direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C2×Dic59, C118⋊C4, C22.D59, C2.2D118, C118.4C22, C59⋊2(C2×C4), (C2×C118).C2, SmallGroup(472,6)
Series: Derived ►Chief ►Lower central ►Upper central
| C59 — C2×Dic59 |
Generators and relations for C2×Dic59
G = < a,b,c | a2=b118=1, c2=b59, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C2×Dic59
►Regular action on 472 points
Generators in S472
(1 130)(2 131)(3 132)(4 133)(5 134)(6 135)(7 136)(8 137)(9 138)(10 139)(11 140)(12 141)(13 142)(14 143)(15 144)(16 145)(17 146)(18 147)(19 148)(20 149)(21 150)(22 151)(23 152)(24 153)(25 154)(26 155)(27 156)(28 157)(29 158)(30 159)(31 160)(32 161)(33 162)(34 163)(35 164)(36 165)(37 166)(38 167)(39 168)(40 169)(41 170)(42 171)(43 172)(44 173)(45 174)(46 175)(47 176)(48 177)(49 178)(50 179)(51 180)(52 181)(53 182)(54 183)(55 184)(56 185)(57 186)(58 187)(59 188)(60 189)(61 190)(62 191)(63 192)(64 193)(65 194)(66 195)(67 196)(68 197)(69 198)(70 199)(71 200)(72 201)(73 202)(74 203)(75 204)(76 205)(77 206)(78 207)(79 208)(80 209)(81 210)(82 211)(83 212)(84 213)(85 214)(86 215)(87 216)(88 217)(89 218)(90 219)(91 220)(92 221)(93 222)(94 223)(95 224)(96 225)(97 226)(98 227)(99 228)(100 229)(101 230)(102 231)(103 232)(104 233)(105 234)(106 235)(107 236)(108 119)(109 120)(110 121)(111 122)(112 123)(113 124)(114 125)(115 126)(116 127)(117 128)(118 129)(237 414)(238 415)(239 416)(240 417)(241 418)(242 419)(243 420)(244 421)(245 422)(246 423)(247 424)(248 425)(249 426)(250 427)(251 428)(252 429)(253 430)(254 431)(255 432)(256 433)(257 434)(258 435)(259 436)(260 437)(261 438)(262 439)(263 440)(264 441)(265 442)(266 443)(267 444)(268 445)(269 446)(270 447)(271 448)(272 449)(273 450)(274 451)(275 452)(276 453)(277 454)(278 455)(279 456)(280 457)(281 458)(282 459)(283 460)(284 461)(285 462)(286 463)(287 464)(288 465)(289 466)(290 467)(291 468)(292 469)(293 470)(294 471)(295 472)(296 355)(297 356)(298 357)(299 358)(300 359)(301 360)(302 361)(303 362)(304 363)(305 364)(306 365)(307 366)(308 367)(309 368)(310 369)(311 370)(312 371)(313 372)(314 373)(315 374)(316 375)(317 376)(318 377)(319 378)(320 379)(321 380)(322 381)(323 382)(324 383)(325 384)(326 385)(327 386)(328 387)(329 388)(330 389)(331 390)(332 391)(333 392)(334 393)(335 394)(336 395)(337 396)(338 397)(339 398)(340 399)(341 400)(342 401)(343 402)(344 403)(345 404)(346 405)(347 406)(348 407)(349 408)(350 409)(351 410)(352 411)(353 412)(354 413)
(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)
(1 237 60 296)(2 354 61 295)(3 353 62 294)(4 352 63 293)(5 351 64 292)(6 350 65 291)(7 349 66 290)(8 348 67 289)(9 347 68 288)(10 346 69 287)(11 345 70 286)(12 344 71 285)(13 343 72 284)(14 342 73 283)(15 341 74 282)(16 340 75 281)(17 339 76 280)(18 338 77 279)(19 337 78 278)(20 336 79 277)(21 335 80 276)(22 334 81 275)(23 333 82 274)(24 332 83 273)(25 331 84 272)(26 330 85 271)(27 329 86 270)(28 328 87 269)(29 327 88 268)(30 326 89 267)(31 325 90 266)(32 324 91 265)(33 323 92 264)(34 322 93 263)(35 321 94 262)(36 320 95 261)(37 319 96 260)(38 318 97 259)(39 317 98 258)(40 316 99 257)(41 315 100 256)(42 314 101 255)(43 313 102 254)(44 312 103 253)(45 311 104 252)(46 310 105 251)(47 309 106 250)(48 308 107 249)(49 307 108 248)(50 306 109 247)(51 305 110 246)(52 304 111 245)(53 303 112 244)(54 302 113 243)(55 301 114 242)(56 300 115 241)(57 299 116 240)(58 298 117 239)(59 297 118 238)(119 425 178 366)(120 424 179 365)(121 423 180 364)(122 422 181 363)(123 421 182 362)(124 420 183 361)(125 419 184 360)(126 418 185 359)(127 417 186 358)(128 416 187 357)(129 415 188 356)(130 414 189 355)(131 413 190 472)(132 412 191 471)(133 411 192 470)(134 410 193 469)(135 409 194 468)(136 408 195 467)(137 407 196 466)(138 406 197 465)(139 405 198 464)(140 404 199 463)(141 403 200 462)(142 402 201 461)(143 401 202 460)(144 400 203 459)(145 399 204 458)(146 398 205 457)(147 397 206 456)(148 396 207 455)(149 395 208 454)(150 394 209 453)(151 393 210 452)(152 392 211 451)(153 391 212 450)(154 390 213 449)(155 389 214 448)(156 388 215 447)(157 387 216 446)(158 386 217 445)(159 385 218 444)(160 384 219 443)(161 383 220 442)(162 382 221 441)(163 381 222 440)(164 380 223 439)(165 379 224 438)(166 378 225 437)(167 377 226 436)(168 376 227 435)(169 375 228 434)(170 374 229 433)(171 373 230 432)(172 372 231 431)(173 371 232 430)(174 370 233 429)(175 369 234 428)(176 368 235 427)(177 367 236 426)
G:=sub<Sym(472)| (1,130)(2,131)(3,132)(4,133)(5,134)(6,135)(7,136)(8,137)(9,138)(10,139)(11,140)(12,141)(13,142)(14,143)(15,144)(16,145)(17,146)(18,147)(19,148)(20,149)(21,150)(22,151)(23,152)(24,153)(25,154)(26,155)(27,156)(28,157)(29,158)(30,159)(31,160)(32,161)(33,162)(34,163)(35,164)(36,165)(37,166)(38,167)(39,168)(40,169)(41,170)(42,171)(43,172)(44,173)(45,174)(46,175)(47,176)(48,177)(49,178)(50,179)(51,180)(52,181)(53,182)(54,183)(55,184)(56,185)(57,186)(58,187)(59,188)(60,189)(61,190)(62,191)(63,192)(64,193)(65,194)(66,195)(67,196)(68,197)(69,198)(70,199)(71,200)(72,201)(73,202)(74,203)(75,204)(76,205)(77,206)(78,207)(79,208)(80,209)(81,210)(82,211)(83,212)(84,213)(85,214)(86,215)(87,216)(88,217)(89,218)(90,219)(91,220)(92,221)(93,222)(94,223)(95,224)(96,225)(97,226)(98,227)(99,228)(100,229)(101,230)(102,231)(103,232)(104,233)(105,234)(106,235)(107,236)(108,119)(109,120)(110,121)(111,122)(112,123)(113,124)(114,125)(115,126)(116,127)(117,128)(118,129)(237,414)(238,415)(239,416)(240,417)(241,418)(242,419)(243,420)(244,421)(245,422)(246,423)(247,424)(248,425)(249,426)(250,427)(251,428)(252,429)(253,430)(254,431)(255,432)(256,433)(257,434)(258,435)(259,436)(260,437)(261,438)(262,439)(263,440)(264,441)(265,442)(266,443)(267,444)(268,445)(269,446)(270,447)(271,448)(272,449)(273,450)(274,451)(275,452)(276,453)(277,454)(278,455)(279,456)(280,457)(281,458)(282,459)(283,460)(284,461)(285,462)(286,463)(287,464)(288,465)(289,466)(290,467)(291,468)(292,469)(293,470)(294,471)(295,472)(296,355)(297,356)(298,357)(299,358)(300,359)(301,360)(302,361)(303,362)(304,363)(305,364)(306,365)(307,366)(308,367)(309,368)(310,369)(311,370)(312,371)(313,372)(314,373)(315,374)(316,375)(317,376)(318,377)(319,378)(320,379)(321,380)(322,381)(323,382)(324,383)(325,384)(326,385)(327,386)(328,387)(329,388)(330,389)(331,390)(332,391)(333,392)(334,393)(335,394)(336,395)(337,396)(338,397)(339,398)(340,399)(341,400)(342,401)(343,402)(344,403)(345,404)(346,405)(347,406)(348,407)(349,408)(350,409)(351,410)(352,411)(353,412)(354,413), (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), (1,237,60,296)(2,354,61,295)(3,353,62,294)(4,352,63,293)(5,351,64,292)(6,350,65,291)(7,349,66,290)(8,348,67,289)(9,347,68,288)(10,346,69,287)(11,345,70,286)(12,344,71,285)(13,343,72,284)(14,342,73,283)(15,341,74,282)(16,340,75,281)(17,339,76,280)(18,338,77,279)(19,337,78,278)(20,336,79,277)(21,335,80,276)(22,334,81,275)(23,333,82,274)(24,332,83,273)(25,331,84,272)(26,330,85,271)(27,329,86,270)(28,328,87,269)(29,327,88,268)(30,326,89,267)(31,325,90,266)(32,324,91,265)(33,323,92,264)(34,322,93,263)(35,321,94,262)(36,320,95,261)(37,319,96,260)(38,318,97,259)(39,317,98,258)(40,316,99,257)(41,315,100,256)(42,314,101,255)(43,313,102,254)(44,312,103,253)(45,311,104,252)(46,310,105,251)(47,309,106,250)(48,308,107,249)(49,307,108,248)(50,306,109,247)(51,305,110,246)(52,304,111,245)(53,303,112,244)(54,302,113,243)(55,301,114,242)(56,300,115,241)(57,299,116,240)(58,298,117,239)(59,297,118,238)(119,425,178,366)(120,424,179,365)(121,423,180,364)(122,422,181,363)(123,421,182,362)(124,420,183,361)(125,419,184,360)(126,418,185,359)(127,417,186,358)(128,416,187,357)(129,415,188,356)(130,414,189,355)(131,413,190,472)(132,412,191,471)(133,411,192,470)(134,410,193,469)(135,409,194,468)(136,408,195,467)(137,407,196,466)(138,406,197,465)(139,405,198,464)(140,404,199,463)(141,403,200,462)(142,402,201,461)(143,401,202,460)(144,400,203,459)(145,399,204,458)(146,398,205,457)(147,397,206,456)(148,396,207,455)(149,395,208,454)(150,394,209,453)(151,393,210,452)(152,392,211,451)(153,391,212,450)(154,390,213,449)(155,389,214,448)(156,388,215,447)(157,387,216,446)(158,386,217,445)(159,385,218,444)(160,384,219,443)(161,383,220,442)(162,382,221,441)(163,381,222,440)(164,380,223,439)(165,379,224,438)(166,378,225,437)(167,377,226,436)(168,376,227,435)(169,375,228,434)(170,374,229,433)(171,373,230,432)(172,372,231,431)(173,371,232,430)(174,370,233,429)(175,369,234,428)(176,368,235,427)(177,367,236,426)>;
G:=Group( (1,130)(2,131)(3,132)(4,133)(5,134)(6,135)(7,136)(8,137)(9,138)(10,139)(11,140)(12,141)(13,142)(14,143)(15,144)(16,145)(17,146)(18,147)(19,148)(20,149)(21,150)(22,151)(23,152)(24,153)(25,154)(26,155)(27,156)(28,157)(29,158)(30,159)(31,160)(32,161)(33,162)(34,163)(35,164)(36,165)(37,166)(38,167)(39,168)(40,169)(41,170)(42,171)(43,172)(44,173)(45,174)(46,175)(47,176)(48,177)(49,178)(50,179)(51,180)(52,181)(53,182)(54,183)(55,184)(56,185)(57,186)(58,187)(59,188)(60,189)(61,190)(62,191)(63,192)(64,193)(65,194)(66,195)(67,196)(68,197)(69,198)(70,199)(71,200)(72,201)(73,202)(74,203)(75,204)(76,205)(77,206)(78,207)(79,208)(80,209)(81,210)(82,211)(83,212)(84,213)(85,214)(86,215)(87,216)(88,217)(89,218)(90,219)(91,220)(92,221)(93,222)(94,223)(95,224)(96,225)(97,226)(98,227)(99,228)(100,229)(101,230)(102,231)(103,232)(104,233)(105,234)(106,235)(107,236)(108,119)(109,120)(110,121)(111,122)(112,123)(113,124)(114,125)(115,126)(116,127)(117,128)(118,129)(237,414)(238,415)(239,416)(240,417)(241,418)(242,419)(243,420)(244,421)(245,422)(246,423)(247,424)(248,425)(249,426)(250,427)(251,428)(252,429)(253,430)(254,431)(255,432)(256,433)(257,434)(258,435)(259,436)(260,437)(261,438)(262,439)(263,440)(264,441)(265,442)(266,443)(267,444)(268,445)(269,446)(270,447)(271,448)(272,449)(273,450)(274,451)(275,452)(276,453)(277,454)(278,455)(279,456)(280,457)(281,458)(282,459)(283,460)(284,461)(285,462)(286,463)(287,464)(288,465)(289,466)(290,467)(291,468)(292,469)(293,470)(294,471)(295,472)(296,355)(297,356)(298,357)(299,358)(300,359)(301,360)(302,361)(303,362)(304,363)(305,364)(306,365)(307,366)(308,367)(309,368)(310,369)(311,370)(312,371)(313,372)(314,373)(315,374)(316,375)(317,376)(318,377)(319,378)(320,379)(321,380)(322,381)(323,382)(324,383)(325,384)(326,385)(327,386)(328,387)(329,388)(330,389)(331,390)(332,391)(333,392)(334,393)(335,394)(336,395)(337,396)(338,397)(339,398)(340,399)(341,400)(342,401)(343,402)(344,403)(345,404)(346,405)(347,406)(348,407)(349,408)(350,409)(351,410)(352,411)(353,412)(354,413), (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), (1,237,60,296)(2,354,61,295)(3,353,62,294)(4,352,63,293)(5,351,64,292)(6,350,65,291)(7,349,66,290)(8,348,67,289)(9,347,68,288)(10,346,69,287)(11,345,70,286)(12,344,71,285)(13,343,72,284)(14,342,73,283)(15,341,74,282)(16,340,75,281)(17,339,76,280)(18,338,77,279)(19,337,78,278)(20,336,79,277)(21,335,80,276)(22,334,81,275)(23,333,82,274)(24,332,83,273)(25,331,84,272)(26,330,85,271)(27,329,86,270)(28,328,87,269)(29,327,88,268)(30,326,89,267)(31,325,90,266)(32,324,91,265)(33,323,92,264)(34,322,93,263)(35,321,94,262)(36,320,95,261)(37,319,96,260)(38,318,97,259)(39,317,98,258)(40,316,99,257)(41,315,100,256)(42,314,101,255)(43,313,102,254)(44,312,103,253)(45,311,104,252)(46,310,105,251)(47,309,106,250)(48,308,107,249)(49,307,108,248)(50,306,109,247)(51,305,110,246)(52,304,111,245)(53,303,112,244)(54,302,113,243)(55,301,114,242)(56,300,115,241)(57,299,116,240)(58,298,117,239)(59,297,118,238)(119,425,178,366)(120,424,179,365)(121,423,180,364)(122,422,181,363)(123,421,182,362)(124,420,183,361)(125,419,184,360)(126,418,185,359)(127,417,186,358)(128,416,187,357)(129,415,188,356)(130,414,189,355)(131,413,190,472)(132,412,191,471)(133,411,192,470)(134,410,193,469)(135,409,194,468)(136,408,195,467)(137,407,196,466)(138,406,197,465)(139,405,198,464)(140,404,199,463)(141,403,200,462)(142,402,201,461)(143,401,202,460)(144,400,203,459)(145,399,204,458)(146,398,205,457)(147,397,206,456)(148,396,207,455)(149,395,208,454)(150,394,209,453)(151,393,210,452)(152,392,211,451)(153,391,212,450)(154,390,213,449)(155,389,214,448)(156,388,215,447)(157,387,216,446)(158,386,217,445)(159,385,218,444)(160,384,219,443)(161,383,220,442)(162,382,221,441)(163,381,222,440)(164,380,223,439)(165,379,224,438)(166,378,225,437)(167,377,226,436)(168,376,227,435)(169,375,228,434)(170,374,229,433)(171,373,230,432)(172,372,231,431)(173,371,232,430)(174,370,233,429)(175,369,234,428)(176,368,235,427)(177,367,236,426) );
G=PermutationGroup([[(1,130),(2,131),(3,132),(4,133),(5,134),(6,135),(7,136),(8,137),(9,138),(10,139),(11,140),(12,141),(13,142),(14,143),(15,144),(16,145),(17,146),(18,147),(19,148),(20,149),(21,150),(22,151),(23,152),(24,153),(25,154),(26,155),(27,156),(28,157),(29,158),(30,159),(31,160),(32,161),(33,162),(34,163),(35,164),(36,165),(37,166),(38,167),(39,168),(40,169),(41,170),(42,171),(43,172),(44,173),(45,174),(46,175),(47,176),(48,177),(49,178),(50,179),(51,180),(52,181),(53,182),(54,183),(55,184),(56,185),(57,186),(58,187),(59,188),(60,189),(61,190),(62,191),(63,192),(64,193),(65,194),(66,195),(67,196),(68,197),(69,198),(70,199),(71,200),(72,201),(73,202),(74,203),(75,204),(76,205),(77,206),(78,207),(79,208),(80,209),(81,210),(82,211),(83,212),(84,213),(85,214),(86,215),(87,216),(88,217),(89,218),(90,219),(91,220),(92,221),(93,222),(94,223),(95,224),(96,225),(97,226),(98,227),(99,228),(100,229),(101,230),(102,231),(103,232),(104,233),(105,234),(106,235),(107,236),(108,119),(109,120),(110,121),(111,122),(112,123),(113,124),(114,125),(115,126),(116,127),(117,128),(118,129),(237,414),(238,415),(239,416),(240,417),(241,418),(242,419),(243,420),(244,421),(245,422),(246,423),(247,424),(248,425),(249,426),(250,427),(251,428),(252,429),(253,430),(254,431),(255,432),(256,433),(257,434),(258,435),(259,436),(260,437),(261,438),(262,439),(263,440),(264,441),(265,442),(266,443),(267,444),(268,445),(269,446),(270,447),(271,448),(272,449),(273,450),(274,451),(275,452),(276,453),(277,454),(278,455),(279,456),(280,457),(281,458),(282,459),(283,460),(284,461),(285,462),(286,463),(287,464),(288,465),(289,466),(290,467),(291,468),(292,469),(293,470),(294,471),(295,472),(296,355),(297,356),(298,357),(299,358),(300,359),(301,360),(302,361),(303,362),(304,363),(305,364),(306,365),(307,366),(308,367),(309,368),(310,369),(311,370),(312,371),(313,372),(314,373),(315,374),(316,375),(317,376),(318,377),(319,378),(320,379),(321,380),(322,381),(323,382),(324,383),(325,384),(326,385),(327,386),(328,387),(329,388),(330,389),(331,390),(332,391),(333,392),(334,393),(335,394),(336,395),(337,396),(338,397),(339,398),(340,399),(341,400),(342,401),(343,402),(344,403),(345,404),(346,405),(347,406),(348,407),(349,408),(350,409),(351,410),(352,411),(353,412),(354,413)], [(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)], [(1,237,60,296),(2,354,61,295),(3,353,62,294),(4,352,63,293),(5,351,64,292),(6,350,65,291),(7,349,66,290),(8,348,67,289),(9,347,68,288),(10,346,69,287),(11,345,70,286),(12,344,71,285),(13,343,72,284),(14,342,73,283),(15,341,74,282),(16,340,75,281),(17,339,76,280),(18,338,77,279),(19,337,78,278),(20,336,79,277),(21,335,80,276),(22,334,81,275),(23,333,82,274),(24,332,83,273),(25,331,84,272),(26,330,85,271),(27,329,86,270),(28,328,87,269),(29,327,88,268),(30,326,89,267),(31,325,90,266),(32,324,91,265),(33,323,92,264),(34,322,93,263),(35,321,94,262),(36,320,95,261),(37,319,96,260),(38,318,97,259),(39,317,98,258),(40,316,99,257),(41,315,100,256),(42,314,101,255),(43,313,102,254),(44,312,103,253),(45,311,104,252),(46,310,105,251),(47,309,106,250),(48,308,107,249),(49,307,108,248),(50,306,109,247),(51,305,110,246),(52,304,111,245),(53,303,112,244),(54,302,113,243),(55,301,114,242),(56,300,115,241),(57,299,116,240),(58,298,117,239),(59,297,118,238),(119,425,178,366),(120,424,179,365),(121,423,180,364),(122,422,181,363),(123,421,182,362),(124,420,183,361),(125,419,184,360),(126,418,185,359),(127,417,186,358),(128,416,187,357),(129,415,188,356),(130,414,189,355),(131,413,190,472),(132,412,191,471),(133,411,192,470),(134,410,193,469),(135,409,194,468),(136,408,195,467),(137,407,196,466),(138,406,197,465),(139,405,198,464),(140,404,199,463),(141,403,200,462),(142,402,201,461),(143,401,202,460),(144,400,203,459),(145,399,204,458),(146,398,205,457),(147,397,206,456),(148,396,207,455),(149,395,208,454),(150,394,209,453),(151,393,210,452),(152,392,211,451),(153,391,212,450),(154,390,213,449),(155,389,214,448),(156,388,215,447),(157,387,216,446),(158,386,217,445),(159,385,218,444),(160,384,219,443),(161,383,220,442),(162,382,221,441),(163,381,222,440),(164,380,223,439),(165,379,224,438),(166,378,225,437),(167,377,226,436),(168,376,227,435),(169,375,228,434),(170,374,229,433),(171,373,230,432),(172,372,231,431),(173,371,232,430),(174,370,233,429),(175,369,234,428),(176,368,235,427),(177,367,236,426)]])
124 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 59A | ··· | 59AC | 118A | ··· | 118CI |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 59 | ··· | 59 | 118 | ··· | 118 |
| size | 1 | 1 | 1 | 1 | 59 | 59 | 59 | 59 | 2 | ··· | 2 | 2 | ··· | 2 |
124 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | |
| image | C1 | C2 | C2 | C4 | D59 | Dic59 | D118 |
| kernel | C2×Dic59 | Dic59 | C2×C118 | C118 | C22 | C2 | C2 |
| # reps | 1 | 2 | 1 | 4 | 29 | 58 | 29 |
Matrix representation of C2×Dic59 ►in GL3(𝔽709) generated by
| 708 | 0 | 0 |
| 0 | 708 | 0 |
| 0 | 0 | 708 |
| 1 | 0 | 0 |
| 0 | 0 | 708 |
| 0 | 1 | 27 |
| 708 | 0 | 0 |
| 0 | 655 | 535 |
| 0 | 575 | 54 |
G:=sub<GL(3,GF(709))| [708,0,0,0,708,0,0,0,708],[1,0,0,0,0,1,0,708,27],[708,0,0,0,655,575,0,535,54] >;
C2×Dic59 in GAP, Magma, Sage, TeX
C_2\times {\rm Dic}_{59} % in TeX
G:=Group("C2xDic59"); // GroupNames label
G:=SmallGroup(472,6);
// by ID
G=gap.SmallGroup(472,6);
# by ID
G:=PCGroup([4,-2,-2,-2,-59,16,7427]);
// Polycyclic
G:=Group<a,b,c|a^2=b^118=1,c^2=b^59,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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