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G = C29⋊C16order 464 = 24·29

The semidirect product of C29 and C16 acting via C16/C4=C4

metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary

Aliases: C29⋊C16, C58.C8, C116.2C4, C2.(C29⋊C8), C4.2(C29⋊C4), C292C8.2C2, SmallGroup(464,3)

Series: Derived Chief Lower central Upper central

C1C29 — C29⋊C16
C1C29C58C116C292C8 — C29⋊C16
C29 — C29⋊C16
C1C4

Generators and relations for C29⋊C16
 G = < a,b | a29=b16=1, bab-1=a17 >

29C8
29C16

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

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

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

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

44 conjugacy classes

class 1  2 4A4B8A8B8C8D16A···16H29A···29G58A···58G116A···116N
order1244888816···1629···2958···58116···116
size11112929292929···294···44···44···4

44 irreducible representations

dim11111444
type+++-
imageC1C2C4C8C16C29⋊C4C29⋊C8C29⋊C16
kernelC29⋊C16C292C8C116C58C29C4C2C1
# reps112487714

Matrix representation of C29⋊C16 in GL5(𝔽929)

10000
0928100
0928010
0928001
0436323606492
,
1010000
0793502536456
0222424804697
0781510645521
013958691925

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

Subgroup lattice of C29⋊C16 in TeX

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