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G = C292C16order 464 = 24·29

The semidirect product of C29 and C16 acting via C16/C8=C2

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

Aliases: C292C16, C58.2C8, C8.2D29, C232.2C2, C116.5C4, C4.2Dic29, C2.(C292C8), SmallGroup(464,1)

Series: Derived Chief Lower central Upper central

C1C29 — C292C16
C1C29C58C116C232 — C292C16
C29 — C292C16
C1C8

Generators and relations for C292C16
 G = < a,b | a29=b16=1, bab-1=a-1 >

29C16

Smallest permutation representation of C292C16
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)
(1 436 226 320 98 378 174 262 42 407 203 291 59 349 142 233)(2 464 227 348 99 406 146 290 43 435 175 319 60 377 143 261)(3 463 228 347 100 405 147 289 44 434 176 318 61 376 144 260)(4 462 229 346 101 404 148 288 45 433 177 317 62 375 145 259)(5 461 230 345 102 403 149 287 46 432 178 316 63 374 117 258)(6 460 231 344 103 402 150 286 47 431 179 315 64 373 118 257)(7 459 232 343 104 401 151 285 48 430 180 314 65 372 119 256)(8 458 204 342 105 400 152 284 49 429 181 313 66 371 120 255)(9 457 205 341 106 399 153 283 50 428 182 312 67 370 121 254)(10 456 206 340 107 398 154 282 51 427 183 311 68 369 122 253)(11 455 207 339 108 397 155 281 52 426 184 310 69 368 123 252)(12 454 208 338 109 396 156 280 53 425 185 309 70 367 124 251)(13 453 209 337 110 395 157 279 54 424 186 308 71 366 125 250)(14 452 210 336 111 394 158 278 55 423 187 307 72 365 126 249)(15 451 211 335 112 393 159 277 56 422 188 306 73 364 127 248)(16 450 212 334 113 392 160 276 57 421 189 305 74 363 128 247)(17 449 213 333 114 391 161 275 58 420 190 304 75 362 129 246)(18 448 214 332 115 390 162 274 30 419 191 303 76 361 130 245)(19 447 215 331 116 389 163 273 31 418 192 302 77 360 131 244)(20 446 216 330 88 388 164 272 32 417 193 301 78 359 132 243)(21 445 217 329 89 387 165 271 33 416 194 300 79 358 133 242)(22 444 218 328 90 386 166 270 34 415 195 299 80 357 134 241)(23 443 219 327 91 385 167 269 35 414 196 298 81 356 135 240)(24 442 220 326 92 384 168 268 36 413 197 297 82 355 136 239)(25 441 221 325 93 383 169 267 37 412 198 296 83 354 137 238)(26 440 222 324 94 382 170 266 38 411 199 295 84 353 138 237)(27 439 223 323 95 381 171 265 39 410 200 294 85 352 139 236)(28 438 224 322 96 380 172 264 40 409 201 293 86 351 140 235)(29 437 225 321 97 379 173 263 41 408 202 292 87 350 141 234)

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

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

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

128 conjugacy classes

class 1  2 4A4B8A8B8C8D16A···16H29A···29N58A···58N116A···116AB232A···232BD
order1244888816···1629···2958···58116···116232···232
size1111111129···292···22···22···22···2

128 irreducible representations

dim111112222
type+++-
imageC1C2C4C8C16D29Dic29C292C8C292C16
kernelC292C16C232C116C58C29C8C4C2C1
# reps1124814142856

Matrix representation of C292C16 in GL3(𝔽929) generated by

100
09281
0727201
,
4600
058646
0391343
G:=sub<GL(3,GF(929))| [1,0,0,0,928,727,0,1,201],[46,0,0,0,586,391,0,46,343] >;

C292C16 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

Subgroup lattice of C292C16 in TeX

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