direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×Dic58, C58⋊Q8, C4.11D58, C58.1C23, C22.8D58, C116.11C22, Dic29.1C22, C29⋊1(C2×Q8), (C2×C4).4D29, (C2×C116).4C2, (C2×C58).8C22, C2.3(C22×D29), (C2×Dic29).3C2, SmallGroup(464,35)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×Dic58
G = < a,b,c | a2=b116=1, c2=b58, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C2×Dic58
►Regular action on 464 points
Generators in S464
(1 222)(2 223)(3 224)(4 225)(5 226)(6 227)(7 228)(8 229)(9 230)(10 231)(11 232)(12 117)(13 118)(14 119)(15 120)(16 121)(17 122)(18 123)(19 124)(20 125)(21 126)(22 127)(23 128)(24 129)(25 130)(26 131)(27 132)(28 133)(29 134)(30 135)(31 136)(32 137)(33 138)(34 139)(35 140)(36 141)(37 142)(38 143)(39 144)(40 145)(41 146)(42 147)(43 148)(44 149)(45 150)(46 151)(47 152)(48 153)(49 154)(50 155)(51 156)(52 157)(53 158)(54 159)(55 160)(56 161)(57 162)(58 163)(59 164)(60 165)(61 166)(62 167)(63 168)(64 169)(65 170)(66 171)(67 172)(68 173)(69 174)(70 175)(71 176)(72 177)(73 178)(74 179)(75 180)(76 181)(77 182)(78 183)(79 184)(80 185)(81 186)(82 187)(83 188)(84 189)(85 190)(86 191)(87 192)(88 193)(89 194)(90 195)(91 196)(92 197)(93 198)(94 199)(95 200)(96 201)(97 202)(98 203)(99 204)(100 205)(101 206)(102 207)(103 208)(104 209)(105 210)(106 211)(107 212)(108 213)(109 214)(110 215)(111 216)(112 217)(113 218)(114 219)(115 220)(116 221)(233 378)(234 379)(235 380)(236 381)(237 382)(238 383)(239 384)(240 385)(241 386)(242 387)(243 388)(244 389)(245 390)(246 391)(247 392)(248 393)(249 394)(250 395)(251 396)(252 397)(253 398)(254 399)(255 400)(256 401)(257 402)(258 403)(259 404)(260 405)(261 406)(262 407)(263 408)(264 409)(265 410)(266 411)(267 412)(268 413)(269 414)(270 415)(271 416)(272 417)(273 418)(274 419)(275 420)(276 421)(277 422)(278 423)(279 424)(280 425)(281 426)(282 427)(283 428)(284 429)(285 430)(286 431)(287 432)(288 433)(289 434)(290 435)(291 436)(292 437)(293 438)(294 439)(295 440)(296 441)(297 442)(298 443)(299 444)(300 445)(301 446)(302 447)(303 448)(304 449)(305 450)(306 451)(307 452)(308 453)(309 454)(310 455)(311 456)(312 457)(313 458)(314 459)(315 460)(316 461)(317 462)(318 463)(319 464)(320 349)(321 350)(322 351)(323 352)(324 353)(325 354)(326 355)(327 356)(328 357)(329 358)(330 359)(331 360)(332 361)(333 362)(334 363)(335 364)(336 365)(337 366)(338 367)(339 368)(340 369)(341 370)(342 371)(343 372)(344 373)(345 374)(346 375)(347 376)(348 377)
(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)
(1 291 59 233)(2 290 60 348)(3 289 61 347)(4 288 62 346)(5 287 63 345)(6 286 64 344)(7 285 65 343)(8 284 66 342)(9 283 67 341)(10 282 68 340)(11 281 69 339)(12 280 70 338)(13 279 71 337)(14 278 72 336)(15 277 73 335)(16 276 74 334)(17 275 75 333)(18 274 76 332)(19 273 77 331)(20 272 78 330)(21 271 79 329)(22 270 80 328)(23 269 81 327)(24 268 82 326)(25 267 83 325)(26 266 84 324)(27 265 85 323)(28 264 86 322)(29 263 87 321)(30 262 88 320)(31 261 89 319)(32 260 90 318)(33 259 91 317)(34 258 92 316)(35 257 93 315)(36 256 94 314)(37 255 95 313)(38 254 96 312)(39 253 97 311)(40 252 98 310)(41 251 99 309)(42 250 100 308)(43 249 101 307)(44 248 102 306)(45 247 103 305)(46 246 104 304)(47 245 105 303)(48 244 106 302)(49 243 107 301)(50 242 108 300)(51 241 109 299)(52 240 110 298)(53 239 111 297)(54 238 112 296)(55 237 113 295)(56 236 114 294)(57 235 115 293)(58 234 116 292)(117 425 175 367)(118 424 176 366)(119 423 177 365)(120 422 178 364)(121 421 179 363)(122 420 180 362)(123 419 181 361)(124 418 182 360)(125 417 183 359)(126 416 184 358)(127 415 185 357)(128 414 186 356)(129 413 187 355)(130 412 188 354)(131 411 189 353)(132 410 190 352)(133 409 191 351)(134 408 192 350)(135 407 193 349)(136 406 194 464)(137 405 195 463)(138 404 196 462)(139 403 197 461)(140 402 198 460)(141 401 199 459)(142 400 200 458)(143 399 201 457)(144 398 202 456)(145 397 203 455)(146 396 204 454)(147 395 205 453)(148 394 206 452)(149 393 207 451)(150 392 208 450)(151 391 209 449)(152 390 210 448)(153 389 211 447)(154 388 212 446)(155 387 213 445)(156 386 214 444)(157 385 215 443)(158 384 216 442)(159 383 217 441)(160 382 218 440)(161 381 219 439)(162 380 220 438)(163 379 221 437)(164 378 222 436)(165 377 223 435)(166 376 224 434)(167 375 225 433)(168 374 226 432)(169 373 227 431)(170 372 228 430)(171 371 229 429)(172 370 230 428)(173 369 231 427)(174 368 232 426)
G:=sub<Sym(464)| (1,222)(2,223)(3,224)(4,225)(5,226)(6,227)(7,228)(8,229)(9,230)(10,231)(11,232)(12,117)(13,118)(14,119)(15,120)(16,121)(17,122)(18,123)(19,124)(20,125)(21,126)(22,127)(23,128)(24,129)(25,130)(26,131)(27,132)(28,133)(29,134)(30,135)(31,136)(32,137)(33,138)(34,139)(35,140)(36,141)(37,142)(38,143)(39,144)(40,145)(41,146)(42,147)(43,148)(44,149)(45,150)(46,151)(47,152)(48,153)(49,154)(50,155)(51,156)(52,157)(53,158)(54,159)(55,160)(56,161)(57,162)(58,163)(59,164)(60,165)(61,166)(62,167)(63,168)(64,169)(65,170)(66,171)(67,172)(68,173)(69,174)(70,175)(71,176)(72,177)(73,178)(74,179)(75,180)(76,181)(77,182)(78,183)(79,184)(80,185)(81,186)(82,187)(83,188)(84,189)(85,190)(86,191)(87,192)(88,193)(89,194)(90,195)(91,196)(92,197)(93,198)(94,199)(95,200)(96,201)(97,202)(98,203)(99,204)(100,205)(101,206)(102,207)(103,208)(104,209)(105,210)(106,211)(107,212)(108,213)(109,214)(110,215)(111,216)(112,217)(113,218)(114,219)(115,220)(116,221)(233,378)(234,379)(235,380)(236,381)(237,382)(238,383)(239,384)(240,385)(241,386)(242,387)(243,388)(244,389)(245,390)(246,391)(247,392)(248,393)(249,394)(250,395)(251,396)(252,397)(253,398)(254,399)(255,400)(256,401)(257,402)(258,403)(259,404)(260,405)(261,406)(262,407)(263,408)(264,409)(265,410)(266,411)(267,412)(268,413)(269,414)(270,415)(271,416)(272,417)(273,418)(274,419)(275,420)(276,421)(277,422)(278,423)(279,424)(280,425)(281,426)(282,427)(283,428)(284,429)(285,430)(286,431)(287,432)(288,433)(289,434)(290,435)(291,436)(292,437)(293,438)(294,439)(295,440)(296,441)(297,442)(298,443)(299,444)(300,445)(301,446)(302,447)(303,448)(304,449)(305,450)(306,451)(307,452)(308,453)(309,454)(310,455)(311,456)(312,457)(313,458)(314,459)(315,460)(316,461)(317,462)(318,463)(319,464)(320,349)(321,350)(322,351)(323,352)(324,353)(325,354)(326,355)(327,356)(328,357)(329,358)(330,359)(331,360)(332,361)(333,362)(334,363)(335,364)(336,365)(337,366)(338,367)(339,368)(340,369)(341,370)(342,371)(343,372)(344,373)(345,374)(346,375)(347,376)(348,377), (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), (1,291,59,233)(2,290,60,348)(3,289,61,347)(4,288,62,346)(5,287,63,345)(6,286,64,344)(7,285,65,343)(8,284,66,342)(9,283,67,341)(10,282,68,340)(11,281,69,339)(12,280,70,338)(13,279,71,337)(14,278,72,336)(15,277,73,335)(16,276,74,334)(17,275,75,333)(18,274,76,332)(19,273,77,331)(20,272,78,330)(21,271,79,329)(22,270,80,328)(23,269,81,327)(24,268,82,326)(25,267,83,325)(26,266,84,324)(27,265,85,323)(28,264,86,322)(29,263,87,321)(30,262,88,320)(31,261,89,319)(32,260,90,318)(33,259,91,317)(34,258,92,316)(35,257,93,315)(36,256,94,314)(37,255,95,313)(38,254,96,312)(39,253,97,311)(40,252,98,310)(41,251,99,309)(42,250,100,308)(43,249,101,307)(44,248,102,306)(45,247,103,305)(46,246,104,304)(47,245,105,303)(48,244,106,302)(49,243,107,301)(50,242,108,300)(51,241,109,299)(52,240,110,298)(53,239,111,297)(54,238,112,296)(55,237,113,295)(56,236,114,294)(57,235,115,293)(58,234,116,292)(117,425,175,367)(118,424,176,366)(119,423,177,365)(120,422,178,364)(121,421,179,363)(122,420,180,362)(123,419,181,361)(124,418,182,360)(125,417,183,359)(126,416,184,358)(127,415,185,357)(128,414,186,356)(129,413,187,355)(130,412,188,354)(131,411,189,353)(132,410,190,352)(133,409,191,351)(134,408,192,350)(135,407,193,349)(136,406,194,464)(137,405,195,463)(138,404,196,462)(139,403,197,461)(140,402,198,460)(141,401,199,459)(142,400,200,458)(143,399,201,457)(144,398,202,456)(145,397,203,455)(146,396,204,454)(147,395,205,453)(148,394,206,452)(149,393,207,451)(150,392,208,450)(151,391,209,449)(152,390,210,448)(153,389,211,447)(154,388,212,446)(155,387,213,445)(156,386,214,444)(157,385,215,443)(158,384,216,442)(159,383,217,441)(160,382,218,440)(161,381,219,439)(162,380,220,438)(163,379,221,437)(164,378,222,436)(165,377,223,435)(166,376,224,434)(167,375,225,433)(168,374,226,432)(169,373,227,431)(170,372,228,430)(171,371,229,429)(172,370,230,428)(173,369,231,427)(174,368,232,426)>;
G:=Group( (1,222)(2,223)(3,224)(4,225)(5,226)(6,227)(7,228)(8,229)(9,230)(10,231)(11,232)(12,117)(13,118)(14,119)(15,120)(16,121)(17,122)(18,123)(19,124)(20,125)(21,126)(22,127)(23,128)(24,129)(25,130)(26,131)(27,132)(28,133)(29,134)(30,135)(31,136)(32,137)(33,138)(34,139)(35,140)(36,141)(37,142)(38,143)(39,144)(40,145)(41,146)(42,147)(43,148)(44,149)(45,150)(46,151)(47,152)(48,153)(49,154)(50,155)(51,156)(52,157)(53,158)(54,159)(55,160)(56,161)(57,162)(58,163)(59,164)(60,165)(61,166)(62,167)(63,168)(64,169)(65,170)(66,171)(67,172)(68,173)(69,174)(70,175)(71,176)(72,177)(73,178)(74,179)(75,180)(76,181)(77,182)(78,183)(79,184)(80,185)(81,186)(82,187)(83,188)(84,189)(85,190)(86,191)(87,192)(88,193)(89,194)(90,195)(91,196)(92,197)(93,198)(94,199)(95,200)(96,201)(97,202)(98,203)(99,204)(100,205)(101,206)(102,207)(103,208)(104,209)(105,210)(106,211)(107,212)(108,213)(109,214)(110,215)(111,216)(112,217)(113,218)(114,219)(115,220)(116,221)(233,378)(234,379)(235,380)(236,381)(237,382)(238,383)(239,384)(240,385)(241,386)(242,387)(243,388)(244,389)(245,390)(246,391)(247,392)(248,393)(249,394)(250,395)(251,396)(252,397)(253,398)(254,399)(255,400)(256,401)(257,402)(258,403)(259,404)(260,405)(261,406)(262,407)(263,408)(264,409)(265,410)(266,411)(267,412)(268,413)(269,414)(270,415)(271,416)(272,417)(273,418)(274,419)(275,420)(276,421)(277,422)(278,423)(279,424)(280,425)(281,426)(282,427)(283,428)(284,429)(285,430)(286,431)(287,432)(288,433)(289,434)(290,435)(291,436)(292,437)(293,438)(294,439)(295,440)(296,441)(297,442)(298,443)(299,444)(300,445)(301,446)(302,447)(303,448)(304,449)(305,450)(306,451)(307,452)(308,453)(309,454)(310,455)(311,456)(312,457)(313,458)(314,459)(315,460)(316,461)(317,462)(318,463)(319,464)(320,349)(321,350)(322,351)(323,352)(324,353)(325,354)(326,355)(327,356)(328,357)(329,358)(330,359)(331,360)(332,361)(333,362)(334,363)(335,364)(336,365)(337,366)(338,367)(339,368)(340,369)(341,370)(342,371)(343,372)(344,373)(345,374)(346,375)(347,376)(348,377), (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), (1,291,59,233)(2,290,60,348)(3,289,61,347)(4,288,62,346)(5,287,63,345)(6,286,64,344)(7,285,65,343)(8,284,66,342)(9,283,67,341)(10,282,68,340)(11,281,69,339)(12,280,70,338)(13,279,71,337)(14,278,72,336)(15,277,73,335)(16,276,74,334)(17,275,75,333)(18,274,76,332)(19,273,77,331)(20,272,78,330)(21,271,79,329)(22,270,80,328)(23,269,81,327)(24,268,82,326)(25,267,83,325)(26,266,84,324)(27,265,85,323)(28,264,86,322)(29,263,87,321)(30,262,88,320)(31,261,89,319)(32,260,90,318)(33,259,91,317)(34,258,92,316)(35,257,93,315)(36,256,94,314)(37,255,95,313)(38,254,96,312)(39,253,97,311)(40,252,98,310)(41,251,99,309)(42,250,100,308)(43,249,101,307)(44,248,102,306)(45,247,103,305)(46,246,104,304)(47,245,105,303)(48,244,106,302)(49,243,107,301)(50,242,108,300)(51,241,109,299)(52,240,110,298)(53,239,111,297)(54,238,112,296)(55,237,113,295)(56,236,114,294)(57,235,115,293)(58,234,116,292)(117,425,175,367)(118,424,176,366)(119,423,177,365)(120,422,178,364)(121,421,179,363)(122,420,180,362)(123,419,181,361)(124,418,182,360)(125,417,183,359)(126,416,184,358)(127,415,185,357)(128,414,186,356)(129,413,187,355)(130,412,188,354)(131,411,189,353)(132,410,190,352)(133,409,191,351)(134,408,192,350)(135,407,193,349)(136,406,194,464)(137,405,195,463)(138,404,196,462)(139,403,197,461)(140,402,198,460)(141,401,199,459)(142,400,200,458)(143,399,201,457)(144,398,202,456)(145,397,203,455)(146,396,204,454)(147,395,205,453)(148,394,206,452)(149,393,207,451)(150,392,208,450)(151,391,209,449)(152,390,210,448)(153,389,211,447)(154,388,212,446)(155,387,213,445)(156,386,214,444)(157,385,215,443)(158,384,216,442)(159,383,217,441)(160,382,218,440)(161,381,219,439)(162,380,220,438)(163,379,221,437)(164,378,222,436)(165,377,223,435)(166,376,224,434)(167,375,225,433)(168,374,226,432)(169,373,227,431)(170,372,228,430)(171,371,229,429)(172,370,230,428)(173,369,231,427)(174,368,232,426) );
G=PermutationGroup([[(1,222),(2,223),(3,224),(4,225),(5,226),(6,227),(7,228),(8,229),(9,230),(10,231),(11,232),(12,117),(13,118),(14,119),(15,120),(16,121),(17,122),(18,123),(19,124),(20,125),(21,126),(22,127),(23,128),(24,129),(25,130),(26,131),(27,132),(28,133),(29,134),(30,135),(31,136),(32,137),(33,138),(34,139),(35,140),(36,141),(37,142),(38,143),(39,144),(40,145),(41,146),(42,147),(43,148),(44,149),(45,150),(46,151),(47,152),(48,153),(49,154),(50,155),(51,156),(52,157),(53,158),(54,159),(55,160),(56,161),(57,162),(58,163),(59,164),(60,165),(61,166),(62,167),(63,168),(64,169),(65,170),(66,171),(67,172),(68,173),(69,174),(70,175),(71,176),(72,177),(73,178),(74,179),(75,180),(76,181),(77,182),(78,183),(79,184),(80,185),(81,186),(82,187),(83,188),(84,189),(85,190),(86,191),(87,192),(88,193),(89,194),(90,195),(91,196),(92,197),(93,198),(94,199),(95,200),(96,201),(97,202),(98,203),(99,204),(100,205),(101,206),(102,207),(103,208),(104,209),(105,210),(106,211),(107,212),(108,213),(109,214),(110,215),(111,216),(112,217),(113,218),(114,219),(115,220),(116,221),(233,378),(234,379),(235,380),(236,381),(237,382),(238,383),(239,384),(240,385),(241,386),(242,387),(243,388),(244,389),(245,390),(246,391),(247,392),(248,393),(249,394),(250,395),(251,396),(252,397),(253,398),(254,399),(255,400),(256,401),(257,402),(258,403),(259,404),(260,405),(261,406),(262,407),(263,408),(264,409),(265,410),(266,411),(267,412),(268,413),(269,414),(270,415),(271,416),(272,417),(273,418),(274,419),(275,420),(276,421),(277,422),(278,423),(279,424),(280,425),(281,426),(282,427),(283,428),(284,429),(285,430),(286,431),(287,432),(288,433),(289,434),(290,435),(291,436),(292,437),(293,438),(294,439),(295,440),(296,441),(297,442),(298,443),(299,444),(300,445),(301,446),(302,447),(303,448),(304,449),(305,450),(306,451),(307,452),(308,453),(309,454),(310,455),(311,456),(312,457),(313,458),(314,459),(315,460),(316,461),(317,462),(318,463),(319,464),(320,349),(321,350),(322,351),(323,352),(324,353),(325,354),(326,355),(327,356),(328,357),(329,358),(330,359),(331,360),(332,361),(333,362),(334,363),(335,364),(336,365),(337,366),(338,367),(339,368),(340,369),(341,370),(342,371),(343,372),(344,373),(345,374),(346,375),(347,376),(348,377)], [(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)], [(1,291,59,233),(2,290,60,348),(3,289,61,347),(4,288,62,346),(5,287,63,345),(6,286,64,344),(7,285,65,343),(8,284,66,342),(9,283,67,341),(10,282,68,340),(11,281,69,339),(12,280,70,338),(13,279,71,337),(14,278,72,336),(15,277,73,335),(16,276,74,334),(17,275,75,333),(18,274,76,332),(19,273,77,331),(20,272,78,330),(21,271,79,329),(22,270,80,328),(23,269,81,327),(24,268,82,326),(25,267,83,325),(26,266,84,324),(27,265,85,323),(28,264,86,322),(29,263,87,321),(30,262,88,320),(31,261,89,319),(32,260,90,318),(33,259,91,317),(34,258,92,316),(35,257,93,315),(36,256,94,314),(37,255,95,313),(38,254,96,312),(39,253,97,311),(40,252,98,310),(41,251,99,309),(42,250,100,308),(43,249,101,307),(44,248,102,306),(45,247,103,305),(46,246,104,304),(47,245,105,303),(48,244,106,302),(49,243,107,301),(50,242,108,300),(51,241,109,299),(52,240,110,298),(53,239,111,297),(54,238,112,296),(55,237,113,295),(56,236,114,294),(57,235,115,293),(58,234,116,292),(117,425,175,367),(118,424,176,366),(119,423,177,365),(120,422,178,364),(121,421,179,363),(122,420,180,362),(123,419,181,361),(124,418,182,360),(125,417,183,359),(126,416,184,358),(127,415,185,357),(128,414,186,356),(129,413,187,355),(130,412,188,354),(131,411,189,353),(132,410,190,352),(133,409,191,351),(134,408,192,350),(135,407,193,349),(136,406,194,464),(137,405,195,463),(138,404,196,462),(139,403,197,461),(140,402,198,460),(141,401,199,459),(142,400,200,458),(143,399,201,457),(144,398,202,456),(145,397,203,455),(146,396,204,454),(147,395,205,453),(148,394,206,452),(149,393,207,451),(150,392,208,450),(151,391,209,449),(152,390,210,448),(153,389,211,447),(154,388,212,446),(155,387,213,445),(156,386,214,444),(157,385,215,443),(158,384,216,442),(159,383,217,441),(160,382,218,440),(161,381,219,439),(162,380,220,438),(163,379,221,437),(164,378,222,436),(165,377,223,435),(166,376,224,434),(167,375,225,433),(168,374,226,432),(169,373,227,431),(170,372,228,430),(171,371,229,429),(172,370,230,428),(173,369,231,427),(174,368,232,426)]])
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 |
| type | + | + | + | + | - | + | + | + | - |
| image | C1 | C2 | C2 | C2 | Q8 | D29 | D58 | D58 | Dic58 |
| kernel | C2×Dic58 | Dic58 | C2×Dic29 | C2×C116 | C58 | C2×C4 | C4 | C22 | C2 |
| # reps | 1 | 4 | 2 | 1 | 2 | 14 | 28 | 14 | 56 |
Matrix representation of C2×Dic58 ►in GL4(𝔽233) generated by
| 232 | 0 | 0 | 0 |
| 0 | 232 | 0 | 0 |
| 0 | 0 | 232 | 0 |
| 0 | 0 | 0 | 232 |
| 0 | 232 | 0 | 0 |
| 1 | 115 | 0 | 0 |
| 0 | 0 | 144 | 14 |
| 0 | 0 | 172 | 41 |
| 46 | 214 | 0 | 0 |
| 50 | 187 | 0 | 0 |
| 0 | 0 | 189 | 192 |
| 0 | 0 | 195 | 44 |
G:=sub<GL(4,GF(233))| [232,0,0,0,0,232,0,0,0,0,232,0,0,0,0,232],[0,1,0,0,232,115,0,0,0,0,144,172,0,0,14,41],[46,50,0,0,214,187,0,0,0,0,189,195,0,0,192,44] >;
C2×Dic58 in GAP, Magma, Sage, TeX
C_2\times {\rm Dic}_{58} % in TeX
G:=Group("C2xDic58"); // GroupNames label
G:=SmallGroup(464,35);
// by ID
G=gap.SmallGroup(464,35);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-29,40,182,42,11204]);
// Polycyclic
G:=Group<a,b,c|a^2=b^116=1,c^2=b^58,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
Export