metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: C29⋊2C16, C58.2C8, C8.2D29, C232.2C2, C116.5C4, C4.2Dic29, C2.(C29⋊2C8), SmallGroup(464,1)
Series: Derived ►Chief ►Lower central ►Upper central
| C29 — C29⋊2C16 |
Generators and relations for C29⋊2C16
G = < a,b | a29=b16=1, bab-1=a-1 >
Smallest permutation representation of C29⋊2C16
►Regular action on 464 points
Generators in S464
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29)(30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58)(59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87)(88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116)(117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145)(146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174)(175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203)(204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232)(233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261)(262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290)(291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319)(320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348)(349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377)(378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406)(407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435)(436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464)
(1 436 218 320 106 378 173 262 31 407 197 291 71 349 129 233)(2 464 219 348 107 406 174 290 32 435 198 319 72 377 130 261)(3 463 220 347 108 405 146 289 33 434 199 318 73 376 131 260)(4 462 221 346 109 404 147 288 34 433 200 317 74 375 132 259)(5 461 222 345 110 403 148 287 35 432 201 316 75 374 133 258)(6 460 223 344 111 402 149 286 36 431 202 315 76 373 134 257)(7 459 224 343 112 401 150 285 37 430 203 314 77 372 135 256)(8 458 225 342 113 400 151 284 38 429 175 313 78 371 136 255)(9 457 226 341 114 399 152 283 39 428 176 312 79 370 137 254)(10 456 227 340 115 398 153 282 40 427 177 311 80 369 138 253)(11 455 228 339 116 397 154 281 41 426 178 310 81 368 139 252)(12 454 229 338 88 396 155 280 42 425 179 309 82 367 140 251)(13 453 230 337 89 395 156 279 43 424 180 308 83 366 141 250)(14 452 231 336 90 394 157 278 44 423 181 307 84 365 142 249)(15 451 232 335 91 393 158 277 45 422 182 306 85 364 143 248)(16 450 204 334 92 392 159 276 46 421 183 305 86 363 144 247)(17 449 205 333 93 391 160 275 47 420 184 304 87 362 145 246)(18 448 206 332 94 390 161 274 48 419 185 303 59 361 117 245)(19 447 207 331 95 389 162 273 49 418 186 302 60 360 118 244)(20 446 208 330 96 388 163 272 50 417 187 301 61 359 119 243)(21 445 209 329 97 387 164 271 51 416 188 300 62 358 120 242)(22 444 210 328 98 386 165 270 52 415 189 299 63 357 121 241)(23 443 211 327 99 385 166 269 53 414 190 298 64 356 122 240)(24 442 212 326 100 384 167 268 54 413 191 297 65 355 123 239)(25 441 213 325 101 383 168 267 55 412 192 296 66 354 124 238)(26 440 214 324 102 382 169 266 56 411 193 295 67 353 125 237)(27 439 215 323 103 381 170 265 57 410 194 294 68 352 126 236)(28 438 216 322 104 380 171 264 58 409 195 293 69 351 127 235)(29 437 217 321 105 379 172 263 30 408 196 292 70 350 128 234)
G:=sub<Sym(464)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)(30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58)(59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87)(88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116)(117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145)(146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174)(175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203)(204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232)(233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261)(262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290)(291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319)(320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348)(349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377)(378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406)(407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435)(436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464), (1,436,218,320,106,378,173,262,31,407,197,291,71,349,129,233)(2,464,219,348,107,406,174,290,32,435,198,319,72,377,130,261)(3,463,220,347,108,405,146,289,33,434,199,318,73,376,131,260)(4,462,221,346,109,404,147,288,34,433,200,317,74,375,132,259)(5,461,222,345,110,403,148,287,35,432,201,316,75,374,133,258)(6,460,223,344,111,402,149,286,36,431,202,315,76,373,134,257)(7,459,224,343,112,401,150,285,37,430,203,314,77,372,135,256)(8,458,225,342,113,400,151,284,38,429,175,313,78,371,136,255)(9,457,226,341,114,399,152,283,39,428,176,312,79,370,137,254)(10,456,227,340,115,398,153,282,40,427,177,311,80,369,138,253)(11,455,228,339,116,397,154,281,41,426,178,310,81,368,139,252)(12,454,229,338,88,396,155,280,42,425,179,309,82,367,140,251)(13,453,230,337,89,395,156,279,43,424,180,308,83,366,141,250)(14,452,231,336,90,394,157,278,44,423,181,307,84,365,142,249)(15,451,232,335,91,393,158,277,45,422,182,306,85,364,143,248)(16,450,204,334,92,392,159,276,46,421,183,305,86,363,144,247)(17,449,205,333,93,391,160,275,47,420,184,304,87,362,145,246)(18,448,206,332,94,390,161,274,48,419,185,303,59,361,117,245)(19,447,207,331,95,389,162,273,49,418,186,302,60,360,118,244)(20,446,208,330,96,388,163,272,50,417,187,301,61,359,119,243)(21,445,209,329,97,387,164,271,51,416,188,300,62,358,120,242)(22,444,210,328,98,386,165,270,52,415,189,299,63,357,121,241)(23,443,211,327,99,385,166,269,53,414,190,298,64,356,122,240)(24,442,212,326,100,384,167,268,54,413,191,297,65,355,123,239)(25,441,213,325,101,383,168,267,55,412,192,296,66,354,124,238)(26,440,214,324,102,382,169,266,56,411,193,295,67,353,125,237)(27,439,215,323,103,381,170,265,57,410,194,294,68,352,126,236)(28,438,216,322,104,380,171,264,58,409,195,293,69,351,127,235)(29,437,217,321,105,379,172,263,30,408,196,292,70,350,128,234)>;
G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)(30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58)(59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87)(88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116)(117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145)(146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174)(175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203)(204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232)(233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261)(262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290)(291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319)(320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348)(349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377)(378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406)(407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435)(436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464), (1,436,218,320,106,378,173,262,31,407,197,291,71,349,129,233)(2,464,219,348,107,406,174,290,32,435,198,319,72,377,130,261)(3,463,220,347,108,405,146,289,33,434,199,318,73,376,131,260)(4,462,221,346,109,404,147,288,34,433,200,317,74,375,132,259)(5,461,222,345,110,403,148,287,35,432,201,316,75,374,133,258)(6,460,223,344,111,402,149,286,36,431,202,315,76,373,134,257)(7,459,224,343,112,401,150,285,37,430,203,314,77,372,135,256)(8,458,225,342,113,400,151,284,38,429,175,313,78,371,136,255)(9,457,226,341,114,399,152,283,39,428,176,312,79,370,137,254)(10,456,227,340,115,398,153,282,40,427,177,311,80,369,138,253)(11,455,228,339,116,397,154,281,41,426,178,310,81,368,139,252)(12,454,229,338,88,396,155,280,42,425,179,309,82,367,140,251)(13,453,230,337,89,395,156,279,43,424,180,308,83,366,141,250)(14,452,231,336,90,394,157,278,44,423,181,307,84,365,142,249)(15,451,232,335,91,393,158,277,45,422,182,306,85,364,143,248)(16,450,204,334,92,392,159,276,46,421,183,305,86,363,144,247)(17,449,205,333,93,391,160,275,47,420,184,304,87,362,145,246)(18,448,206,332,94,390,161,274,48,419,185,303,59,361,117,245)(19,447,207,331,95,389,162,273,49,418,186,302,60,360,118,244)(20,446,208,330,96,388,163,272,50,417,187,301,61,359,119,243)(21,445,209,329,97,387,164,271,51,416,188,300,62,358,120,242)(22,444,210,328,98,386,165,270,52,415,189,299,63,357,121,241)(23,443,211,327,99,385,166,269,53,414,190,298,64,356,122,240)(24,442,212,326,100,384,167,268,54,413,191,297,65,355,123,239)(25,441,213,325,101,383,168,267,55,412,192,296,66,354,124,238)(26,440,214,324,102,382,169,266,56,411,193,295,67,353,125,237)(27,439,215,323,103,381,170,265,57,410,194,294,68,352,126,236)(28,438,216,322,104,380,171,264,58,409,195,293,69,351,127,235)(29,437,217,321,105,379,172,263,30,408,196,292,70,350,128,234) );
G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29),(30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58),(59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87),(88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116),(117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145),(146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174),(175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203),(204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232),(233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261),(262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290),(291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319),(320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348),(349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377),(378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406),(407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435),(436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464)], [(1,436,218,320,106,378,173,262,31,407,197,291,71,349,129,233),(2,464,219,348,107,406,174,290,32,435,198,319,72,377,130,261),(3,463,220,347,108,405,146,289,33,434,199,318,73,376,131,260),(4,462,221,346,109,404,147,288,34,433,200,317,74,375,132,259),(5,461,222,345,110,403,148,287,35,432,201,316,75,374,133,258),(6,460,223,344,111,402,149,286,36,431,202,315,76,373,134,257),(7,459,224,343,112,401,150,285,37,430,203,314,77,372,135,256),(8,458,225,342,113,400,151,284,38,429,175,313,78,371,136,255),(9,457,226,341,114,399,152,283,39,428,176,312,79,370,137,254),(10,456,227,340,115,398,153,282,40,427,177,311,80,369,138,253),(11,455,228,339,116,397,154,281,41,426,178,310,81,368,139,252),(12,454,229,338,88,396,155,280,42,425,179,309,82,367,140,251),(13,453,230,337,89,395,156,279,43,424,180,308,83,366,141,250),(14,452,231,336,90,394,157,278,44,423,181,307,84,365,142,249),(15,451,232,335,91,393,158,277,45,422,182,306,85,364,143,248),(16,450,204,334,92,392,159,276,46,421,183,305,86,363,144,247),(17,449,205,333,93,391,160,275,47,420,184,304,87,362,145,246),(18,448,206,332,94,390,161,274,48,419,185,303,59,361,117,245),(19,447,207,331,95,389,162,273,49,418,186,302,60,360,118,244),(20,446,208,330,96,388,163,272,50,417,187,301,61,359,119,243),(21,445,209,329,97,387,164,271,51,416,188,300,62,358,120,242),(22,444,210,328,98,386,165,270,52,415,189,299,63,357,121,241),(23,443,211,327,99,385,166,269,53,414,190,298,64,356,122,240),(24,442,212,326,100,384,167,268,54,413,191,297,65,355,123,239),(25,441,213,325,101,383,168,267,55,412,192,296,66,354,124,238),(26,440,214,324,102,382,169,266,56,411,193,295,67,353,125,237),(27,439,215,323,103,381,170,265,57,410,194,294,68,352,126,236),(28,438,216,322,104,380,171,264,58,409,195,293,69,351,127,235),(29,437,217,321,105,379,172,263,30,408,196,292,70,350,128,234)]])
128 conjugacy classes
| class | 1 | 2 | 4A | 4B | 8A | 8B | 8C | 8D | 16A | ··· | 16H | 29A | ··· | 29N | 58A | ··· | 58N | 116A | ··· | 116AB | 232A | ··· | 232BD |
| order | 1 | 2 | 4 | 4 | 8 | 8 | 8 | 8 | 16 | ··· | 16 | 29 | ··· | 29 | 58 | ··· | 58 | 116 | ··· | 116 | 232 | ··· | 232 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 29 | ··· | 29 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
128 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | |||||
| image | C1 | C2 | C4 | C8 | C16 | D29 | Dic29 | C29⋊2C8 | C29⋊2C16 |
| kernel | C29⋊2C16 | C232 | C116 | C58 | C29 | C8 | C4 | C2 | C1 |
| # reps | 1 | 1 | 2 | 4 | 8 | 14 | 14 | 28 | 56 |
Matrix representation of C29⋊2C16 ►in GL3(𝔽929) generated by
| 1 | 0 | 0 |
| 0 | 928 | 1 |
| 0 | 727 | 201 |
| 46 | 0 | 0 |
| 0 | 586 | 46 |
| 0 | 391 | 343 |
G:=sub<GL(3,GF(929))| [1,0,0,0,928,727,0,1,201],[46,0,0,0,586,391,0,46,343] >;
C29⋊2C16 in GAP, Magma, Sage, TeX
C_{29}\rtimes_2C_{16} % in TeX
G:=Group("C29:2C16"); // GroupNames label
G:=SmallGroup(464,1);
// by ID
G=gap.SmallGroup(464,1);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-29,10,26,42,11204]);
// Polycyclic
G:=Group<a,b|a^29=b^16=1,b*a*b^-1=a^-1>;
// generators/relations
Export