metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C31⋊2Q16, Q8.D31, C4.4D62, C62.10D4, C124.4C22, Dic62.2C2, C31⋊C8.C2, (Q8×C31).1C2, C2.7(C31⋊D4), SmallGroup(496,17)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C31⋊Q16
G = < a,b,c | a31=b8=1, c2=b4, bab-1=a-1, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C31⋊Q16
►Regular action on 496 points
Generators in S496
(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)(435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465)(466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496)
(1 435 82 404 34 466 111 373)(2 465 83 434 35 496 112 403)(3 464 84 433 36 495 113 402)(4 463 85 432 37 494 114 401)(5 462 86 431 38 493 115 400)(6 461 87 430 39 492 116 399)(7 460 88 429 40 491 117 398)(8 459 89 428 41 490 118 397)(9 458 90 427 42 489 119 396)(10 457 91 426 43 488 120 395)(11 456 92 425 44 487 121 394)(12 455 93 424 45 486 122 393)(13 454 63 423 46 485 123 392)(14 453 64 422 47 484 124 391)(15 452 65 421 48 483 94 390)(16 451 66 420 49 482 95 389)(17 450 67 419 50 481 96 388)(18 449 68 418 51 480 97 387)(19 448 69 417 52 479 98 386)(20 447 70 416 53 478 99 385)(21 446 71 415 54 477 100 384)(22 445 72 414 55 476 101 383)(23 444 73 413 56 475 102 382)(24 443 74 412 57 474 103 381)(25 442 75 411 58 473 104 380)(26 441 76 410 59 472 105 379)(27 440 77 409 60 471 106 378)(28 439 78 408 61 470 107 377)(29 438 79 407 62 469 108 376)(30 437 80 406 32 468 109 375)(31 436 81 405 33 467 110 374)(125 324 232 262 171 355 216 293)(126 323 233 261 172 354 217 292)(127 322 234 260 173 353 187 291)(128 321 235 259 174 352 188 290)(129 320 236 258 175 351 189 289)(130 319 237 257 176 350 190 288)(131 318 238 256 177 349 191 287)(132 317 239 255 178 348 192 286)(133 316 240 254 179 347 193 285)(134 315 241 253 180 346 194 284)(135 314 242 252 181 345 195 283)(136 313 243 251 182 344 196 282)(137 312 244 250 183 343 197 281)(138 311 245 249 184 342 198 280)(139 341 246 279 185 372 199 310)(140 340 247 278 186 371 200 309)(141 339 248 277 156 370 201 308)(142 338 218 276 157 369 202 307)(143 337 219 275 158 368 203 306)(144 336 220 274 159 367 204 305)(145 335 221 273 160 366 205 304)(146 334 222 272 161 365 206 303)(147 333 223 271 162 364 207 302)(148 332 224 270 163 363 208 301)(149 331 225 269 164 362 209 300)(150 330 226 268 165 361 210 299)(151 329 227 267 166 360 211 298)(152 328 228 266 167 359 212 297)(153 327 229 265 168 358 213 296)(154 326 230 264 169 357 214 295)(155 325 231 263 170 356 215 294)
(1 184 34 138)(2 185 35 139)(3 186 36 140)(4 156 37 141)(5 157 38 142)(6 158 39 143)(7 159 40 144)(8 160 41 145)(9 161 42 146)(10 162 43 147)(11 163 44 148)(12 164 45 149)(13 165 46 150)(14 166 47 151)(15 167 48 152)(16 168 49 153)(17 169 50 154)(18 170 51 155)(19 171 52 125)(20 172 53 126)(21 173 54 127)(22 174 55 128)(23 175 56 129)(24 176 57 130)(25 177 58 131)(26 178 59 132)(27 179 60 133)(28 180 61 134)(29 181 62 135)(30 182 32 136)(31 183 33 137)(63 226 123 210)(64 227 124 211)(65 228 94 212)(66 229 95 213)(67 230 96 214)(68 231 97 215)(69 232 98 216)(70 233 99 217)(71 234 100 187)(72 235 101 188)(73 236 102 189)(74 237 103 190)(75 238 104 191)(76 239 105 192)(77 240 106 193)(78 241 107 194)(79 242 108 195)(80 243 109 196)(81 244 110 197)(82 245 111 198)(83 246 112 199)(84 247 113 200)(85 248 114 201)(86 218 115 202)(87 219 116 203)(88 220 117 204)(89 221 118 205)(90 222 119 206)(91 223 120 207)(92 224 121 208)(93 225 122 209)(249 466 280 435)(250 467 281 436)(251 468 282 437)(252 469 283 438)(253 470 284 439)(254 471 285 440)(255 472 286 441)(256 473 287 442)(257 474 288 443)(258 475 289 444)(259 476 290 445)(260 477 291 446)(261 478 292 447)(262 479 293 448)(263 480 294 449)(264 481 295 450)(265 482 296 451)(266 483 297 452)(267 484 298 453)(268 485 299 454)(269 486 300 455)(270 487 301 456)(271 488 302 457)(272 489 303 458)(273 490 304 459)(274 491 305 460)(275 492 306 461)(276 493 307 462)(277 494 308 463)(278 495 309 464)(279 496 310 465)(311 373 342 404)(312 374 343 405)(313 375 344 406)(314 376 345 407)(315 377 346 408)(316 378 347 409)(317 379 348 410)(318 380 349 411)(319 381 350 412)(320 382 351 413)(321 383 352 414)(322 384 353 415)(323 385 354 416)(324 386 355 417)(325 387 356 418)(326 388 357 419)(327 389 358 420)(328 390 359 421)(329 391 360 422)(330 392 361 423)(331 393 362 424)(332 394 363 425)(333 395 364 426)(334 396 365 427)(335 397 366 428)(336 398 367 429)(337 399 368 430)(338 400 369 431)(339 401 370 432)(340 402 371 433)(341 403 372 434)
G:=sub<Sym(496)| (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)(435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465)(466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496), (1,435,82,404,34,466,111,373)(2,465,83,434,35,496,112,403)(3,464,84,433,36,495,113,402)(4,463,85,432,37,494,114,401)(5,462,86,431,38,493,115,400)(6,461,87,430,39,492,116,399)(7,460,88,429,40,491,117,398)(8,459,89,428,41,490,118,397)(9,458,90,427,42,489,119,396)(10,457,91,426,43,488,120,395)(11,456,92,425,44,487,121,394)(12,455,93,424,45,486,122,393)(13,454,63,423,46,485,123,392)(14,453,64,422,47,484,124,391)(15,452,65,421,48,483,94,390)(16,451,66,420,49,482,95,389)(17,450,67,419,50,481,96,388)(18,449,68,418,51,480,97,387)(19,448,69,417,52,479,98,386)(20,447,70,416,53,478,99,385)(21,446,71,415,54,477,100,384)(22,445,72,414,55,476,101,383)(23,444,73,413,56,475,102,382)(24,443,74,412,57,474,103,381)(25,442,75,411,58,473,104,380)(26,441,76,410,59,472,105,379)(27,440,77,409,60,471,106,378)(28,439,78,408,61,470,107,377)(29,438,79,407,62,469,108,376)(30,437,80,406,32,468,109,375)(31,436,81,405,33,467,110,374)(125,324,232,262,171,355,216,293)(126,323,233,261,172,354,217,292)(127,322,234,260,173,353,187,291)(128,321,235,259,174,352,188,290)(129,320,236,258,175,351,189,289)(130,319,237,257,176,350,190,288)(131,318,238,256,177,349,191,287)(132,317,239,255,178,348,192,286)(133,316,240,254,179,347,193,285)(134,315,241,253,180,346,194,284)(135,314,242,252,181,345,195,283)(136,313,243,251,182,344,196,282)(137,312,244,250,183,343,197,281)(138,311,245,249,184,342,198,280)(139,341,246,279,185,372,199,310)(140,340,247,278,186,371,200,309)(141,339,248,277,156,370,201,308)(142,338,218,276,157,369,202,307)(143,337,219,275,158,368,203,306)(144,336,220,274,159,367,204,305)(145,335,221,273,160,366,205,304)(146,334,222,272,161,365,206,303)(147,333,223,271,162,364,207,302)(148,332,224,270,163,363,208,301)(149,331,225,269,164,362,209,300)(150,330,226,268,165,361,210,299)(151,329,227,267,166,360,211,298)(152,328,228,266,167,359,212,297)(153,327,229,265,168,358,213,296)(154,326,230,264,169,357,214,295)(155,325,231,263,170,356,215,294), (1,184,34,138)(2,185,35,139)(3,186,36,140)(4,156,37,141)(5,157,38,142)(6,158,39,143)(7,159,40,144)(8,160,41,145)(9,161,42,146)(10,162,43,147)(11,163,44,148)(12,164,45,149)(13,165,46,150)(14,166,47,151)(15,167,48,152)(16,168,49,153)(17,169,50,154)(18,170,51,155)(19,171,52,125)(20,172,53,126)(21,173,54,127)(22,174,55,128)(23,175,56,129)(24,176,57,130)(25,177,58,131)(26,178,59,132)(27,179,60,133)(28,180,61,134)(29,181,62,135)(30,182,32,136)(31,183,33,137)(63,226,123,210)(64,227,124,211)(65,228,94,212)(66,229,95,213)(67,230,96,214)(68,231,97,215)(69,232,98,216)(70,233,99,217)(71,234,100,187)(72,235,101,188)(73,236,102,189)(74,237,103,190)(75,238,104,191)(76,239,105,192)(77,240,106,193)(78,241,107,194)(79,242,108,195)(80,243,109,196)(81,244,110,197)(82,245,111,198)(83,246,112,199)(84,247,113,200)(85,248,114,201)(86,218,115,202)(87,219,116,203)(88,220,117,204)(89,221,118,205)(90,222,119,206)(91,223,120,207)(92,224,121,208)(93,225,122,209)(249,466,280,435)(250,467,281,436)(251,468,282,437)(252,469,283,438)(253,470,284,439)(254,471,285,440)(255,472,286,441)(256,473,287,442)(257,474,288,443)(258,475,289,444)(259,476,290,445)(260,477,291,446)(261,478,292,447)(262,479,293,448)(263,480,294,449)(264,481,295,450)(265,482,296,451)(266,483,297,452)(267,484,298,453)(268,485,299,454)(269,486,300,455)(270,487,301,456)(271,488,302,457)(272,489,303,458)(273,490,304,459)(274,491,305,460)(275,492,306,461)(276,493,307,462)(277,494,308,463)(278,495,309,464)(279,496,310,465)(311,373,342,404)(312,374,343,405)(313,375,344,406)(314,376,345,407)(315,377,346,408)(316,378,347,409)(317,379,348,410)(318,380,349,411)(319,381,350,412)(320,382,351,413)(321,383,352,414)(322,384,353,415)(323,385,354,416)(324,386,355,417)(325,387,356,418)(326,388,357,419)(327,389,358,420)(328,390,359,421)(329,391,360,422)(330,392,361,423)(331,393,362,424)(332,394,363,425)(333,395,364,426)(334,396,365,427)(335,397,366,428)(336,398,367,429)(337,399,368,430)(338,400,369,431)(339,401,370,432)(340,402,371,433)(341,403,372,434)>;
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)(435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465)(466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496), (1,435,82,404,34,466,111,373)(2,465,83,434,35,496,112,403)(3,464,84,433,36,495,113,402)(4,463,85,432,37,494,114,401)(5,462,86,431,38,493,115,400)(6,461,87,430,39,492,116,399)(7,460,88,429,40,491,117,398)(8,459,89,428,41,490,118,397)(9,458,90,427,42,489,119,396)(10,457,91,426,43,488,120,395)(11,456,92,425,44,487,121,394)(12,455,93,424,45,486,122,393)(13,454,63,423,46,485,123,392)(14,453,64,422,47,484,124,391)(15,452,65,421,48,483,94,390)(16,451,66,420,49,482,95,389)(17,450,67,419,50,481,96,388)(18,449,68,418,51,480,97,387)(19,448,69,417,52,479,98,386)(20,447,70,416,53,478,99,385)(21,446,71,415,54,477,100,384)(22,445,72,414,55,476,101,383)(23,444,73,413,56,475,102,382)(24,443,74,412,57,474,103,381)(25,442,75,411,58,473,104,380)(26,441,76,410,59,472,105,379)(27,440,77,409,60,471,106,378)(28,439,78,408,61,470,107,377)(29,438,79,407,62,469,108,376)(30,437,80,406,32,468,109,375)(31,436,81,405,33,467,110,374)(125,324,232,262,171,355,216,293)(126,323,233,261,172,354,217,292)(127,322,234,260,173,353,187,291)(128,321,235,259,174,352,188,290)(129,320,236,258,175,351,189,289)(130,319,237,257,176,350,190,288)(131,318,238,256,177,349,191,287)(132,317,239,255,178,348,192,286)(133,316,240,254,179,347,193,285)(134,315,241,253,180,346,194,284)(135,314,242,252,181,345,195,283)(136,313,243,251,182,344,196,282)(137,312,244,250,183,343,197,281)(138,311,245,249,184,342,198,280)(139,341,246,279,185,372,199,310)(140,340,247,278,186,371,200,309)(141,339,248,277,156,370,201,308)(142,338,218,276,157,369,202,307)(143,337,219,275,158,368,203,306)(144,336,220,274,159,367,204,305)(145,335,221,273,160,366,205,304)(146,334,222,272,161,365,206,303)(147,333,223,271,162,364,207,302)(148,332,224,270,163,363,208,301)(149,331,225,269,164,362,209,300)(150,330,226,268,165,361,210,299)(151,329,227,267,166,360,211,298)(152,328,228,266,167,359,212,297)(153,327,229,265,168,358,213,296)(154,326,230,264,169,357,214,295)(155,325,231,263,170,356,215,294), (1,184,34,138)(2,185,35,139)(3,186,36,140)(4,156,37,141)(5,157,38,142)(6,158,39,143)(7,159,40,144)(8,160,41,145)(9,161,42,146)(10,162,43,147)(11,163,44,148)(12,164,45,149)(13,165,46,150)(14,166,47,151)(15,167,48,152)(16,168,49,153)(17,169,50,154)(18,170,51,155)(19,171,52,125)(20,172,53,126)(21,173,54,127)(22,174,55,128)(23,175,56,129)(24,176,57,130)(25,177,58,131)(26,178,59,132)(27,179,60,133)(28,180,61,134)(29,181,62,135)(30,182,32,136)(31,183,33,137)(63,226,123,210)(64,227,124,211)(65,228,94,212)(66,229,95,213)(67,230,96,214)(68,231,97,215)(69,232,98,216)(70,233,99,217)(71,234,100,187)(72,235,101,188)(73,236,102,189)(74,237,103,190)(75,238,104,191)(76,239,105,192)(77,240,106,193)(78,241,107,194)(79,242,108,195)(80,243,109,196)(81,244,110,197)(82,245,111,198)(83,246,112,199)(84,247,113,200)(85,248,114,201)(86,218,115,202)(87,219,116,203)(88,220,117,204)(89,221,118,205)(90,222,119,206)(91,223,120,207)(92,224,121,208)(93,225,122,209)(249,466,280,435)(250,467,281,436)(251,468,282,437)(252,469,283,438)(253,470,284,439)(254,471,285,440)(255,472,286,441)(256,473,287,442)(257,474,288,443)(258,475,289,444)(259,476,290,445)(260,477,291,446)(261,478,292,447)(262,479,293,448)(263,480,294,449)(264,481,295,450)(265,482,296,451)(266,483,297,452)(267,484,298,453)(268,485,299,454)(269,486,300,455)(270,487,301,456)(271,488,302,457)(272,489,303,458)(273,490,304,459)(274,491,305,460)(275,492,306,461)(276,493,307,462)(277,494,308,463)(278,495,309,464)(279,496,310,465)(311,373,342,404)(312,374,343,405)(313,375,344,406)(314,376,345,407)(315,377,346,408)(316,378,347,409)(317,379,348,410)(318,380,349,411)(319,381,350,412)(320,382,351,413)(321,383,352,414)(322,384,353,415)(323,385,354,416)(324,386,355,417)(325,387,356,418)(326,388,357,419)(327,389,358,420)(328,390,359,421)(329,391,360,422)(330,392,361,423)(331,393,362,424)(332,394,363,425)(333,395,364,426)(334,396,365,427)(335,397,366,428)(336,398,367,429)(337,399,368,430)(338,400,369,431)(339,401,370,432)(340,402,371,433)(341,403,372,434) );
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),(435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465),(466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496)], [(1,435,82,404,34,466,111,373),(2,465,83,434,35,496,112,403),(3,464,84,433,36,495,113,402),(4,463,85,432,37,494,114,401),(5,462,86,431,38,493,115,400),(6,461,87,430,39,492,116,399),(7,460,88,429,40,491,117,398),(8,459,89,428,41,490,118,397),(9,458,90,427,42,489,119,396),(10,457,91,426,43,488,120,395),(11,456,92,425,44,487,121,394),(12,455,93,424,45,486,122,393),(13,454,63,423,46,485,123,392),(14,453,64,422,47,484,124,391),(15,452,65,421,48,483,94,390),(16,451,66,420,49,482,95,389),(17,450,67,419,50,481,96,388),(18,449,68,418,51,480,97,387),(19,448,69,417,52,479,98,386),(20,447,70,416,53,478,99,385),(21,446,71,415,54,477,100,384),(22,445,72,414,55,476,101,383),(23,444,73,413,56,475,102,382),(24,443,74,412,57,474,103,381),(25,442,75,411,58,473,104,380),(26,441,76,410,59,472,105,379),(27,440,77,409,60,471,106,378),(28,439,78,408,61,470,107,377),(29,438,79,407,62,469,108,376),(30,437,80,406,32,468,109,375),(31,436,81,405,33,467,110,374),(125,324,232,262,171,355,216,293),(126,323,233,261,172,354,217,292),(127,322,234,260,173,353,187,291),(128,321,235,259,174,352,188,290),(129,320,236,258,175,351,189,289),(130,319,237,257,176,350,190,288),(131,318,238,256,177,349,191,287),(132,317,239,255,178,348,192,286),(133,316,240,254,179,347,193,285),(134,315,241,253,180,346,194,284),(135,314,242,252,181,345,195,283),(136,313,243,251,182,344,196,282),(137,312,244,250,183,343,197,281),(138,311,245,249,184,342,198,280),(139,341,246,279,185,372,199,310),(140,340,247,278,186,371,200,309),(141,339,248,277,156,370,201,308),(142,338,218,276,157,369,202,307),(143,337,219,275,158,368,203,306),(144,336,220,274,159,367,204,305),(145,335,221,273,160,366,205,304),(146,334,222,272,161,365,206,303),(147,333,223,271,162,364,207,302),(148,332,224,270,163,363,208,301),(149,331,225,269,164,362,209,300),(150,330,226,268,165,361,210,299),(151,329,227,267,166,360,211,298),(152,328,228,266,167,359,212,297),(153,327,229,265,168,358,213,296),(154,326,230,264,169,357,214,295),(155,325,231,263,170,356,215,294)], [(1,184,34,138),(2,185,35,139),(3,186,36,140),(4,156,37,141),(5,157,38,142),(6,158,39,143),(7,159,40,144),(8,160,41,145),(9,161,42,146),(10,162,43,147),(11,163,44,148),(12,164,45,149),(13,165,46,150),(14,166,47,151),(15,167,48,152),(16,168,49,153),(17,169,50,154),(18,170,51,155),(19,171,52,125),(20,172,53,126),(21,173,54,127),(22,174,55,128),(23,175,56,129),(24,176,57,130),(25,177,58,131),(26,178,59,132),(27,179,60,133),(28,180,61,134),(29,181,62,135),(30,182,32,136),(31,183,33,137),(63,226,123,210),(64,227,124,211),(65,228,94,212),(66,229,95,213),(67,230,96,214),(68,231,97,215),(69,232,98,216),(70,233,99,217),(71,234,100,187),(72,235,101,188),(73,236,102,189),(74,237,103,190),(75,238,104,191),(76,239,105,192),(77,240,106,193),(78,241,107,194),(79,242,108,195),(80,243,109,196),(81,244,110,197),(82,245,111,198),(83,246,112,199),(84,247,113,200),(85,248,114,201),(86,218,115,202),(87,219,116,203),(88,220,117,204),(89,221,118,205),(90,222,119,206),(91,223,120,207),(92,224,121,208),(93,225,122,209),(249,466,280,435),(250,467,281,436),(251,468,282,437),(252,469,283,438),(253,470,284,439),(254,471,285,440),(255,472,286,441),(256,473,287,442),(257,474,288,443),(258,475,289,444),(259,476,290,445),(260,477,291,446),(261,478,292,447),(262,479,293,448),(263,480,294,449),(264,481,295,450),(265,482,296,451),(266,483,297,452),(267,484,298,453),(268,485,299,454),(269,486,300,455),(270,487,301,456),(271,488,302,457),(272,489,303,458),(273,490,304,459),(274,491,305,460),(275,492,306,461),(276,493,307,462),(277,494,308,463),(278,495,309,464),(279,496,310,465),(311,373,342,404),(312,374,343,405),(313,375,344,406),(314,376,345,407),(315,377,346,408),(316,378,347,409),(317,379,348,410),(318,380,349,411),(319,381,350,412),(320,382,351,413),(321,383,352,414),(322,384,353,415),(323,385,354,416),(324,386,355,417),(325,387,356,418),(326,388,357,419),(327,389,358,420),(328,390,359,421),(329,391,360,422),(330,392,361,423),(331,393,362,424),(332,394,363,425),(333,395,364,426),(334,396,365,427),(335,397,366,428),(336,398,367,429),(337,399,368,430),(338,400,369,431),(339,401,370,432),(340,402,371,433),(341,403,372,434)]])
82 conjugacy classes
| class | 1 | 2 | 4A | 4B | 4C | 8A | 8B | 31A | ··· | 31O | 62A | ··· | 62O | 124A | ··· | 124AS |
| order | 1 | 2 | 4 | 4 | 4 | 8 | 8 | 31 | ··· | 31 | 62 | ··· | 62 | 124 | ··· | 124 |
| size | 1 | 1 | 2 | 4 | 124 | 62 | 62 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | - | + | + | - | |
| image | C1 | C2 | C2 | C2 | D4 | Q16 | D31 | D62 | C31⋊D4 | C31⋊Q16 |
| kernel | C31⋊Q16 | C31⋊C8 | Dic62 | Q8×C31 | C62 | C31 | Q8 | C4 | C2 | C1 |
| # reps | 1 | 1 | 1 | 1 | 1 | 2 | 15 | 15 | 30 | 15 |
Matrix representation of C31⋊Q16 ►in GL4(𝔽1489) generated by
| 883 | 1 | 0 | 0 |
| 42 | 769 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 252 | 1395 | 0 | 0 |
| 533 | 1237 | 0 | 0 |
| 0 | 0 | 0 | 1020 |
| 0 | 0 | 1035 | 1107 |
| 1488 | 0 | 0 | 0 |
| 0 | 1488 | 0 | 0 |
| 0 | 0 | 1198 | 980 |
| 0 | 0 | 1278 | 291 |
G:=sub<GL(4,GF(1489))| [883,42,0,0,1,769,0,0,0,0,1,0,0,0,0,1],[252,533,0,0,1395,1237,0,0,0,0,0,1035,0,0,1020,1107],[1488,0,0,0,0,1488,0,0,0,0,1198,1278,0,0,980,291] >;
C31⋊Q16 in GAP, Magma, Sage, TeX
C_{31}\rtimes Q_{16} % in TeX
G:=Group("C31:Q16"); // GroupNames label
G:=SmallGroup(496,17);
// by ID
G=gap.SmallGroup(496,17);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-31,40,61,46,182,97,42,12004]);
// Polycyclic
G:=Group<a,b,c|a^31=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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