direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C2×C29⋊2C8, C58⋊2C8, C116.6C4, C4.14D58, C4.3Dic29, C116.14C22, C22.2Dic29, C29⋊4(C2×C8), (C2×C58).4C4, (C2×C4).5D29, C58.13(C2×C4), (C2×C116).6C2, C2.1(C2×Dic29), SmallGroup(464,9)
Series: Derived ►Chief ►Lower central ►Upper central
| C29 — C2×C29⋊2C8 |
Generators and relations for C2×C29⋊2C8
G = < a,b,c | a2=b29=c8=1, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C2×C29⋊2C8
►Regular action on 464 points
Generators in S464
(1 117)(2 118)(3 119)(4 120)(5 121)(6 122)(7 123)(8 124)(9 125)(10 126)(11 127)(12 128)(13 129)(14 130)(15 131)(16 132)(17 133)(18 134)(19 135)(20 136)(21 137)(22 138)(23 139)(24 140)(25 141)(26 142)(27 143)(28 144)(29 145)(30 146)(31 147)(32 148)(33 149)(34 150)(35 151)(36 152)(37 153)(38 154)(39 155)(40 156)(41 157)(42 158)(43 159)(44 160)(45 161)(46 162)(47 163)(48 164)(49 165)(50 166)(51 167)(52 168)(53 169)(54 170)(55 171)(56 172)(57 173)(58 174)(59 175)(60 176)(61 177)(62 178)(63 179)(64 180)(65 181)(66 182)(67 183)(68 184)(69 185)(70 186)(71 187)(72 188)(73 189)(74 190)(75 191)(76 192)(77 193)(78 194)(79 195)(80 196)(81 197)(82 198)(83 199)(84 200)(85 201)(86 202)(87 203)(88 204)(89 205)(90 206)(91 207)(92 208)(93 209)(94 210)(95 211)(96 212)(97 213)(98 214)(99 215)(100 216)(101 217)(102 218)(103 219)(104 220)(105 221)(106 222)(107 223)(108 224)(109 225)(110 226)(111 227)(112 228)(113 229)(114 230)(115 231)(116 232)(233 350)(234 351)(235 352)(236 353)(237 354)(238 355)(239 356)(240 357)(241 358)(242 359)(243 360)(244 361)(245 362)(246 363)(247 364)(248 365)(249 366)(250 367)(251 368)(252 369)(253 370)(254 371)(255 372)(256 373)(257 374)(258 375)(259 376)(260 377)(261 349)(262 402)(263 403)(264 404)(265 405)(266 406)(267 378)(268 379)(269 380)(270 381)(271 382)(272 383)(273 384)(274 385)(275 386)(276 387)(277 388)(278 389)(279 390)(280 391)(281 392)(282 393)(283 394)(284 395)(285 396)(286 397)(287 398)(288 399)(289 400)(290 401)(291 416)(292 417)(293 418)(294 419)(295 420)(296 421)(297 422)(298 423)(299 424)(300 425)(301 426)(302 427)(303 428)(304 429)(305 430)(306 431)(307 432)(308 433)(309 434)(310 435)(311 407)(312 408)(313 409)(314 410)(315 411)(316 412)(317 413)(318 414)(319 415)(320 461)(321 462)(322 463)(323 464)(324 436)(325 437)(326 438)(327 439)(328 440)(329 441)(330 442)(331 443)(332 444)(333 445)(334 446)(335 447)(336 448)(337 449)(338 450)(339 451)(340 452)(341 453)(342 454)(343 455)(344 456)(345 457)(346 458)(347 459)(348 460)
(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)
(1 454 88 400 30 426 59 354)(2 453 89 399 31 425 60 353)(3 452 90 398 32 424 61 352)(4 451 91 397 33 423 62 351)(5 450 92 396 34 422 63 350)(6 449 93 395 35 421 64 349)(7 448 94 394 36 420 65 377)(8 447 95 393 37 419 66 376)(9 446 96 392 38 418 67 375)(10 445 97 391 39 417 68 374)(11 444 98 390 40 416 69 373)(12 443 99 389 41 415 70 372)(13 442 100 388 42 414 71 371)(14 441 101 387 43 413 72 370)(15 440 102 386 44 412 73 369)(16 439 103 385 45 411 74 368)(17 438 104 384 46 410 75 367)(18 437 105 383 47 409 76 366)(19 436 106 382 48 408 77 365)(20 464 107 381 49 407 78 364)(21 463 108 380 50 435 79 363)(22 462 109 379 51 434 80 362)(23 461 110 378 52 433 81 361)(24 460 111 406 53 432 82 360)(25 459 112 405 54 431 83 359)(26 458 113 404 55 430 84 358)(27 457 114 403 56 429 85 357)(28 456 115 402 57 428 86 356)(29 455 116 401 58 427 87 355)(117 342 204 289 146 301 175 237)(118 341 205 288 147 300 176 236)(119 340 206 287 148 299 177 235)(120 339 207 286 149 298 178 234)(121 338 208 285 150 297 179 233)(122 337 209 284 151 296 180 261)(123 336 210 283 152 295 181 260)(124 335 211 282 153 294 182 259)(125 334 212 281 154 293 183 258)(126 333 213 280 155 292 184 257)(127 332 214 279 156 291 185 256)(128 331 215 278 157 319 186 255)(129 330 216 277 158 318 187 254)(130 329 217 276 159 317 188 253)(131 328 218 275 160 316 189 252)(132 327 219 274 161 315 190 251)(133 326 220 273 162 314 191 250)(134 325 221 272 163 313 192 249)(135 324 222 271 164 312 193 248)(136 323 223 270 165 311 194 247)(137 322 224 269 166 310 195 246)(138 321 225 268 167 309 196 245)(139 320 226 267 168 308 197 244)(140 348 227 266 169 307 198 243)(141 347 228 265 170 306 199 242)(142 346 229 264 171 305 200 241)(143 345 230 263 172 304 201 240)(144 344 231 262 173 303 202 239)(145 343 232 290 174 302 203 238)
G:=sub<Sym(464)| (1,117)(2,118)(3,119)(4,120)(5,121)(6,122)(7,123)(8,124)(9,125)(10,126)(11,127)(12,128)(13,129)(14,130)(15,131)(16,132)(17,133)(18,134)(19,135)(20,136)(21,137)(22,138)(23,139)(24,140)(25,141)(26,142)(27,143)(28,144)(29,145)(30,146)(31,147)(32,148)(33,149)(34,150)(35,151)(36,152)(37,153)(38,154)(39,155)(40,156)(41,157)(42,158)(43,159)(44,160)(45,161)(46,162)(47,163)(48,164)(49,165)(50,166)(51,167)(52,168)(53,169)(54,170)(55,171)(56,172)(57,173)(58,174)(59,175)(60,176)(61,177)(62,178)(63,179)(64,180)(65,181)(66,182)(67,183)(68,184)(69,185)(70,186)(71,187)(72,188)(73,189)(74,190)(75,191)(76,192)(77,193)(78,194)(79,195)(80,196)(81,197)(82,198)(83,199)(84,200)(85,201)(86,202)(87,203)(88,204)(89,205)(90,206)(91,207)(92,208)(93,209)(94,210)(95,211)(96,212)(97,213)(98,214)(99,215)(100,216)(101,217)(102,218)(103,219)(104,220)(105,221)(106,222)(107,223)(108,224)(109,225)(110,226)(111,227)(112,228)(113,229)(114,230)(115,231)(116,232)(233,350)(234,351)(235,352)(236,353)(237,354)(238,355)(239,356)(240,357)(241,358)(242,359)(243,360)(244,361)(245,362)(246,363)(247,364)(248,365)(249,366)(250,367)(251,368)(252,369)(253,370)(254,371)(255,372)(256,373)(257,374)(258,375)(259,376)(260,377)(261,349)(262,402)(263,403)(264,404)(265,405)(266,406)(267,378)(268,379)(269,380)(270,381)(271,382)(272,383)(273,384)(274,385)(275,386)(276,387)(277,388)(278,389)(279,390)(280,391)(281,392)(282,393)(283,394)(284,395)(285,396)(286,397)(287,398)(288,399)(289,400)(290,401)(291,416)(292,417)(293,418)(294,419)(295,420)(296,421)(297,422)(298,423)(299,424)(300,425)(301,426)(302,427)(303,428)(304,429)(305,430)(306,431)(307,432)(308,433)(309,434)(310,435)(311,407)(312,408)(313,409)(314,410)(315,411)(316,412)(317,413)(318,414)(319,415)(320,461)(321,462)(322,463)(323,464)(324,436)(325,437)(326,438)(327,439)(328,440)(329,441)(330,442)(331,443)(332,444)(333,445)(334,446)(335,447)(336,448)(337,449)(338,450)(339,451)(340,452)(341,453)(342,454)(343,455)(344,456)(345,457)(346,458)(347,459)(348,460), (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), (1,454,88,400,30,426,59,354)(2,453,89,399,31,425,60,353)(3,452,90,398,32,424,61,352)(4,451,91,397,33,423,62,351)(5,450,92,396,34,422,63,350)(6,449,93,395,35,421,64,349)(7,448,94,394,36,420,65,377)(8,447,95,393,37,419,66,376)(9,446,96,392,38,418,67,375)(10,445,97,391,39,417,68,374)(11,444,98,390,40,416,69,373)(12,443,99,389,41,415,70,372)(13,442,100,388,42,414,71,371)(14,441,101,387,43,413,72,370)(15,440,102,386,44,412,73,369)(16,439,103,385,45,411,74,368)(17,438,104,384,46,410,75,367)(18,437,105,383,47,409,76,366)(19,436,106,382,48,408,77,365)(20,464,107,381,49,407,78,364)(21,463,108,380,50,435,79,363)(22,462,109,379,51,434,80,362)(23,461,110,378,52,433,81,361)(24,460,111,406,53,432,82,360)(25,459,112,405,54,431,83,359)(26,458,113,404,55,430,84,358)(27,457,114,403,56,429,85,357)(28,456,115,402,57,428,86,356)(29,455,116,401,58,427,87,355)(117,342,204,289,146,301,175,237)(118,341,205,288,147,300,176,236)(119,340,206,287,148,299,177,235)(120,339,207,286,149,298,178,234)(121,338,208,285,150,297,179,233)(122,337,209,284,151,296,180,261)(123,336,210,283,152,295,181,260)(124,335,211,282,153,294,182,259)(125,334,212,281,154,293,183,258)(126,333,213,280,155,292,184,257)(127,332,214,279,156,291,185,256)(128,331,215,278,157,319,186,255)(129,330,216,277,158,318,187,254)(130,329,217,276,159,317,188,253)(131,328,218,275,160,316,189,252)(132,327,219,274,161,315,190,251)(133,326,220,273,162,314,191,250)(134,325,221,272,163,313,192,249)(135,324,222,271,164,312,193,248)(136,323,223,270,165,311,194,247)(137,322,224,269,166,310,195,246)(138,321,225,268,167,309,196,245)(139,320,226,267,168,308,197,244)(140,348,227,266,169,307,198,243)(141,347,228,265,170,306,199,242)(142,346,229,264,171,305,200,241)(143,345,230,263,172,304,201,240)(144,344,231,262,173,303,202,239)(145,343,232,290,174,302,203,238)>;
G:=Group( (1,117)(2,118)(3,119)(4,120)(5,121)(6,122)(7,123)(8,124)(9,125)(10,126)(11,127)(12,128)(13,129)(14,130)(15,131)(16,132)(17,133)(18,134)(19,135)(20,136)(21,137)(22,138)(23,139)(24,140)(25,141)(26,142)(27,143)(28,144)(29,145)(30,146)(31,147)(32,148)(33,149)(34,150)(35,151)(36,152)(37,153)(38,154)(39,155)(40,156)(41,157)(42,158)(43,159)(44,160)(45,161)(46,162)(47,163)(48,164)(49,165)(50,166)(51,167)(52,168)(53,169)(54,170)(55,171)(56,172)(57,173)(58,174)(59,175)(60,176)(61,177)(62,178)(63,179)(64,180)(65,181)(66,182)(67,183)(68,184)(69,185)(70,186)(71,187)(72,188)(73,189)(74,190)(75,191)(76,192)(77,193)(78,194)(79,195)(80,196)(81,197)(82,198)(83,199)(84,200)(85,201)(86,202)(87,203)(88,204)(89,205)(90,206)(91,207)(92,208)(93,209)(94,210)(95,211)(96,212)(97,213)(98,214)(99,215)(100,216)(101,217)(102,218)(103,219)(104,220)(105,221)(106,222)(107,223)(108,224)(109,225)(110,226)(111,227)(112,228)(113,229)(114,230)(115,231)(116,232)(233,350)(234,351)(235,352)(236,353)(237,354)(238,355)(239,356)(240,357)(241,358)(242,359)(243,360)(244,361)(245,362)(246,363)(247,364)(248,365)(249,366)(250,367)(251,368)(252,369)(253,370)(254,371)(255,372)(256,373)(257,374)(258,375)(259,376)(260,377)(261,349)(262,402)(263,403)(264,404)(265,405)(266,406)(267,378)(268,379)(269,380)(270,381)(271,382)(272,383)(273,384)(274,385)(275,386)(276,387)(277,388)(278,389)(279,390)(280,391)(281,392)(282,393)(283,394)(284,395)(285,396)(286,397)(287,398)(288,399)(289,400)(290,401)(291,416)(292,417)(293,418)(294,419)(295,420)(296,421)(297,422)(298,423)(299,424)(300,425)(301,426)(302,427)(303,428)(304,429)(305,430)(306,431)(307,432)(308,433)(309,434)(310,435)(311,407)(312,408)(313,409)(314,410)(315,411)(316,412)(317,413)(318,414)(319,415)(320,461)(321,462)(322,463)(323,464)(324,436)(325,437)(326,438)(327,439)(328,440)(329,441)(330,442)(331,443)(332,444)(333,445)(334,446)(335,447)(336,448)(337,449)(338,450)(339,451)(340,452)(341,453)(342,454)(343,455)(344,456)(345,457)(346,458)(347,459)(348,460), (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), (1,454,88,400,30,426,59,354)(2,453,89,399,31,425,60,353)(3,452,90,398,32,424,61,352)(4,451,91,397,33,423,62,351)(5,450,92,396,34,422,63,350)(6,449,93,395,35,421,64,349)(7,448,94,394,36,420,65,377)(8,447,95,393,37,419,66,376)(9,446,96,392,38,418,67,375)(10,445,97,391,39,417,68,374)(11,444,98,390,40,416,69,373)(12,443,99,389,41,415,70,372)(13,442,100,388,42,414,71,371)(14,441,101,387,43,413,72,370)(15,440,102,386,44,412,73,369)(16,439,103,385,45,411,74,368)(17,438,104,384,46,410,75,367)(18,437,105,383,47,409,76,366)(19,436,106,382,48,408,77,365)(20,464,107,381,49,407,78,364)(21,463,108,380,50,435,79,363)(22,462,109,379,51,434,80,362)(23,461,110,378,52,433,81,361)(24,460,111,406,53,432,82,360)(25,459,112,405,54,431,83,359)(26,458,113,404,55,430,84,358)(27,457,114,403,56,429,85,357)(28,456,115,402,57,428,86,356)(29,455,116,401,58,427,87,355)(117,342,204,289,146,301,175,237)(118,341,205,288,147,300,176,236)(119,340,206,287,148,299,177,235)(120,339,207,286,149,298,178,234)(121,338,208,285,150,297,179,233)(122,337,209,284,151,296,180,261)(123,336,210,283,152,295,181,260)(124,335,211,282,153,294,182,259)(125,334,212,281,154,293,183,258)(126,333,213,280,155,292,184,257)(127,332,214,279,156,291,185,256)(128,331,215,278,157,319,186,255)(129,330,216,277,158,318,187,254)(130,329,217,276,159,317,188,253)(131,328,218,275,160,316,189,252)(132,327,219,274,161,315,190,251)(133,326,220,273,162,314,191,250)(134,325,221,272,163,313,192,249)(135,324,222,271,164,312,193,248)(136,323,223,270,165,311,194,247)(137,322,224,269,166,310,195,246)(138,321,225,268,167,309,196,245)(139,320,226,267,168,308,197,244)(140,348,227,266,169,307,198,243)(141,347,228,265,170,306,199,242)(142,346,229,264,171,305,200,241)(143,345,230,263,172,304,201,240)(144,344,231,262,173,303,202,239)(145,343,232,290,174,302,203,238) );
G=PermutationGroup([[(1,117),(2,118),(3,119),(4,120),(5,121),(6,122),(7,123),(8,124),(9,125),(10,126),(11,127),(12,128),(13,129),(14,130),(15,131),(16,132),(17,133),(18,134),(19,135),(20,136),(21,137),(22,138),(23,139),(24,140),(25,141),(26,142),(27,143),(28,144),(29,145),(30,146),(31,147),(32,148),(33,149),(34,150),(35,151),(36,152),(37,153),(38,154),(39,155),(40,156),(41,157),(42,158),(43,159),(44,160),(45,161),(46,162),(47,163),(48,164),(49,165),(50,166),(51,167),(52,168),(53,169),(54,170),(55,171),(56,172),(57,173),(58,174),(59,175),(60,176),(61,177),(62,178),(63,179),(64,180),(65,181),(66,182),(67,183),(68,184),(69,185),(70,186),(71,187),(72,188),(73,189),(74,190),(75,191),(76,192),(77,193),(78,194),(79,195),(80,196),(81,197),(82,198),(83,199),(84,200),(85,201),(86,202),(87,203),(88,204),(89,205),(90,206),(91,207),(92,208),(93,209),(94,210),(95,211),(96,212),(97,213),(98,214),(99,215),(100,216),(101,217),(102,218),(103,219),(104,220),(105,221),(106,222),(107,223),(108,224),(109,225),(110,226),(111,227),(112,228),(113,229),(114,230),(115,231),(116,232),(233,350),(234,351),(235,352),(236,353),(237,354),(238,355),(239,356),(240,357),(241,358),(242,359),(243,360),(244,361),(245,362),(246,363),(247,364),(248,365),(249,366),(250,367),(251,368),(252,369),(253,370),(254,371),(255,372),(256,373),(257,374),(258,375),(259,376),(260,377),(261,349),(262,402),(263,403),(264,404),(265,405),(266,406),(267,378),(268,379),(269,380),(270,381),(271,382),(272,383),(273,384),(274,385),(275,386),(276,387),(277,388),(278,389),(279,390),(280,391),(281,392),(282,393),(283,394),(284,395),(285,396),(286,397),(287,398),(288,399),(289,400),(290,401),(291,416),(292,417),(293,418),(294,419),(295,420),(296,421),(297,422),(298,423),(299,424),(300,425),(301,426),(302,427),(303,428),(304,429),(305,430),(306,431),(307,432),(308,433),(309,434),(310,435),(311,407),(312,408),(313,409),(314,410),(315,411),(316,412),(317,413),(318,414),(319,415),(320,461),(321,462),(322,463),(323,464),(324,436),(325,437),(326,438),(327,439),(328,440),(329,441),(330,442),(331,443),(332,444),(333,445),(334,446),(335,447),(336,448),(337,449),(338,450),(339,451),(340,452),(341,453),(342,454),(343,455),(344,456),(345,457),(346,458),(347,459),(348,460)], [(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)], [(1,454,88,400,30,426,59,354),(2,453,89,399,31,425,60,353),(3,452,90,398,32,424,61,352),(4,451,91,397,33,423,62,351),(5,450,92,396,34,422,63,350),(6,449,93,395,35,421,64,349),(7,448,94,394,36,420,65,377),(8,447,95,393,37,419,66,376),(9,446,96,392,38,418,67,375),(10,445,97,391,39,417,68,374),(11,444,98,390,40,416,69,373),(12,443,99,389,41,415,70,372),(13,442,100,388,42,414,71,371),(14,441,101,387,43,413,72,370),(15,440,102,386,44,412,73,369),(16,439,103,385,45,411,74,368),(17,438,104,384,46,410,75,367),(18,437,105,383,47,409,76,366),(19,436,106,382,48,408,77,365),(20,464,107,381,49,407,78,364),(21,463,108,380,50,435,79,363),(22,462,109,379,51,434,80,362),(23,461,110,378,52,433,81,361),(24,460,111,406,53,432,82,360),(25,459,112,405,54,431,83,359),(26,458,113,404,55,430,84,358),(27,457,114,403,56,429,85,357),(28,456,115,402,57,428,86,356),(29,455,116,401,58,427,87,355),(117,342,204,289,146,301,175,237),(118,341,205,288,147,300,176,236),(119,340,206,287,148,299,177,235),(120,339,207,286,149,298,178,234),(121,338,208,285,150,297,179,233),(122,337,209,284,151,296,180,261),(123,336,210,283,152,295,181,260),(124,335,211,282,153,294,182,259),(125,334,212,281,154,293,183,258),(126,333,213,280,155,292,184,257),(127,332,214,279,156,291,185,256),(128,331,215,278,157,319,186,255),(129,330,216,277,158,318,187,254),(130,329,217,276,159,317,188,253),(131,328,218,275,160,316,189,252),(132,327,219,274,161,315,190,251),(133,326,220,273,162,314,191,250),(134,325,221,272,163,313,192,249),(135,324,222,271,164,312,193,248),(136,323,223,270,165,311,194,247),(137,322,224,269,166,310,195,246),(138,321,225,268,167,309,196,245),(139,320,226,267,168,308,197,244),(140,348,227,266,169,307,198,243),(141,347,228,265,170,306,199,242),(142,346,229,264,171,305,200,241),(143,345,230,263,172,304,201,240),(144,344,231,262,173,303,202,239),(145,343,232,290,174,302,203,238)]])
128 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 8A | ··· | 8H | 29A | ··· | 29N | 58A | ··· | 58AP | 116A | ··· | 116BD |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 8 | ··· | 8 | 29 | ··· | 29 | 58 | ··· | 58 | 116 | ··· | 116 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 29 | ··· | 29 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
128 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | - | ||||
| image | C1 | C2 | C2 | C4 | C4 | C8 | D29 | Dic29 | D58 | Dic29 | C29⋊2C8 |
| kernel | C2×C29⋊2C8 | C29⋊2C8 | C2×C116 | C116 | C2×C58 | C58 | C2×C4 | C4 | C4 | C22 | C2 |
| # reps | 1 | 2 | 1 | 2 | 2 | 8 | 14 | 14 | 14 | 14 | 56 |
Matrix representation of C2×C29⋊2C8 ►in GL4(𝔽233) generated by
| 1 | 0 | 0 | 0 |
| 0 | 232 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 199 | 232 |
| 0 | 0 | 1 | 0 |
| 136 | 0 | 0 | 0 |
| 0 | 232 | 0 | 0 |
| 0 | 0 | 189 | 184 |
| 0 | 0 | 49 | 44 |
G:=sub<GL(4,GF(233))| [1,0,0,0,0,232,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,199,1,0,0,232,0],[136,0,0,0,0,232,0,0,0,0,189,49,0,0,184,44] >;
C2×C29⋊2C8 in GAP, Magma, Sage, TeX
C_2\times C_{29}\rtimes_2C_8 % in TeX
G:=Group("C2xC29:2C8"); // GroupNames label
G:=SmallGroup(464,9);
// by ID
G=gap.SmallGroup(464,9);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-29,20,42,11204]);
// 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^-1>;
// generators/relations
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