direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C2×C29⋊C8, C58⋊C8, Dic29.2C4, Dic29.6C22, C29⋊2(C2×C8), C58.5(C2×C4), (C2×C58).1C4, C22.2(C29⋊C4), (C2×Dic29).4C2, C2.3(C2×C29⋊C4), SmallGroup(464,32)
Series: Derived ►Chief ►Lower central ►Upper central
| C29 — C2×C29⋊C8 |
Generators and relations for C2×C29⋊C8
G = < a,b,c | a2=b29=c8=1, ab=ba, ac=ca, cbc-1=b17 >
Smallest permutation representation of C2×C29⋊C8
►Regular action on 464 points
Generators in S464
(1 146)(2 147)(3 148)(4 149)(5 150)(6 151)(7 152)(8 153)(9 154)(10 155)(11 156)(12 157)(13 158)(14 159)(15 160)(16 161)(17 162)(18 163)(19 164)(20 165)(21 166)(22 167)(23 168)(24 169)(25 170)(26 171)(27 172)(28 173)(29 174)(30 117)(31 118)(32 119)(33 120)(34 121)(35 122)(36 123)(37 124)(38 125)(39 126)(40 127)(41 128)(42 129)(43 130)(44 131)(45 132)(46 133)(47 134)(48 135)(49 136)(50 137)(51 138)(52 139)(53 140)(54 141)(55 142)(56 143)(57 144)(58 145)(59 225)(60 226)(61 227)(62 228)(63 229)(64 230)(65 231)(66 232)(67 204)(68 205)(69 206)(70 207)(71 208)(72 209)(73 210)(74 211)(75 212)(76 213)(77 214)(78 215)(79 216)(80 217)(81 218)(82 219)(83 220)(84 221)(85 222)(86 223)(87 224)(88 194)(89 195)(90 196)(91 197)(92 198)(93 199)(94 200)(95 201)(96 202)(97 203)(98 175)(99 176)(100 177)(101 178)(102 179)(103 180)(104 181)(105 182)(106 183)(107 184)(108 185)(109 186)(110 187)(111 188)(112 189)(113 190)(114 191)(115 192)(116 193)(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)(262 358)(263 359)(264 360)(265 361)(266 362)(267 363)(268 364)(269 365)(270 366)(271 367)(272 368)(273 369)(274 370)(275 371)(276 372)(277 373)(278 374)(279 375)(280 376)(281 377)(282 349)(283 350)(284 351)(285 352)(286 353)(287 354)(288 355)(289 356)(290 357)(291 461)(292 462)(293 463)(294 464)(295 436)(296 437)(297 438)(298 439)(299 440)(300 441)(301 442)(302 443)(303 444)(304 445)(305 446)(306 447)(307 448)(308 449)(309 450)(310 451)(311 452)(312 453)(313 454)(314 455)(315 456)(316 457)(317 458)(318 459)(319 460)(320 415)(321 416)(322 417)(323 418)(324 419)(325 420)(326 421)(327 422)(328 423)(329 424)(330 425)(331 426)(332 427)(333 428)(334 429)(335 430)(336 431)(337 432)(338 433)(339 434)(340 435)(341 407)(342 408)(343 409)(344 410)(345 411)(346 412)(347 413)(348 414)
(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)
(1 343 109 265 30 317 75 242)(2 326 108 282 31 300 74 259)(3 338 107 270 32 312 73 247)(4 321 106 287 33 295 72 235)(5 333 105 275 34 307 71 252)(6 345 104 263 35 319 70 240)(7 328 103 280 36 302 69 257)(8 340 102 268 37 314 68 245)(9 323 101 285 38 297 67 233)(10 335 100 273 39 309 66 250)(11 347 99 290 40 292 65 238)(12 330 98 278 41 304 64 255)(13 342 97 266 42 316 63 243)(14 325 96 283 43 299 62 260)(15 337 95 271 44 311 61 248)(16 320 94 288 45 294 60 236)(17 332 93 276 46 306 59 253)(18 344 92 264 47 318 87 241)(19 327 91 281 48 301 86 258)(20 339 90 269 49 313 85 246)(21 322 89 286 50 296 84 234)(22 334 88 274 51 308 83 251)(23 346 116 262 52 291 82 239)(24 329 115 279 53 303 81 256)(25 341 114 267 54 315 80 244)(26 324 113 284 55 298 79 261)(27 336 112 272 56 310 78 249)(28 348 111 289 57 293 77 237)(29 331 110 277 58 305 76 254)(117 458 212 387 146 409 186 361)(118 441 211 404 147 421 185 349)(119 453 210 392 148 433 184 366)(120 436 209 380 149 416 183 354)(121 448 208 397 150 428 182 371)(122 460 207 385 151 411 181 359)(123 443 206 402 152 423 180 376)(124 455 205 390 153 435 179 364)(125 438 204 378 154 418 178 352)(126 450 232 395 155 430 177 369)(127 462 231 383 156 413 176 357)(128 445 230 400 157 425 175 374)(129 457 229 388 158 408 203 362)(130 440 228 405 159 420 202 350)(131 452 227 393 160 432 201 367)(132 464 226 381 161 415 200 355)(133 447 225 398 162 427 199 372)(134 459 224 386 163 410 198 360)(135 442 223 403 164 422 197 377)(136 454 222 391 165 434 196 365)(137 437 221 379 166 417 195 353)(138 449 220 396 167 429 194 370)(139 461 219 384 168 412 193 358)(140 444 218 401 169 424 192 375)(141 456 217 389 170 407 191 363)(142 439 216 406 171 419 190 351)(143 451 215 394 172 431 189 368)(144 463 214 382 173 414 188 356)(145 446 213 399 174 426 187 373)
G:=sub<Sym(464)| (1,146)(2,147)(3,148)(4,149)(5,150)(6,151)(7,152)(8,153)(9,154)(10,155)(11,156)(12,157)(13,158)(14,159)(15,160)(16,161)(17,162)(18,163)(19,164)(20,165)(21,166)(22,167)(23,168)(24,169)(25,170)(26,171)(27,172)(28,173)(29,174)(30,117)(31,118)(32,119)(33,120)(34,121)(35,122)(36,123)(37,124)(38,125)(39,126)(40,127)(41,128)(42,129)(43,130)(44,131)(45,132)(46,133)(47,134)(48,135)(49,136)(50,137)(51,138)(52,139)(53,140)(54,141)(55,142)(56,143)(57,144)(58,145)(59,225)(60,226)(61,227)(62,228)(63,229)(64,230)(65,231)(66,232)(67,204)(68,205)(69,206)(70,207)(71,208)(72,209)(73,210)(74,211)(75,212)(76,213)(77,214)(78,215)(79,216)(80,217)(81,218)(82,219)(83,220)(84,221)(85,222)(86,223)(87,224)(88,194)(89,195)(90,196)(91,197)(92,198)(93,199)(94,200)(95,201)(96,202)(97,203)(98,175)(99,176)(100,177)(101,178)(102,179)(103,180)(104,181)(105,182)(106,183)(107,184)(108,185)(109,186)(110,187)(111,188)(112,189)(113,190)(114,191)(115,192)(116,193)(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)(262,358)(263,359)(264,360)(265,361)(266,362)(267,363)(268,364)(269,365)(270,366)(271,367)(272,368)(273,369)(274,370)(275,371)(276,372)(277,373)(278,374)(279,375)(280,376)(281,377)(282,349)(283,350)(284,351)(285,352)(286,353)(287,354)(288,355)(289,356)(290,357)(291,461)(292,462)(293,463)(294,464)(295,436)(296,437)(297,438)(298,439)(299,440)(300,441)(301,442)(302,443)(303,444)(304,445)(305,446)(306,447)(307,448)(308,449)(309,450)(310,451)(311,452)(312,453)(313,454)(314,455)(315,456)(316,457)(317,458)(318,459)(319,460)(320,415)(321,416)(322,417)(323,418)(324,419)(325,420)(326,421)(327,422)(328,423)(329,424)(330,425)(331,426)(332,427)(333,428)(334,429)(335,430)(336,431)(337,432)(338,433)(339,434)(340,435)(341,407)(342,408)(343,409)(344,410)(345,411)(346,412)(347,413)(348,414), (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), (1,343,109,265,30,317,75,242)(2,326,108,282,31,300,74,259)(3,338,107,270,32,312,73,247)(4,321,106,287,33,295,72,235)(5,333,105,275,34,307,71,252)(6,345,104,263,35,319,70,240)(7,328,103,280,36,302,69,257)(8,340,102,268,37,314,68,245)(9,323,101,285,38,297,67,233)(10,335,100,273,39,309,66,250)(11,347,99,290,40,292,65,238)(12,330,98,278,41,304,64,255)(13,342,97,266,42,316,63,243)(14,325,96,283,43,299,62,260)(15,337,95,271,44,311,61,248)(16,320,94,288,45,294,60,236)(17,332,93,276,46,306,59,253)(18,344,92,264,47,318,87,241)(19,327,91,281,48,301,86,258)(20,339,90,269,49,313,85,246)(21,322,89,286,50,296,84,234)(22,334,88,274,51,308,83,251)(23,346,116,262,52,291,82,239)(24,329,115,279,53,303,81,256)(25,341,114,267,54,315,80,244)(26,324,113,284,55,298,79,261)(27,336,112,272,56,310,78,249)(28,348,111,289,57,293,77,237)(29,331,110,277,58,305,76,254)(117,458,212,387,146,409,186,361)(118,441,211,404,147,421,185,349)(119,453,210,392,148,433,184,366)(120,436,209,380,149,416,183,354)(121,448,208,397,150,428,182,371)(122,460,207,385,151,411,181,359)(123,443,206,402,152,423,180,376)(124,455,205,390,153,435,179,364)(125,438,204,378,154,418,178,352)(126,450,232,395,155,430,177,369)(127,462,231,383,156,413,176,357)(128,445,230,400,157,425,175,374)(129,457,229,388,158,408,203,362)(130,440,228,405,159,420,202,350)(131,452,227,393,160,432,201,367)(132,464,226,381,161,415,200,355)(133,447,225,398,162,427,199,372)(134,459,224,386,163,410,198,360)(135,442,223,403,164,422,197,377)(136,454,222,391,165,434,196,365)(137,437,221,379,166,417,195,353)(138,449,220,396,167,429,194,370)(139,461,219,384,168,412,193,358)(140,444,218,401,169,424,192,375)(141,456,217,389,170,407,191,363)(142,439,216,406,171,419,190,351)(143,451,215,394,172,431,189,368)(144,463,214,382,173,414,188,356)(145,446,213,399,174,426,187,373)>;
G:=Group( (1,146)(2,147)(3,148)(4,149)(5,150)(6,151)(7,152)(8,153)(9,154)(10,155)(11,156)(12,157)(13,158)(14,159)(15,160)(16,161)(17,162)(18,163)(19,164)(20,165)(21,166)(22,167)(23,168)(24,169)(25,170)(26,171)(27,172)(28,173)(29,174)(30,117)(31,118)(32,119)(33,120)(34,121)(35,122)(36,123)(37,124)(38,125)(39,126)(40,127)(41,128)(42,129)(43,130)(44,131)(45,132)(46,133)(47,134)(48,135)(49,136)(50,137)(51,138)(52,139)(53,140)(54,141)(55,142)(56,143)(57,144)(58,145)(59,225)(60,226)(61,227)(62,228)(63,229)(64,230)(65,231)(66,232)(67,204)(68,205)(69,206)(70,207)(71,208)(72,209)(73,210)(74,211)(75,212)(76,213)(77,214)(78,215)(79,216)(80,217)(81,218)(82,219)(83,220)(84,221)(85,222)(86,223)(87,224)(88,194)(89,195)(90,196)(91,197)(92,198)(93,199)(94,200)(95,201)(96,202)(97,203)(98,175)(99,176)(100,177)(101,178)(102,179)(103,180)(104,181)(105,182)(106,183)(107,184)(108,185)(109,186)(110,187)(111,188)(112,189)(113,190)(114,191)(115,192)(116,193)(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)(262,358)(263,359)(264,360)(265,361)(266,362)(267,363)(268,364)(269,365)(270,366)(271,367)(272,368)(273,369)(274,370)(275,371)(276,372)(277,373)(278,374)(279,375)(280,376)(281,377)(282,349)(283,350)(284,351)(285,352)(286,353)(287,354)(288,355)(289,356)(290,357)(291,461)(292,462)(293,463)(294,464)(295,436)(296,437)(297,438)(298,439)(299,440)(300,441)(301,442)(302,443)(303,444)(304,445)(305,446)(306,447)(307,448)(308,449)(309,450)(310,451)(311,452)(312,453)(313,454)(314,455)(315,456)(316,457)(317,458)(318,459)(319,460)(320,415)(321,416)(322,417)(323,418)(324,419)(325,420)(326,421)(327,422)(328,423)(329,424)(330,425)(331,426)(332,427)(333,428)(334,429)(335,430)(336,431)(337,432)(338,433)(339,434)(340,435)(341,407)(342,408)(343,409)(344,410)(345,411)(346,412)(347,413)(348,414), (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), (1,343,109,265,30,317,75,242)(2,326,108,282,31,300,74,259)(3,338,107,270,32,312,73,247)(4,321,106,287,33,295,72,235)(5,333,105,275,34,307,71,252)(6,345,104,263,35,319,70,240)(7,328,103,280,36,302,69,257)(8,340,102,268,37,314,68,245)(9,323,101,285,38,297,67,233)(10,335,100,273,39,309,66,250)(11,347,99,290,40,292,65,238)(12,330,98,278,41,304,64,255)(13,342,97,266,42,316,63,243)(14,325,96,283,43,299,62,260)(15,337,95,271,44,311,61,248)(16,320,94,288,45,294,60,236)(17,332,93,276,46,306,59,253)(18,344,92,264,47,318,87,241)(19,327,91,281,48,301,86,258)(20,339,90,269,49,313,85,246)(21,322,89,286,50,296,84,234)(22,334,88,274,51,308,83,251)(23,346,116,262,52,291,82,239)(24,329,115,279,53,303,81,256)(25,341,114,267,54,315,80,244)(26,324,113,284,55,298,79,261)(27,336,112,272,56,310,78,249)(28,348,111,289,57,293,77,237)(29,331,110,277,58,305,76,254)(117,458,212,387,146,409,186,361)(118,441,211,404,147,421,185,349)(119,453,210,392,148,433,184,366)(120,436,209,380,149,416,183,354)(121,448,208,397,150,428,182,371)(122,460,207,385,151,411,181,359)(123,443,206,402,152,423,180,376)(124,455,205,390,153,435,179,364)(125,438,204,378,154,418,178,352)(126,450,232,395,155,430,177,369)(127,462,231,383,156,413,176,357)(128,445,230,400,157,425,175,374)(129,457,229,388,158,408,203,362)(130,440,228,405,159,420,202,350)(131,452,227,393,160,432,201,367)(132,464,226,381,161,415,200,355)(133,447,225,398,162,427,199,372)(134,459,224,386,163,410,198,360)(135,442,223,403,164,422,197,377)(136,454,222,391,165,434,196,365)(137,437,221,379,166,417,195,353)(138,449,220,396,167,429,194,370)(139,461,219,384,168,412,193,358)(140,444,218,401,169,424,192,375)(141,456,217,389,170,407,191,363)(142,439,216,406,171,419,190,351)(143,451,215,394,172,431,189,368)(144,463,214,382,173,414,188,356)(145,446,213,399,174,426,187,373) );
G=PermutationGroup([[(1,146),(2,147),(3,148),(4,149),(5,150),(6,151),(7,152),(8,153),(9,154),(10,155),(11,156),(12,157),(13,158),(14,159),(15,160),(16,161),(17,162),(18,163),(19,164),(20,165),(21,166),(22,167),(23,168),(24,169),(25,170),(26,171),(27,172),(28,173),(29,174),(30,117),(31,118),(32,119),(33,120),(34,121),(35,122),(36,123),(37,124),(38,125),(39,126),(40,127),(41,128),(42,129),(43,130),(44,131),(45,132),(46,133),(47,134),(48,135),(49,136),(50,137),(51,138),(52,139),(53,140),(54,141),(55,142),(56,143),(57,144),(58,145),(59,225),(60,226),(61,227),(62,228),(63,229),(64,230),(65,231),(66,232),(67,204),(68,205),(69,206),(70,207),(71,208),(72,209),(73,210),(74,211),(75,212),(76,213),(77,214),(78,215),(79,216),(80,217),(81,218),(82,219),(83,220),(84,221),(85,222),(86,223),(87,224),(88,194),(89,195),(90,196),(91,197),(92,198),(93,199),(94,200),(95,201),(96,202),(97,203),(98,175),(99,176),(100,177),(101,178),(102,179),(103,180),(104,181),(105,182),(106,183),(107,184),(108,185),(109,186),(110,187),(111,188),(112,189),(113,190),(114,191),(115,192),(116,193),(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),(262,358),(263,359),(264,360),(265,361),(266,362),(267,363),(268,364),(269,365),(270,366),(271,367),(272,368),(273,369),(274,370),(275,371),(276,372),(277,373),(278,374),(279,375),(280,376),(281,377),(282,349),(283,350),(284,351),(285,352),(286,353),(287,354),(288,355),(289,356),(290,357),(291,461),(292,462),(293,463),(294,464),(295,436),(296,437),(297,438),(298,439),(299,440),(300,441),(301,442),(302,443),(303,444),(304,445),(305,446),(306,447),(307,448),(308,449),(309,450),(310,451),(311,452),(312,453),(313,454),(314,455),(315,456),(316,457),(317,458),(318,459),(319,460),(320,415),(321,416),(322,417),(323,418),(324,419),(325,420),(326,421),(327,422),(328,423),(329,424),(330,425),(331,426),(332,427),(333,428),(334,429),(335,430),(336,431),(337,432),(338,433),(339,434),(340,435),(341,407),(342,408),(343,409),(344,410),(345,411),(346,412),(347,413),(348,414)], [(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)], [(1,343,109,265,30,317,75,242),(2,326,108,282,31,300,74,259),(3,338,107,270,32,312,73,247),(4,321,106,287,33,295,72,235),(5,333,105,275,34,307,71,252),(6,345,104,263,35,319,70,240),(7,328,103,280,36,302,69,257),(8,340,102,268,37,314,68,245),(9,323,101,285,38,297,67,233),(10,335,100,273,39,309,66,250),(11,347,99,290,40,292,65,238),(12,330,98,278,41,304,64,255),(13,342,97,266,42,316,63,243),(14,325,96,283,43,299,62,260),(15,337,95,271,44,311,61,248),(16,320,94,288,45,294,60,236),(17,332,93,276,46,306,59,253),(18,344,92,264,47,318,87,241),(19,327,91,281,48,301,86,258),(20,339,90,269,49,313,85,246),(21,322,89,286,50,296,84,234),(22,334,88,274,51,308,83,251),(23,346,116,262,52,291,82,239),(24,329,115,279,53,303,81,256),(25,341,114,267,54,315,80,244),(26,324,113,284,55,298,79,261),(27,336,112,272,56,310,78,249),(28,348,111,289,57,293,77,237),(29,331,110,277,58,305,76,254),(117,458,212,387,146,409,186,361),(118,441,211,404,147,421,185,349),(119,453,210,392,148,433,184,366),(120,436,209,380,149,416,183,354),(121,448,208,397,150,428,182,371),(122,460,207,385,151,411,181,359),(123,443,206,402,152,423,180,376),(124,455,205,390,153,435,179,364),(125,438,204,378,154,418,178,352),(126,450,232,395,155,430,177,369),(127,462,231,383,156,413,176,357),(128,445,230,400,157,425,175,374),(129,457,229,388,158,408,203,362),(130,440,228,405,159,420,202,350),(131,452,227,393,160,432,201,367),(132,464,226,381,161,415,200,355),(133,447,225,398,162,427,199,372),(134,459,224,386,163,410,198,360),(135,442,223,403,164,422,197,377),(136,454,222,391,165,434,196,365),(137,437,221,379,166,417,195,353),(138,449,220,396,167,429,194,370),(139,461,219,384,168,412,193,358),(140,444,218,401,169,424,192,375),(141,456,217,389,170,407,191,363),(142,439,216,406,171,419,190,351),(143,451,215,394,172,431,189,368),(144,463,214,382,173,414,188,356),(145,446,213,399,174,426,187,373)]])
44 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 8A | ··· | 8H | 29A | ··· | 29G | 58A | ··· | 58U |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 8 | ··· | 8 | 29 | ··· | 29 | 58 | ··· | 58 |
| size | 1 | 1 | 1 | 1 | 29 | 29 | 29 | 29 | 29 | ··· | 29 | 4 | ··· | 4 | 4 | ··· | 4 |
44 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 4 | 4 | 4 |
| type | + | + | + | + | - | + | |||
| image | C1 | C2 | C2 | C4 | C4 | C8 | C29⋊C4 | C29⋊C8 | C2×C29⋊C4 |
| kernel | C2×C29⋊C8 | C29⋊C8 | C2×Dic29 | Dic29 | C2×C58 | C58 | C22 | C2 | C2 |
| # reps | 1 | 2 | 1 | 2 | 2 | 8 | 7 | 14 | 7 |
Matrix representation of C2×C29⋊C8 ►in GL6(𝔽233)
| 232 | 0 | 0 | 0 | 0 | 0 |
| 0 | 232 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 209 | 24 | 30 | 232 |
| 0 | 0 | 210 | 24 | 30 | 232 |
| 0 | 0 | 209 | 25 | 30 | 232 |
| 0 | 0 | 209 | 24 | 31 | 232 |
| 136 | 0 | 0 | 0 | 0 | 0 |
| 0 | 232 | 0 | 0 | 0 | 0 |
| 0 | 0 | 138 | 64 | 64 | 100 |
| 0 | 0 | 140 | 19 | 24 | 156 |
| 0 | 0 | 178 | 214 | 119 | 13 |
| 0 | 0 | 20 | 6 | 45 | 190 |
G:=sub<GL(6,GF(233))| [232,0,0,0,0,0,0,232,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,209,210,209,209,0,0,24,24,25,24,0,0,30,30,30,31,0,0,232,232,232,232],[136,0,0,0,0,0,0,232,0,0,0,0,0,0,138,140,178,20,0,0,64,19,214,6,0,0,64,24,119,45,0,0,100,156,13,190] >;
C2×C29⋊C8 in GAP, Magma, Sage, TeX
C_2\times C_{29}\rtimes C_8 % in TeX
G:=Group("C2xC29:C8"); // GroupNames label
G:=SmallGroup(464,32);
// by ID
G=gap.SmallGroup(464,32);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-29,20,42,4804,2814]);
// Polycyclic
G:=Group<a,b,c|a^2=b^29=c^8=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^17>;
// generators/relations
Export