metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C29⋊2Q16, Q8.D29, C4.4D58, C58.10D4, C116.4C22, Dic58.2C2, C29⋊2C8.1C2, (Q8×C29).1C2, C2.7(C29⋊D4), SmallGroup(464,18)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C29⋊Q16
G = < a,b,c | a29=b8=1, c2=b4, bab-1=a-1, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C29⋊Q16
►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)
(1 407 80 378 31 436 93 349)(2 435 81 406 32 464 94 377)(3 434 82 405 33 463 95 376)(4 433 83 404 34 462 96 375)(5 432 84 403 35 461 97 374)(6 431 85 402 36 460 98 373)(7 430 86 401 37 459 99 372)(8 429 87 400 38 458 100 371)(9 428 59 399 39 457 101 370)(10 427 60 398 40 456 102 369)(11 426 61 397 41 455 103 368)(12 425 62 396 42 454 104 367)(13 424 63 395 43 453 105 366)(14 423 64 394 44 452 106 365)(15 422 65 393 45 451 107 364)(16 421 66 392 46 450 108 363)(17 420 67 391 47 449 109 362)(18 419 68 390 48 448 110 361)(19 418 69 389 49 447 111 360)(20 417 70 388 50 446 112 359)(21 416 71 387 51 445 113 358)(22 415 72 386 52 444 114 357)(23 414 73 385 53 443 115 356)(24 413 74 384 54 442 116 355)(25 412 75 383 55 441 88 354)(26 411 76 382 56 440 89 353)(27 410 77 381 57 439 90 352)(28 409 78 380 58 438 91 351)(29 408 79 379 30 437 92 350)(117 295 215 237 161 324 178 266)(118 294 216 236 162 323 179 265)(119 293 217 235 163 322 180 264)(120 292 218 234 164 321 181 263)(121 291 219 233 165 320 182 262)(122 319 220 261 166 348 183 290)(123 318 221 260 167 347 184 289)(124 317 222 259 168 346 185 288)(125 316 223 258 169 345 186 287)(126 315 224 257 170 344 187 286)(127 314 225 256 171 343 188 285)(128 313 226 255 172 342 189 284)(129 312 227 254 173 341 190 283)(130 311 228 253 174 340 191 282)(131 310 229 252 146 339 192 281)(132 309 230 251 147 338 193 280)(133 308 231 250 148 337 194 279)(134 307 232 249 149 336 195 278)(135 306 204 248 150 335 196 277)(136 305 205 247 151 334 197 276)(137 304 206 246 152 333 198 275)(138 303 207 245 153 332 199 274)(139 302 208 244 154 331 200 273)(140 301 209 243 155 330 201 272)(141 300 210 242 156 329 202 271)(142 299 211 241 157 328 203 270)(143 298 212 240 158 327 175 269)(144 297 213 239 159 326 176 268)(145 296 214 238 160 325 177 267)
(1 165 31 121)(2 166 32 122)(3 167 33 123)(4 168 34 124)(5 169 35 125)(6 170 36 126)(7 171 37 127)(8 172 38 128)(9 173 39 129)(10 174 40 130)(11 146 41 131)(12 147 42 132)(13 148 43 133)(14 149 44 134)(15 150 45 135)(16 151 46 136)(17 152 47 137)(18 153 48 138)(19 154 49 139)(20 155 50 140)(21 156 51 141)(22 157 52 142)(23 158 53 143)(24 159 54 144)(25 160 55 145)(26 161 56 117)(27 162 57 118)(28 163 58 119)(29 164 30 120)(59 227 101 190)(60 228 102 191)(61 229 103 192)(62 230 104 193)(63 231 105 194)(64 232 106 195)(65 204 107 196)(66 205 108 197)(67 206 109 198)(68 207 110 199)(69 208 111 200)(70 209 112 201)(71 210 113 202)(72 211 114 203)(73 212 115 175)(74 213 116 176)(75 214 88 177)(76 215 89 178)(77 216 90 179)(78 217 91 180)(79 218 92 181)(80 219 93 182)(81 220 94 183)(82 221 95 184)(83 222 96 185)(84 223 97 186)(85 224 98 187)(86 225 99 188)(87 226 100 189)(233 436 262 407)(234 437 263 408)(235 438 264 409)(236 439 265 410)(237 440 266 411)(238 441 267 412)(239 442 268 413)(240 443 269 414)(241 444 270 415)(242 445 271 416)(243 446 272 417)(244 447 273 418)(245 448 274 419)(246 449 275 420)(247 450 276 421)(248 451 277 422)(249 452 278 423)(250 453 279 424)(251 454 280 425)(252 455 281 426)(253 456 282 427)(254 457 283 428)(255 458 284 429)(256 459 285 430)(257 460 286 431)(258 461 287 432)(259 462 288 433)(260 463 289 434)(261 464 290 435)(291 349 320 378)(292 350 321 379)(293 351 322 380)(294 352 323 381)(295 353 324 382)(296 354 325 383)(297 355 326 384)(298 356 327 385)(299 357 328 386)(300 358 329 387)(301 359 330 388)(302 360 331 389)(303 361 332 390)(304 362 333 391)(305 363 334 392)(306 364 335 393)(307 365 336 394)(308 366 337 395)(309 367 338 396)(310 368 339 397)(311 369 340 398)(312 370 341 399)(313 371 342 400)(314 372 343 401)(315 373 344 402)(316 374 345 403)(317 375 346 404)(318 376 347 405)(319 377 348 406)
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), (1,407,80,378,31,436,93,349)(2,435,81,406,32,464,94,377)(3,434,82,405,33,463,95,376)(4,433,83,404,34,462,96,375)(5,432,84,403,35,461,97,374)(6,431,85,402,36,460,98,373)(7,430,86,401,37,459,99,372)(8,429,87,400,38,458,100,371)(9,428,59,399,39,457,101,370)(10,427,60,398,40,456,102,369)(11,426,61,397,41,455,103,368)(12,425,62,396,42,454,104,367)(13,424,63,395,43,453,105,366)(14,423,64,394,44,452,106,365)(15,422,65,393,45,451,107,364)(16,421,66,392,46,450,108,363)(17,420,67,391,47,449,109,362)(18,419,68,390,48,448,110,361)(19,418,69,389,49,447,111,360)(20,417,70,388,50,446,112,359)(21,416,71,387,51,445,113,358)(22,415,72,386,52,444,114,357)(23,414,73,385,53,443,115,356)(24,413,74,384,54,442,116,355)(25,412,75,383,55,441,88,354)(26,411,76,382,56,440,89,353)(27,410,77,381,57,439,90,352)(28,409,78,380,58,438,91,351)(29,408,79,379,30,437,92,350)(117,295,215,237,161,324,178,266)(118,294,216,236,162,323,179,265)(119,293,217,235,163,322,180,264)(120,292,218,234,164,321,181,263)(121,291,219,233,165,320,182,262)(122,319,220,261,166,348,183,290)(123,318,221,260,167,347,184,289)(124,317,222,259,168,346,185,288)(125,316,223,258,169,345,186,287)(126,315,224,257,170,344,187,286)(127,314,225,256,171,343,188,285)(128,313,226,255,172,342,189,284)(129,312,227,254,173,341,190,283)(130,311,228,253,174,340,191,282)(131,310,229,252,146,339,192,281)(132,309,230,251,147,338,193,280)(133,308,231,250,148,337,194,279)(134,307,232,249,149,336,195,278)(135,306,204,248,150,335,196,277)(136,305,205,247,151,334,197,276)(137,304,206,246,152,333,198,275)(138,303,207,245,153,332,199,274)(139,302,208,244,154,331,200,273)(140,301,209,243,155,330,201,272)(141,300,210,242,156,329,202,271)(142,299,211,241,157,328,203,270)(143,298,212,240,158,327,175,269)(144,297,213,239,159,326,176,268)(145,296,214,238,160,325,177,267), (1,165,31,121)(2,166,32,122)(3,167,33,123)(4,168,34,124)(5,169,35,125)(6,170,36,126)(7,171,37,127)(8,172,38,128)(9,173,39,129)(10,174,40,130)(11,146,41,131)(12,147,42,132)(13,148,43,133)(14,149,44,134)(15,150,45,135)(16,151,46,136)(17,152,47,137)(18,153,48,138)(19,154,49,139)(20,155,50,140)(21,156,51,141)(22,157,52,142)(23,158,53,143)(24,159,54,144)(25,160,55,145)(26,161,56,117)(27,162,57,118)(28,163,58,119)(29,164,30,120)(59,227,101,190)(60,228,102,191)(61,229,103,192)(62,230,104,193)(63,231,105,194)(64,232,106,195)(65,204,107,196)(66,205,108,197)(67,206,109,198)(68,207,110,199)(69,208,111,200)(70,209,112,201)(71,210,113,202)(72,211,114,203)(73,212,115,175)(74,213,116,176)(75,214,88,177)(76,215,89,178)(77,216,90,179)(78,217,91,180)(79,218,92,181)(80,219,93,182)(81,220,94,183)(82,221,95,184)(83,222,96,185)(84,223,97,186)(85,224,98,187)(86,225,99,188)(87,226,100,189)(233,436,262,407)(234,437,263,408)(235,438,264,409)(236,439,265,410)(237,440,266,411)(238,441,267,412)(239,442,268,413)(240,443,269,414)(241,444,270,415)(242,445,271,416)(243,446,272,417)(244,447,273,418)(245,448,274,419)(246,449,275,420)(247,450,276,421)(248,451,277,422)(249,452,278,423)(250,453,279,424)(251,454,280,425)(252,455,281,426)(253,456,282,427)(254,457,283,428)(255,458,284,429)(256,459,285,430)(257,460,286,431)(258,461,287,432)(259,462,288,433)(260,463,289,434)(261,464,290,435)(291,349,320,378)(292,350,321,379)(293,351,322,380)(294,352,323,381)(295,353,324,382)(296,354,325,383)(297,355,326,384)(298,356,327,385)(299,357,328,386)(300,358,329,387)(301,359,330,388)(302,360,331,389)(303,361,332,390)(304,362,333,391)(305,363,334,392)(306,364,335,393)(307,365,336,394)(308,366,337,395)(309,367,338,396)(310,368,339,397)(311,369,340,398)(312,370,341,399)(313,371,342,400)(314,372,343,401)(315,373,344,402)(316,374,345,403)(317,375,346,404)(318,376,347,405)(319,377,348,406)>;
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), (1,407,80,378,31,436,93,349)(2,435,81,406,32,464,94,377)(3,434,82,405,33,463,95,376)(4,433,83,404,34,462,96,375)(5,432,84,403,35,461,97,374)(6,431,85,402,36,460,98,373)(7,430,86,401,37,459,99,372)(8,429,87,400,38,458,100,371)(9,428,59,399,39,457,101,370)(10,427,60,398,40,456,102,369)(11,426,61,397,41,455,103,368)(12,425,62,396,42,454,104,367)(13,424,63,395,43,453,105,366)(14,423,64,394,44,452,106,365)(15,422,65,393,45,451,107,364)(16,421,66,392,46,450,108,363)(17,420,67,391,47,449,109,362)(18,419,68,390,48,448,110,361)(19,418,69,389,49,447,111,360)(20,417,70,388,50,446,112,359)(21,416,71,387,51,445,113,358)(22,415,72,386,52,444,114,357)(23,414,73,385,53,443,115,356)(24,413,74,384,54,442,116,355)(25,412,75,383,55,441,88,354)(26,411,76,382,56,440,89,353)(27,410,77,381,57,439,90,352)(28,409,78,380,58,438,91,351)(29,408,79,379,30,437,92,350)(117,295,215,237,161,324,178,266)(118,294,216,236,162,323,179,265)(119,293,217,235,163,322,180,264)(120,292,218,234,164,321,181,263)(121,291,219,233,165,320,182,262)(122,319,220,261,166,348,183,290)(123,318,221,260,167,347,184,289)(124,317,222,259,168,346,185,288)(125,316,223,258,169,345,186,287)(126,315,224,257,170,344,187,286)(127,314,225,256,171,343,188,285)(128,313,226,255,172,342,189,284)(129,312,227,254,173,341,190,283)(130,311,228,253,174,340,191,282)(131,310,229,252,146,339,192,281)(132,309,230,251,147,338,193,280)(133,308,231,250,148,337,194,279)(134,307,232,249,149,336,195,278)(135,306,204,248,150,335,196,277)(136,305,205,247,151,334,197,276)(137,304,206,246,152,333,198,275)(138,303,207,245,153,332,199,274)(139,302,208,244,154,331,200,273)(140,301,209,243,155,330,201,272)(141,300,210,242,156,329,202,271)(142,299,211,241,157,328,203,270)(143,298,212,240,158,327,175,269)(144,297,213,239,159,326,176,268)(145,296,214,238,160,325,177,267), (1,165,31,121)(2,166,32,122)(3,167,33,123)(4,168,34,124)(5,169,35,125)(6,170,36,126)(7,171,37,127)(8,172,38,128)(9,173,39,129)(10,174,40,130)(11,146,41,131)(12,147,42,132)(13,148,43,133)(14,149,44,134)(15,150,45,135)(16,151,46,136)(17,152,47,137)(18,153,48,138)(19,154,49,139)(20,155,50,140)(21,156,51,141)(22,157,52,142)(23,158,53,143)(24,159,54,144)(25,160,55,145)(26,161,56,117)(27,162,57,118)(28,163,58,119)(29,164,30,120)(59,227,101,190)(60,228,102,191)(61,229,103,192)(62,230,104,193)(63,231,105,194)(64,232,106,195)(65,204,107,196)(66,205,108,197)(67,206,109,198)(68,207,110,199)(69,208,111,200)(70,209,112,201)(71,210,113,202)(72,211,114,203)(73,212,115,175)(74,213,116,176)(75,214,88,177)(76,215,89,178)(77,216,90,179)(78,217,91,180)(79,218,92,181)(80,219,93,182)(81,220,94,183)(82,221,95,184)(83,222,96,185)(84,223,97,186)(85,224,98,187)(86,225,99,188)(87,226,100,189)(233,436,262,407)(234,437,263,408)(235,438,264,409)(236,439,265,410)(237,440,266,411)(238,441,267,412)(239,442,268,413)(240,443,269,414)(241,444,270,415)(242,445,271,416)(243,446,272,417)(244,447,273,418)(245,448,274,419)(246,449,275,420)(247,450,276,421)(248,451,277,422)(249,452,278,423)(250,453,279,424)(251,454,280,425)(252,455,281,426)(253,456,282,427)(254,457,283,428)(255,458,284,429)(256,459,285,430)(257,460,286,431)(258,461,287,432)(259,462,288,433)(260,463,289,434)(261,464,290,435)(291,349,320,378)(292,350,321,379)(293,351,322,380)(294,352,323,381)(295,353,324,382)(296,354,325,383)(297,355,326,384)(298,356,327,385)(299,357,328,386)(300,358,329,387)(301,359,330,388)(302,360,331,389)(303,361,332,390)(304,362,333,391)(305,363,334,392)(306,364,335,393)(307,365,336,394)(308,366,337,395)(309,367,338,396)(310,368,339,397)(311,369,340,398)(312,370,341,399)(313,371,342,400)(314,372,343,401)(315,373,344,402)(316,374,345,403)(317,375,346,404)(318,376,347,405)(319,377,348,406) );
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)], [(1,407,80,378,31,436,93,349),(2,435,81,406,32,464,94,377),(3,434,82,405,33,463,95,376),(4,433,83,404,34,462,96,375),(5,432,84,403,35,461,97,374),(6,431,85,402,36,460,98,373),(7,430,86,401,37,459,99,372),(8,429,87,400,38,458,100,371),(9,428,59,399,39,457,101,370),(10,427,60,398,40,456,102,369),(11,426,61,397,41,455,103,368),(12,425,62,396,42,454,104,367),(13,424,63,395,43,453,105,366),(14,423,64,394,44,452,106,365),(15,422,65,393,45,451,107,364),(16,421,66,392,46,450,108,363),(17,420,67,391,47,449,109,362),(18,419,68,390,48,448,110,361),(19,418,69,389,49,447,111,360),(20,417,70,388,50,446,112,359),(21,416,71,387,51,445,113,358),(22,415,72,386,52,444,114,357),(23,414,73,385,53,443,115,356),(24,413,74,384,54,442,116,355),(25,412,75,383,55,441,88,354),(26,411,76,382,56,440,89,353),(27,410,77,381,57,439,90,352),(28,409,78,380,58,438,91,351),(29,408,79,379,30,437,92,350),(117,295,215,237,161,324,178,266),(118,294,216,236,162,323,179,265),(119,293,217,235,163,322,180,264),(120,292,218,234,164,321,181,263),(121,291,219,233,165,320,182,262),(122,319,220,261,166,348,183,290),(123,318,221,260,167,347,184,289),(124,317,222,259,168,346,185,288),(125,316,223,258,169,345,186,287),(126,315,224,257,170,344,187,286),(127,314,225,256,171,343,188,285),(128,313,226,255,172,342,189,284),(129,312,227,254,173,341,190,283),(130,311,228,253,174,340,191,282),(131,310,229,252,146,339,192,281),(132,309,230,251,147,338,193,280),(133,308,231,250,148,337,194,279),(134,307,232,249,149,336,195,278),(135,306,204,248,150,335,196,277),(136,305,205,247,151,334,197,276),(137,304,206,246,152,333,198,275),(138,303,207,245,153,332,199,274),(139,302,208,244,154,331,200,273),(140,301,209,243,155,330,201,272),(141,300,210,242,156,329,202,271),(142,299,211,241,157,328,203,270),(143,298,212,240,158,327,175,269),(144,297,213,239,159,326,176,268),(145,296,214,238,160,325,177,267)], [(1,165,31,121),(2,166,32,122),(3,167,33,123),(4,168,34,124),(5,169,35,125),(6,170,36,126),(7,171,37,127),(8,172,38,128),(9,173,39,129),(10,174,40,130),(11,146,41,131),(12,147,42,132),(13,148,43,133),(14,149,44,134),(15,150,45,135),(16,151,46,136),(17,152,47,137),(18,153,48,138),(19,154,49,139),(20,155,50,140),(21,156,51,141),(22,157,52,142),(23,158,53,143),(24,159,54,144),(25,160,55,145),(26,161,56,117),(27,162,57,118),(28,163,58,119),(29,164,30,120),(59,227,101,190),(60,228,102,191),(61,229,103,192),(62,230,104,193),(63,231,105,194),(64,232,106,195),(65,204,107,196),(66,205,108,197),(67,206,109,198),(68,207,110,199),(69,208,111,200),(70,209,112,201),(71,210,113,202),(72,211,114,203),(73,212,115,175),(74,213,116,176),(75,214,88,177),(76,215,89,178),(77,216,90,179),(78,217,91,180),(79,218,92,181),(80,219,93,182),(81,220,94,183),(82,221,95,184),(83,222,96,185),(84,223,97,186),(85,224,98,187),(86,225,99,188),(87,226,100,189),(233,436,262,407),(234,437,263,408),(235,438,264,409),(236,439,265,410),(237,440,266,411),(238,441,267,412),(239,442,268,413),(240,443,269,414),(241,444,270,415),(242,445,271,416),(243,446,272,417),(244,447,273,418),(245,448,274,419),(246,449,275,420),(247,450,276,421),(248,451,277,422),(249,452,278,423),(250,453,279,424),(251,454,280,425),(252,455,281,426),(253,456,282,427),(254,457,283,428),(255,458,284,429),(256,459,285,430),(257,460,286,431),(258,461,287,432),(259,462,288,433),(260,463,289,434),(261,464,290,435),(291,349,320,378),(292,350,321,379),(293,351,322,380),(294,352,323,381),(295,353,324,382),(296,354,325,383),(297,355,326,384),(298,356,327,385),(299,357,328,386),(300,358,329,387),(301,359,330,388),(302,360,331,389),(303,361,332,390),(304,362,333,391),(305,363,334,392),(306,364,335,393),(307,365,336,394),(308,366,337,395),(309,367,338,396),(310,368,339,397),(311,369,340,398),(312,370,341,399),(313,371,342,400),(314,372,343,401),(315,373,344,402),(316,374,345,403),(317,375,346,404),(318,376,347,405),(319,377,348,406)]])
77 conjugacy classes
| class | 1 | 2 | 4A | 4B | 4C | 8A | 8B | 29A | ··· | 29N | 58A | ··· | 58N | 116A | ··· | 116AP |
| order | 1 | 2 | 4 | 4 | 4 | 8 | 8 | 29 | ··· | 29 | 58 | ··· | 58 | 116 | ··· | 116 |
| size | 1 | 1 | 2 | 4 | 116 | 58 | 58 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
77 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | - | + | + | - | |
| image | C1 | C2 | C2 | C2 | D4 | Q16 | D29 | D58 | C29⋊D4 | C29⋊Q16 |
| kernel | C29⋊Q16 | C29⋊2C8 | Dic58 | Q8×C29 | C58 | C29 | Q8 | C4 | C2 | C1 |
| # reps | 1 | 1 | 1 | 1 | 1 | 2 | 14 | 14 | 28 | 14 |
Matrix representation of C29⋊Q16 ►in GL4(𝔽233) generated by
| 0 | 1 | 0 | 0 |
| 232 | 203 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 14 | 141 | 0 | 0 |
| 187 | 219 | 0 | 0 |
| 0 | 0 | 0 | 195 |
| 0 | 0 | 92 | 148 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 95 | 28 |
| 0 | 0 | 127 | 138 |
G:=sub<GL(4,GF(233))| [0,232,0,0,1,203,0,0,0,0,1,0,0,0,0,1],[14,187,0,0,141,219,0,0,0,0,0,92,0,0,195,148],[1,0,0,0,0,1,0,0,0,0,95,127,0,0,28,138] >;
C29⋊Q16 in GAP, Magma, Sage, TeX
C_{29}\rtimes Q_{16} % in TeX
G:=Group("C29:Q16"); // GroupNames label
G:=SmallGroup(464,18);
// by ID
G=gap.SmallGroup(464,18);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-29,40,61,46,182,97,42,11204]);
// Polycyclic
G:=Group<a,b,c|a^29=b^8=1,c^2=b^4,b*a*b^-1=a^-1,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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