131 362)(46 411 132 361)(47 410 133 360)(48 409 134 359)(49 408 135 358)(50 407 136 357)(51 464 137 356)(52 463 138 355)(53 462 139 354)(54 461 140 353)(55 460 141 352)(56 459 142 351)(57 458 143 350)(58 457 144 349)(59 346 215 255)(60 345 216 254)(61 344 217 253)(62 343 218 252)(63 342 219 251)(64 341 220 250)(65 340 221 249)(66 339 222 248)(67 338 223 247)(68 337 224 246)(69 336 225 245)(70 335 226 244)(71 334 227 243)(72 333 228 242)(73 332 229 241)(74 331 230 240)(75 330 231 239)(76 329 232 238)(77 328 175 237)(78 327 176 236)(79 326 177 235)(80 325 178 234)(81 324 179 233)(82 323 180 290)(83 322 181 289)(84 321 182 288)(85 320 183 287)(86 319 184 286)(87 318 185 285)(88 317 186 284)(89 316 187 283)(90 315 188 282)(91 314 189 281)(92 313 190 280)(93 312 191 279)(94 311 192 278)(95 310 193 277)(96 309 194 276)(97 308 195 275)(98 307 196 274)(99 306 197 273)(100 305 198 272)(101 304 199 271)(102 303 200 270)(103 302 201 269)(104 301 202 268)(105 300 203 267)(106 299 204 266)(107 298 205 265)(108 297 206 264)(109 296 207 263)(110 295 208 262)(111 294 209 261)(112 293 210 260)(113 292 211 259)(114 291 212 258)(115 348 213 257)(116 347 214 256)
(1 197 30 226)(2 196 31 225)(3 195 32 224)(4 194 33 223)(5 193 34 222)(6 192 35 221)(7 191 36 220)(8 190 37 219)(9 189 38 218)(10 188 39 217)(11 187 40 216)(12 186 41 215)(13 185 42 214)(14 184 43 213)(15 183 44 212)(16 182 45 211)(17 181 46 210)(18 180 47 209)(19 179 48 208)(20 178 49 207)(21 177 50 206)(22 176 51 205)(23 175 52 204)(24 232 53 203)(25 231 54 202)(26 230 55 201)(27 229 56 200)(28 228 57 199)(29 227 58 198)(59 156 88 127)(60 155 89 126)(61 154 90 125)(62 153 91 124)(63 152 92 123)(64 151 93 122)(65 150 94 121)(66 149 95 120)(67 148 96 119)(68 147 97 118)(69 146 98 117)(70 145 99 174)(71 144 100 173)(72 143 101 172)(73 142 102 171)(74 141 103 170)(75 140 104 169)(76 139 105 168)(77 138 106 167)(78 137 107 166)(79 136 108 165)(80 135 109 164)(81 134 110 163)(82 133 111 162)(83 132 112 161)(84 131 113 160)(85 130 114 159)(86 129 115 158)(87 128 116 157)(233 359 262 388)(234 358 263 387)(235 357 264 386)(236 356 265 385)(237 355 266 384)(238 354 267 383)(239 353 268 382)(240 352 269 381)(241 351 270 380)(242 350 271 379)(243 349 272 378)(244 406 273 377)(245 405 274 376)(246 404 275 375)(247 403 276 374)(248 402 277 373)(249 401 278 372)(250 400 279 371)(251 399 280 370)(252 398 281 369)(253 397 282 368)(254 396 283 367)(255 395 284 366)(256 394 285 365)(257 393 286 364)(258 392 287 363)(259 391 288 362)(260 390 289 361)(261 389 290 360)(291 442 320 413)(292 441 321 412)(293 440 322 411)(294 439 323 410)(295 438 324 409)(296 437 325 408)(297 436 326 407)(298 435 327 464)(299 434 328 463)(300 433 329 462)(301 432 330 461)(302 431 331 460)(303 430 332 459)(304 429 333 458)(305 428 334 457)(306 427 335 456)(307 426 336 455)(308 425 337 454)(309 424 338 453)(310 423 339 452)(311 422 340 451)(312 421 341 450)(313 420 342 449)(314 419 343 448)(315 418 344 447)(316 417 345 446)(317 416 346 445)(318 415 347 444)(319 414 348 443)
G:=sub<Sym(464)| (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), (1,456,145,406)(2,455,146,405)(3,454,147,404)(4,453,148,403)(5,452,149,402)(6,451,150,401)(7,450,151,400)(8,449,152,399)(9,448,153,398)(10,447,154,397)(11,446,155,396)(12,445,156,395)(13,444,157,394)(14,443,158,393)(15,442,159,392)(16,441,160,391)(17,440,161,390)(18,439,162,389)(19,438,163,388)(20,437,164,387)(21,436,165,386)(22,435,166,385)(23,434,167,384)(24,433,168,383)(25,432,169,382)(26,431,170,381)(27,430,171,380)(28,429,172,379)(29,428,173,378)(30,427,174,377)(31,426,117,376)(32,425,118,375)(33,424,119,374)(34,423,120,373)(35,422,121,372)(36,421,122,371)(37,420,123,370)(38,419,124,369)(39,418,125,368)(40,417,126,367)(41,416,127,366)(42,415,128,365)(43,414,129,364)(44,413,130,363)(45,412,131,362)(46,411,132,361)(47,410,133,360)(48,409,134,359)(49,408,135,358)(50,407,136,357)(51,464,137,356)(52,463,138,355)(53,462,139,354)(54,461,140,353)(55,460,141,352)(56,459,142,351)(57,458,143,350)(58,457,144,349)(59,346,215,255)(60,345,216,254)(61,344,217,253)(62,343,218,252)(63,342,219,251)(64,341,220,250)(65,340,221,249)(66,339,222,248)(67,338,223,247)(68,337,224,246)(69,336,225,245)(70,335,226,244)(71,334,227,243)(72,333,228,242)(73,332,229,241)(74,331,230,240)(75,330,231,239)(76,329,232,238)(77,328,175,237)(78,327,176,236)(79,326,177,235)(80,325,178,234)(81,324,179,233)(82,323,180,290)(83,322,181,289)(84,321,182,288)(85,320,183,287)(86,319,184,286)(87,318,185,285)(88,317,186,284)(89,316,187,283)(90,315,188,282)(91,314,189,281)(92,313,190,280)(93,312,191,279)(94,311,192,278)(95,310,193,277)(96,309,194,276)(97,308,195,275)(98,307,196,274)(99,306,197,273)(100,305,198,272)(101,304,199,271)(102,303,200,270)(103,302,201,269)(104,301,202,268)(105,300,203,267)(106,299,204,266)(107,298,205,265)(108,297,206,264)(109,296,207,263)(110,295,208,262)(111,294,209,261)(112,293,210,260)(113,292,211,259)(114,291,212,258)(115,348,213,257)(116,347,214,256), (1,197,30,226)(2,196,31,225)(3,195,32,224)(4,194,33,223)(5,193,34,222)(6,192,35,221)(7,191,36,220)(8,190,37,219)(9,189,38,218)(10,188,39,217)(11,187,40,216)(12,186,41,215)(13,185,42,214)(14,184,43,213)(15,183,44,212)(16,182,45,211)(17,181,46,210)(18,180,47,209)(19,179,48,208)(20,178,49,207)(21,177,50,206)(22,176,51,205)(23,175,52,204)(24,232,53,203)(25,231,54,202)(26,230,55,201)(27,229,56,200)(28,228,57,199)(29,227,58,198)(59,156,88,127)(60,155,89,126)(61,154,90,125)(62,153,91,124)(63,152,92,123)(64,151,93,122)(65,150,94,121)(66,149,95,120)(67,148,96,119)(68,147,97,118)(69,146,98,117)(70,145,99,174)(71,144,100,173)(72,143,101,172)(73,142,102,171)(74,141,103,170)(75,140,104,169)(76,139,105,168)(77,138,106,167)(78,137,107,166)(79,136,108,165)(80,135,109,164)(81,134,110,163)(82,133,111,162)(83,132,112,161)(84,131,113,160)(85,130,114,159)(86,129,115,158)(87,128,116,157)(233,359,262,388)(234,358,263,387)(235,357,264,386)(236,356,265,385)(237,355,266,384)(238,354,267,383)(239,353,268,382)(240,352,269,381)(241,351,270,380)(242,350,271,379)(243,349,272,378)(244,406,273,377)(245,405,274,376)(246,404,275,375)(247,403,276,374)(248,402,277,373)(249,401,278,372)(250,400,279,371)(251,399,280,370)(252,398,281,369)(253,397,282,368)(254,396,283,367)(255,395,284,366)(256,394,285,365)(257,393,286,364)(258,392,287,363)(259,391,288,362)(260,390,289,361)(261,389,290,360)(291,442,320,413)(292,441,321,412)(293,440,322,411)(294,439,323,410)(295,438,324,409)(296,437,325,408)(297,436,326,407)(298,435,327,464)(299,434,328,463)(300,433,329,462)(301,432,330,461)(302,431,331,460)(303,430,332,459)(304,429,333,458)(305,428,334,457)(306,427,335,456)(307,426,336,455)(308,425,337,454)(309,424,338,453)(310,423,339,452)(311,422,340,451)(312,421,341,450)(313,420,342,449)(314,419,343,448)(315,418,344,447)(316,417,345,446)(317,416,346,445)(318,415,347,444)(319,414,348,443)>;
G:=Group( (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), (1,456,145,406)(2,455,146,405)(3,454,147,404)(4,453,148,403)(5,452,149,402)(6,451,150,401)(7,450,151,400)(8,449,152,399)(9,448,153,398)(10,447,154,397)(11,446,155,396)(12,445,156,395)(13,444,157,394)(14,443,158,393)(15,442,159,392)(16,441,160,391)(17,440,161,390)(18,439,162,389)(19,438,163,388)(20,437,164,387)(21,436,165,386)(22,435,166,385)(23,434,167,384)(24,433,168,383)(25,432,169,382)(26,431,170,381)(27,430,171,380)(28,429,172,379)(29,428,173,378)(30,427,174,377)(31,426,117,376)(32,425,118,375)(33,424,119,374)(34,423,120,373)(35,422,121,372)(36,421,122,371)(37,420,123,370)(38,419,124,369)(39,418,125,368)(40,417,126,367)(41,416,127,366)(42,415,128,365)(43,414,129,364)(44,413,130,363)(45,412,131,362)(46,411,132,361)(47,410,133,360)(48,409,134,359)(49,408,135,358)(50,407,136,357)(51,464,137,356)(52,463,138,355)(53,462,139,354)(54,461,140,353)(55,460,141,352)(56,459,142,351)(57,458,143,350)(58,457,144,349)(59,346,215,255)(60,345,216,254)(61,344,217,253)(62,343,218,252)(63,342,219,251)(64,341,220,250)(65,340,221,249)(66,339,222,248)(67,338,223,247)(68,337,224,246)(69,336,225,245)(70,335,226,244)(71,334,227,243)(72,333,228,242)(73,332,229,241)(74,331,230,240)(75,330,231,239)(76,329,232,238)(77,328,175,237)(78,327,176,236)(79,326,177,235)(80,325,178,234)(81,324,179,233)(82,323,180,290)(83,322,181,289)(84,321,182,288)(85,320,183,287)(86,319,184,286)(87,318,185,285)(88,317,186,284)(89,316,187,283)(90,315,188,282)(91,314,189,281)(92,313,190,280)(93,312,191,279)(94,311,192,278)(95,310,193,277)(96,309,194,276)(97,308,195,275)(98,307,196,274)(99,306,197,273)(100,305,198,272)(101,304,199,271)(102,303,200,270)(103,302,201,269)(104,301,202,268)(105,300,203,267)(106,299,204,266)(107,298,205,265)(108,297,206,264)(109,296,207,263)(110,295,208,262)(111,294,209,261)(112,293,210,260)(113,292,211,259)(114,291,212,258)(115,348,213,257)(116,347,214,256), (1,197,30,226)(2,196,31,225)(3,195,32,224)(4,194,33,223)(5,193,34,222)(6,192,35,221)(7,191,36,220)(8,190,37,219)(9,189,38,218)(10,188,39,217)(11,187,40,216)(12,186,41,215)(13,185,42,214)(14,184,43,213)(15,183,44,212)(16,182,45,211)(17,181,46,210)(18,180,47,209)(19,179,48,208)(20,178,49,207)(21,177,50,206)(22,176,51,205)(23,175,52,204)(24,232,53,203)(25,231,54,202)(26,230,55,201)(27,229,56,200)(28,228,57,199)(29,227,58,198)(59,156,88,127)(60,155,89,126)(61,154,90,125)(62,153,91,124)(63,152,92,123)(64,151,93,122)(65,150,94,121)(66,149,95,120)(67,148,96,119)(68,147,97,118)(69,146,98,117)(70,145,99,174)(71,144,100,173)(72,143,101,172)(73,142,102,171)(74,141,103,170)(75,140,104,169)(76,139,105,168)(77,138,106,167)(78,137,107,166)(79,136,108,165)(80,135,109,164)(81,134,110,163)(82,133,111,162)(83,132,112,161)(84,131,113,160)(85,130,114,159)(86,129,115,158)(87,128,116,157)(233,359,262,388)(234,358,263,387)(235,357,264,386)(236,356,265,385)(237,355,266,384)(238,354,267,383)(239,353,268,382)(240,352,269,381)(241,351,270,380)(242,350,271,379)(243,349,272,378)(244,406,273,377)(245,405,274,376)(246,404,275,375)(247,403,276,374)(248,402,277,373)(249,401,278,372)(250,400,279,371)(251,399,280,370)(252,398,281,369)(253,397,282,368)(254,396,283,367)(255,395,284,366)(256,394,285,365)(257,393,286,364)(258,392,287,363)(259,391,288,362)(260,390,289,361)(261,389,290,360)(291,442,320,413)(292,441,321,412)(293,440,322,411)(294,439,323,410)(295,438,324,409)(296,437,325,408)(297,436,326,407)(298,435,327,464)(299,434,328,463)(300,433,329,462)(301,432,330,461)(302,431,331,460)(303,430,332,459)(304,429,333,458)(305,428,334,457)(306,427,335,456)(307,426,336,455)(308,425,337,454)(309,424,338,453)(310,423,339,452)(311,422,340,451)(312,421,341,450)(313,420,342,449)(314,419,343,448)(315,418,344,447)(316,417,345,446)(317,416,346,445)(318,415,347,444)(319,414,348,443) );
G=PermutationGroup([[(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)], [(1,456,145,406),(2,455,146,405),(3,454,147,404),(4,453,148,403),(5,452,149,402),(6,451,150,401),(7,450,151,400),(8,449,152,399),(9,448,153,398),(10,447,154,397),(11,446,155,396),(12,445,156,395),(13,444,157,394),(14,443,158,393),(15,442,159,392),(16,441,160,391),(17,440,161,390),(18,439,162,389),(19,438,163,388),(20,437,164,387),(21,436,165,386),(22,435,166,385),(23,434,167,384),(24,433,168,383),(25,432,169,382),(26,431,170,381),(27,430,171,380),(28,429,172,379),(29,428,173,378),(30,427,174,377),(31,426,117,376),(32,425,118,375),(33,424,119,374),(34,423,120,373),(35,422,121,372),(36,421,122,371),(37,420,123,370),(38,419,124,369),(39,418,125,368),(40,417,126,367),(41,416,127,366),(42,415,128,365),(43,414,129,364),(44,413,130,363),(45,412,131,362),(46,411,132,361),(47,410,133,360),(48,409,134,359),(49,408,135,358),(50,407,136,357),(51,464,137,356),(52,463,138,355),(53,462,139,354),(54,461,140,353),(55,460,141,352),(56,459,142,351),(57,458,143,350),(58,457,144,349),(59,346,215,255),(60,345,216,254),(61,344,217,253),(62,343,218,252),(63,342,219,251),(64,341,220,250),(65,340,221,249),(66,339,222,248),(67,338,223,247),(68,337,224,246),(69,336,225,245),(70,335,226,244),(71,334,227,243),(72,333,228,242),(73,332,229,241),(74,331,230,240),(75,330,231,239),(76,329,232,238),(77,328,175,237),(78,327,176,236),(79,326,177,235),(80,325,178,234),(81,324,179,233),(82,323,180,290),(83,322,181,289),(84,321,182,288),(85,320,183,287),(86,319,184,286),(87,318,185,285),(88,317,186,284),(89,316,187,283),(90,315,188,282),(91,314,189,281),(92,313,190,280),(93,312,191,279),(94,311,192,278),(95,310,193,277),(96,309,194,276),(97,308,195,275),(98,307,196,274),(99,306,197,273),(100,305,198,272),(101,304,199,271),(102,303,200,270),(103,302,201,269),(104,301,202,268),(105,300,203,267),(106,299,204,266),(107,298,205,265),(108,297,206,264),(109,296,207,263),(110,295,208,262),(111,294,209,261),(112,293,210,260),(113,292,211,259),(114,291,212,258),(115,348,213,257),(116,347,214,256)], [(1,197,30,226),(2,196,31,225),(3,195,32,224),(4,194,33,223),(5,193,34,222),(6,192,35,221),(7,191,36,220),(8,190,37,219),(9,189,38,218),(10,188,39,217),(11,187,40,216),(12,186,41,215),(13,185,42,214),(14,184,43,213),(15,183,44,212),(16,182,45,211),(17,181,46,210),(18,180,47,209),(19,179,48,208),(20,178,49,207),(21,177,50,206),(22,176,51,205),(23,175,52,204),(24,232,53,203),(25,231,54,202),(26,230,55,201),(27,229,56,200),(28,228,57,199),(29,227,58,198),(59,156,88,127),(60,155,89,126),(61,154,90,125),(62,153,91,124),(63,152,92,123),(64,151,93,122),(65,150,94,121),(66,149,95,120),(67,148,96,119),(68,147,97,118),(69,146,98,117),(70,145,99,174),(71,144,100,173),(72,143,101,172),(73,142,102,171),(74,141,103,170),(75,140,104,169),(76,139,105,168),(77,138,106,167),(78,137,107,166),(79,136,108,165),(80,135,109,164),(81,134,110,163),(82,133,111,162),(83,132,112,161),(84,131,113,160),(85,130,114,159),(86,129,115,158),(87,128,116,157),(233,359,262,388),(234,358,263,387),(235,357,264,386),(236,356,265,385),(237,355,266,384),(238,354,267,383),(239,353,268,382),(240,352,269,381),(241,351,270,380),(242,350,271,379),(243,349,272,378),(244,406,273,377),(245,405,274,376),(246,404,275,375),(247,403,276,374),(248,402,277,373),(249,401,278,372),(250,400,279,371),(251,399,280,370),(252,398,281,369),(253,397,282,368),(254,396,283,367),(255,395,284,366),(256,394,285,365),(257,393,286,364),(258,392,287,363),(259,391,288,362),(260,390,289,361),(261,389,290,360),(291,442,320,413),(292,441,321,412),(293,440,322,411),(294,439,323,410),(295,438,324,409),(296,437,325,408),(297,436,326,407),(298,435,327,464),(299,434,328,463),(300,433,329,462),(301,432,330,461),(302,431,331,460),(303,430,332,459),(304,429,333,458),(305,428,334,457),(306,427,335,456),(307,426,336,455),(308,425,337,454),(309,424,338,453),(310,423,339,452),(311,422,340,451),(312,421,341,450),(313,420,342,449),(314,419,343,448),(315,418,344,447),(316,417,345,446),(317,416,346,445),(318,415,347,444),(319,414,348,443)]])
122 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 29A | ··· | 29N | 58A | ··· | 58AP | 116A | ··· | 116BD |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 29 | ··· | 29 | 58 | ··· | 58 | 116 | ··· | 116 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 58 | 58 | 58 | 58 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
122 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | + | - | |||
| image | C1 | C2 | C2 | C4 | D4 | Q8 | D29 | D58 | Dic58 | C4×D29 | C29⋊D4 |
| kernel | C58.D4 | C2×Dic29 | C2×C116 | Dic29 | C58 | C58 | C2×C4 | C22 | C2 | C2 | C2 |
| # reps | 1 | 2 | 1 | 4 | 1 | 1 | 14 | 14 | 28 | 28 | 28 |
Matrix representation of C58.D4 ►in GL3(𝔽233) generated by
| 232 | 0 | 0 |
| 0 | 21 | 21 |
| 0 | 212 | 90 |
| 232 | 0 | 0 |
| 0 | 185 | 212 |
| 0 | 21 | 48 |
| 89 | 0 | 0 |
| 0 | 0 | 89 |
| 0 | 89 | 0 |
G:=sub<GL(3,GF(233))| [232,0,0,0,21,212,0,21,90],[232,0,0,0,185,21,0,212,48],[89,0,0,0,0,89,0,89,0] >;
C58.D4 in GAP, Magma, Sage, TeX
C_{58}.D_4 % in TeX
G:=Group("C58.D4"); // GroupNames label
G:=SmallGroup(464,12);
// by ID
G=gap.SmallGroup(464,12);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-29,40,101,26,11204]);
// Polycyclic
G:=Group<a,b,c|a^58=b^4=1,c^2=a^29,b*a*b^-1=c*a*c^-1=a^-1,c*b*c^-1=b^-1>;
// generators/relations
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