metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: C29⋊C16, C58.C8, C116.2C4, C2.(C29⋊C8), C4.2(C29⋊C4), C29⋊2C8.2C2, SmallGroup(464,3)
Series: Derived ►Chief ►Lower central ►Upper central
| C29 — C29⋊C16 |
Generators and relations for C29⋊C16
G = < a,b | a29=b16=1, bab-1=a17 >
Smallest permutation representation of C29⋊C16
►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)
(1 457 204 347 104 391 146 266 53 412 175 292 63 355 117 249)(2 440 232 335 105 403 174 283 54 424 203 309 64 367 145 237)(3 452 231 323 106 386 173 271 55 407 202 297 65 350 144 254)(4 464 230 340 107 398 172 288 56 419 201 314 66 362 143 242)(5 447 229 328 108 381 171 276 57 431 200 302 67 374 142 259)(6 459 228 345 109 393 170 264 58 414 199 319 68 357 141 247)(7 442 227 333 110 405 169 281 30 426 198 307 69 369 140 235)(8 454 226 321 111 388 168 269 31 409 197 295 70 352 139 252)(9 437 225 338 112 400 167 286 32 421 196 312 71 364 138 240)(10 449 224 326 113 383 166 274 33 433 195 300 72 376 137 257)(11 461 223 343 114 395 165 262 34 416 194 317 73 359 136 245)(12 444 222 331 115 378 164 279 35 428 193 305 74 371 135 233)(13 456 221 348 116 390 163 267 36 411 192 293 75 354 134 250)(14 439 220 336 88 402 162 284 37 423 191 310 76 366 133 238)(15 451 219 324 89 385 161 272 38 435 190 298 77 349 132 255)(16 463 218 341 90 397 160 289 39 418 189 315 78 361 131 243)(17 446 217 329 91 380 159 277 40 430 188 303 79 373 130 260)(18 458 216 346 92 392 158 265 41 413 187 291 80 356 129 248)(19 441 215 334 93 404 157 282 42 425 186 308 81 368 128 236)(20 453 214 322 94 387 156 270 43 408 185 296 82 351 127 253)(21 436 213 339 95 399 155 287 44 420 184 313 83 363 126 241)(22 448 212 327 96 382 154 275 45 432 183 301 84 375 125 258)(23 460 211 344 97 394 153 263 46 415 182 318 85 358 124 246)(24 443 210 332 98 406 152 280 47 427 181 306 86 370 123 234)(25 455 209 320 99 389 151 268 48 410 180 294 87 353 122 251)(26 438 208 337 100 401 150 285 49 422 179 311 59 365 121 239)(27 450 207 325 101 384 149 273 50 434 178 299 60 377 120 256)(28 462 206 342 102 396 148 290 51 417 177 316 61 360 119 244)(29 445 205 330 103 379 147 278 52 429 176 304 62 372 118 261)
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), (1,457,204,347,104,391,146,266,53,412,175,292,63,355,117,249)(2,440,232,335,105,403,174,283,54,424,203,309,64,367,145,237)(3,452,231,323,106,386,173,271,55,407,202,297,65,350,144,254)(4,464,230,340,107,398,172,288,56,419,201,314,66,362,143,242)(5,447,229,328,108,381,171,276,57,431,200,302,67,374,142,259)(6,459,228,345,109,393,170,264,58,414,199,319,68,357,141,247)(7,442,227,333,110,405,169,281,30,426,198,307,69,369,140,235)(8,454,226,321,111,388,168,269,31,409,197,295,70,352,139,252)(9,437,225,338,112,400,167,286,32,421,196,312,71,364,138,240)(10,449,224,326,113,383,166,274,33,433,195,300,72,376,137,257)(11,461,223,343,114,395,165,262,34,416,194,317,73,359,136,245)(12,444,222,331,115,378,164,279,35,428,193,305,74,371,135,233)(13,456,221,348,116,390,163,267,36,411,192,293,75,354,134,250)(14,439,220,336,88,402,162,284,37,423,191,310,76,366,133,238)(15,451,219,324,89,385,161,272,38,435,190,298,77,349,132,255)(16,463,218,341,90,397,160,289,39,418,189,315,78,361,131,243)(17,446,217,329,91,380,159,277,40,430,188,303,79,373,130,260)(18,458,216,346,92,392,158,265,41,413,187,291,80,356,129,248)(19,441,215,334,93,404,157,282,42,425,186,308,81,368,128,236)(20,453,214,322,94,387,156,270,43,408,185,296,82,351,127,253)(21,436,213,339,95,399,155,287,44,420,184,313,83,363,126,241)(22,448,212,327,96,382,154,275,45,432,183,301,84,375,125,258)(23,460,211,344,97,394,153,263,46,415,182,318,85,358,124,246)(24,443,210,332,98,406,152,280,47,427,181,306,86,370,123,234)(25,455,209,320,99,389,151,268,48,410,180,294,87,353,122,251)(26,438,208,337,100,401,150,285,49,422,179,311,59,365,121,239)(27,450,207,325,101,384,149,273,50,434,178,299,60,377,120,256)(28,462,206,342,102,396,148,290,51,417,177,316,61,360,119,244)(29,445,205,330,103,379,147,278,52,429,176,304,62,372,118,261)>;
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), (1,457,204,347,104,391,146,266,53,412,175,292,63,355,117,249)(2,440,232,335,105,403,174,283,54,424,203,309,64,367,145,237)(3,452,231,323,106,386,173,271,55,407,202,297,65,350,144,254)(4,464,230,340,107,398,172,288,56,419,201,314,66,362,143,242)(5,447,229,328,108,381,171,276,57,431,200,302,67,374,142,259)(6,459,228,345,109,393,170,264,58,414,199,319,68,357,141,247)(7,442,227,333,110,405,169,281,30,426,198,307,69,369,140,235)(8,454,226,321,111,388,168,269,31,409,197,295,70,352,139,252)(9,437,225,338,112,400,167,286,32,421,196,312,71,364,138,240)(10,449,224,326,113,383,166,274,33,433,195,300,72,376,137,257)(11,461,223,343,114,395,165,262,34,416,194,317,73,359,136,245)(12,444,222,331,115,378,164,279,35,428,193,305,74,371,135,233)(13,456,221,348,116,390,163,267,36,411,192,293,75,354,134,250)(14,439,220,336,88,402,162,284,37,423,191,310,76,366,133,238)(15,451,219,324,89,385,161,272,38,435,190,298,77,349,132,255)(16,463,218,341,90,397,160,289,39,418,189,315,78,361,131,243)(17,446,217,329,91,380,159,277,40,430,188,303,79,373,130,260)(18,458,216,346,92,392,158,265,41,413,187,291,80,356,129,248)(19,441,215,334,93,404,157,282,42,425,186,308,81,368,128,236)(20,453,214,322,94,387,156,270,43,408,185,296,82,351,127,253)(21,436,213,339,95,399,155,287,44,420,184,313,83,363,126,241)(22,448,212,327,96,382,154,275,45,432,183,301,84,375,125,258)(23,460,211,344,97,394,153,263,46,415,182,318,85,358,124,246)(24,443,210,332,98,406,152,280,47,427,181,306,86,370,123,234)(25,455,209,320,99,389,151,268,48,410,180,294,87,353,122,251)(26,438,208,337,100,401,150,285,49,422,179,311,59,365,121,239)(27,450,207,325,101,384,149,273,50,434,178,299,60,377,120,256)(28,462,206,342,102,396,148,290,51,417,177,316,61,360,119,244)(29,445,205,330,103,379,147,278,52,429,176,304,62,372,118,261) );
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)], [(1,457,204,347,104,391,146,266,53,412,175,292,63,355,117,249),(2,440,232,335,105,403,174,283,54,424,203,309,64,367,145,237),(3,452,231,323,106,386,173,271,55,407,202,297,65,350,144,254),(4,464,230,340,107,398,172,288,56,419,201,314,66,362,143,242),(5,447,229,328,108,381,171,276,57,431,200,302,67,374,142,259),(6,459,228,345,109,393,170,264,58,414,199,319,68,357,141,247),(7,442,227,333,110,405,169,281,30,426,198,307,69,369,140,235),(8,454,226,321,111,388,168,269,31,409,197,295,70,352,139,252),(9,437,225,338,112,400,167,286,32,421,196,312,71,364,138,240),(10,449,224,326,113,383,166,274,33,433,195,300,72,376,137,257),(11,461,223,343,114,395,165,262,34,416,194,317,73,359,136,245),(12,444,222,331,115,378,164,279,35,428,193,305,74,371,135,233),(13,456,221,348,116,390,163,267,36,411,192,293,75,354,134,250),(14,439,220,336,88,402,162,284,37,423,191,310,76,366,133,238),(15,451,219,324,89,385,161,272,38,435,190,298,77,349,132,255),(16,463,218,341,90,397,160,289,39,418,189,315,78,361,131,243),(17,446,217,329,91,380,159,277,40,430,188,303,79,373,130,260),(18,458,216,346,92,392,158,265,41,413,187,291,80,356,129,248),(19,441,215,334,93,404,157,282,42,425,186,308,81,368,128,236),(20,453,214,322,94,387,156,270,43,408,185,296,82,351,127,253),(21,436,213,339,95,399,155,287,44,420,184,313,83,363,126,241),(22,448,212,327,96,382,154,275,45,432,183,301,84,375,125,258),(23,460,211,344,97,394,153,263,46,415,182,318,85,358,124,246),(24,443,210,332,98,406,152,280,47,427,181,306,86,370,123,234),(25,455,209,320,99,389,151,268,48,410,180,294,87,353,122,251),(26,438,208,337,100,401,150,285,49,422,179,311,59,365,121,239),(27,450,207,325,101,384,149,273,50,434,178,299,60,377,120,256),(28,462,206,342,102,396,148,290,51,417,177,316,61,360,119,244),(29,445,205,330,103,379,147,278,52,429,176,304,62,372,118,261)]])
44 conjugacy classes
| class | 1 | 2 | 4A | 4B | 8A | 8B | 8C | 8D | 16A | ··· | 16H | 29A | ··· | 29G | 58A | ··· | 58G | 116A | ··· | 116N |
| order | 1 | 2 | 4 | 4 | 8 | 8 | 8 | 8 | 16 | ··· | 16 | 29 | ··· | 29 | 58 | ··· | 58 | 116 | ··· | 116 |
| size | 1 | 1 | 1 | 1 | 29 | 29 | 29 | 29 | 29 | ··· | 29 | 4 | ··· | 4 | 4 | ··· | 4 | 4 | ··· | 4 |
44 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 4 | 4 | 4 |
| type | + | + | + | - | ||||
| image | C1 | C2 | C4 | C8 | C16 | C29⋊C4 | C29⋊C8 | C29⋊C16 |
| kernel | C29⋊C16 | C29⋊2C8 | C116 | C58 | C29 | C4 | C2 | C1 |
| # reps | 1 | 1 | 2 | 4 | 8 | 7 | 7 | 14 |
Matrix representation of C29⋊C16 ►in GL5(𝔽929)
| 1 | 0 | 0 | 0 | 0 |
| 0 | 928 | 1 | 0 | 0 |
| 0 | 928 | 0 | 1 | 0 |
| 0 | 928 | 0 | 0 | 1 |
| 0 | 436 | 323 | 606 | 492 |
| 101 | 0 | 0 | 0 | 0 |
| 0 | 793 | 502 | 536 | 456 |
| 0 | 222 | 424 | 804 | 697 |
| 0 | 781 | 510 | 645 | 521 |
| 0 | 139 | 586 | 91 | 925 |
G:=sub<GL(5,GF(929))| [1,0,0,0,0,0,928,928,928,436,0,1,0,0,323,0,0,1,0,606,0,0,0,1,492],[101,0,0,0,0,0,793,222,781,139,0,502,424,510,586,0,536,804,645,91,0,456,697,521,925] >;
C29⋊C16 in GAP, Magma, Sage, TeX
C_{29}\rtimes C_{16} % in TeX
G:=Group("C29:C16"); // GroupNames label
G:=SmallGroup(464,3);
// by ID
G=gap.SmallGroup(464,3);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-29,10,26,42,4804,5609]);
// Polycyclic
G:=Group<a,b|a^29=b^16=1,b*a*b^-1=a^17>;
// generators/relations
Export