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G = Q16×C29order 464 = 24·29

Direct product of C29 and Q16

direct product, metacyclic, nilpotent (class 3), monomial, 2-elementary

Aliases: Q16×C29, C8.C58, Q8.C58, C232.3C2, C58.16D4, C116.19C22, C4.3(C2×C58), C2.5(D4×C29), (Q8×C29).2C2, SmallGroup(464,27)

Series: Derived Chief Lower central Upper central

C1C4 — Q16×C29
C1C2C4C116Q8×C29 — Q16×C29
C1C2C4 — Q16×C29
C1C58C116 — Q16×C29

Generators and relations for Q16×C29
 G = < a,b,c | a29=b8=1, c2=b4, ab=ba, ac=ca, cbc-1=b-1 >

2C4
2C4
2C116
2C116

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

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

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

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

203 conjugacy classes

class 1  2 4A4B4C8A8B29A···29AB58A···58AB116A···116AB116AC···116CF232A···232BD
order124448829···2958···58116···116116···116232···232
size11244221···11···12···24···42···2

203 irreducible representations

dim1111112222
type++++-
imageC1C2C2C29C58C58D4Q16D4×C29Q16×C29
kernelQ16×C29C232Q8×C29Q16C8Q8C58C29C2C1
# reps112282856122856

Matrix representation of Q16×C29 in GL2(𝔽233) generated by

20
02
,
0148
159148
,
53137
5180
G:=sub<GL(2,GF(233))| [2,0,0,2],[0,159,148,148],[53,5,137,180] >;

Q16×C29 in GAP, Magma, Sage, TeX

Q_{16}\times C_{29}
% in TeX

G:=Group("Q16xC29");
// GroupNames label

G:=SmallGroup(464,27);
// by ID

G=gap.SmallGroup(464,27);
# by ID

G:=PCGroup([5,-2,-2,-29,-2,-2,1160,1181,1166,6963,3488,58]);
// Polycyclic

G:=Group<a,b,c|a^29=b^8=1,c^2=b^4,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

Export

Subgroup lattice of Q16×C29 in TeX

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