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G = C31⋊C16order 496 = 24·31

The semidirect product of C31 and C16 acting via C16/C8=C2

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

Aliases: C31⋊C16, C62.C8, C8.2D31, C124.2C4, C248.2C2, C4.2Dic31, C2.(C31⋊C8), SmallGroup(496,1)

Series: Derived Chief Lower central Upper central

C1C31 — C31⋊C16
C1C31C62C124C248 — C31⋊C16
C31 — C31⋊C16
C1C8

Generators and relations for C31⋊C16
 G = < a,b | a31=b16=1, bab-1=a-1 >

31C16

Smallest permutation representation of C31⋊C16
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)
(1 466 239 342 104 404 183 280 48 435 214 311 81 373 138 249)(2 496 240 372 105 434 184 310 49 465 215 341 82 403 139 279)(3 495 241 371 106 433 185 309 50 464 216 340 83 402 140 278)(4 494 242 370 107 432 186 308 51 463 217 339 84 401 141 277)(5 493 243 369 108 431 156 307 52 462 187 338 85 400 142 276)(6 492 244 368 109 430 157 306 53 461 188 337 86 399 143 275)(7 491 245 367 110 429 158 305 54 460 189 336 87 398 144 274)(8 490 246 366 111 428 159 304 55 459 190 335 88 397 145 273)(9 489 247 365 112 427 160 303 56 458 191 334 89 396 146 272)(10 488 248 364 113 426 161 302 57 457 192 333 90 395 147 271)(11 487 218 363 114 425 162 301 58 456 193 332 91 394 148 270)(12 486 219 362 115 424 163 300 59 455 194 331 92 393 149 269)(13 485 220 361 116 423 164 299 60 454 195 330 93 392 150 268)(14 484 221 360 117 422 165 298 61 453 196 329 63 391 151 267)(15 483 222 359 118 421 166 297 62 452 197 328 64 390 152 266)(16 482 223 358 119 420 167 296 32 451 198 327 65 389 153 265)(17 481 224 357 120 419 168 295 33 450 199 326 66 388 154 264)(18 480 225 356 121 418 169 294 34 449 200 325 67 387 155 263)(19 479 226 355 122 417 170 293 35 448 201 324 68 386 125 262)(20 478 227 354 123 416 171 292 36 447 202 323 69 385 126 261)(21 477 228 353 124 415 172 291 37 446 203 322 70 384 127 260)(22 476 229 352 94 414 173 290 38 445 204 321 71 383 128 259)(23 475 230 351 95 413 174 289 39 444 205 320 72 382 129 258)(24 474 231 350 96 412 175 288 40 443 206 319 73 381 130 257)(25 473 232 349 97 411 176 287 41 442 207 318 74 380 131 256)(26 472 233 348 98 410 177 286 42 441 208 317 75 379 132 255)(27 471 234 347 99 409 178 285 43 440 209 316 76 378 133 254)(28 470 235 346 100 408 179 284 44 439 210 315 77 377 134 253)(29 469 236 345 101 407 180 283 45 438 211 314 78 376 135 252)(30 468 237 344 102 406 181 282 46 437 212 313 79 375 136 251)(31 467 238 343 103 405 182 281 47 436 213 312 80 374 137 250)

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), (1,466,239,342,104,404,183,280,48,435,214,311,81,373,138,249)(2,496,240,372,105,434,184,310,49,465,215,341,82,403,139,279)(3,495,241,371,106,433,185,309,50,464,216,340,83,402,140,278)(4,494,242,370,107,432,186,308,51,463,217,339,84,401,141,277)(5,493,243,369,108,431,156,307,52,462,187,338,85,400,142,276)(6,492,244,368,109,430,157,306,53,461,188,337,86,399,143,275)(7,491,245,367,110,429,158,305,54,460,189,336,87,398,144,274)(8,490,246,366,111,428,159,304,55,459,190,335,88,397,145,273)(9,489,247,365,112,427,160,303,56,458,191,334,89,396,146,272)(10,488,248,364,113,426,161,302,57,457,192,333,90,395,147,271)(11,487,218,363,114,425,162,301,58,456,193,332,91,394,148,270)(12,486,219,362,115,424,163,300,59,455,194,331,92,393,149,269)(13,485,220,361,116,423,164,299,60,454,195,330,93,392,150,268)(14,484,221,360,117,422,165,298,61,453,196,329,63,391,151,267)(15,483,222,359,118,421,166,297,62,452,197,328,64,390,152,266)(16,482,223,358,119,420,167,296,32,451,198,327,65,389,153,265)(17,481,224,357,120,419,168,295,33,450,199,326,66,388,154,264)(18,480,225,356,121,418,169,294,34,449,200,325,67,387,155,263)(19,479,226,355,122,417,170,293,35,448,201,324,68,386,125,262)(20,478,227,354,123,416,171,292,36,447,202,323,69,385,126,261)(21,477,228,353,124,415,172,291,37,446,203,322,70,384,127,260)(22,476,229,352,94,414,173,290,38,445,204,321,71,383,128,259)(23,475,230,351,95,413,174,289,39,444,205,320,72,382,129,258)(24,474,231,350,96,412,175,288,40,443,206,319,73,381,130,257)(25,473,232,349,97,411,176,287,41,442,207,318,74,380,131,256)(26,472,233,348,98,410,177,286,42,441,208,317,75,379,132,255)(27,471,234,347,99,409,178,285,43,440,209,316,76,378,133,254)(28,470,235,346,100,408,179,284,44,439,210,315,77,377,134,253)(29,469,236,345,101,407,180,283,45,438,211,314,78,376,135,252)(30,468,237,344,102,406,181,282,46,437,212,313,79,375,136,251)(31,467,238,343,103,405,182,281,47,436,213,312,80,374,137,250)>;

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), (1,466,239,342,104,404,183,280,48,435,214,311,81,373,138,249)(2,496,240,372,105,434,184,310,49,465,215,341,82,403,139,279)(3,495,241,371,106,433,185,309,50,464,216,340,83,402,140,278)(4,494,242,370,107,432,186,308,51,463,217,339,84,401,141,277)(5,493,243,369,108,431,156,307,52,462,187,338,85,400,142,276)(6,492,244,368,109,430,157,306,53,461,188,337,86,399,143,275)(7,491,245,367,110,429,158,305,54,460,189,336,87,398,144,274)(8,490,246,366,111,428,159,304,55,459,190,335,88,397,145,273)(9,489,247,365,112,427,160,303,56,458,191,334,89,396,146,272)(10,488,248,364,113,426,161,302,57,457,192,333,90,395,147,271)(11,487,218,363,114,425,162,301,58,456,193,332,91,394,148,270)(12,486,219,362,115,424,163,300,59,455,194,331,92,393,149,269)(13,485,220,361,116,423,164,299,60,454,195,330,93,392,150,268)(14,484,221,360,117,422,165,298,61,453,196,329,63,391,151,267)(15,483,222,359,118,421,166,297,62,452,197,328,64,390,152,266)(16,482,223,358,119,420,167,296,32,451,198,327,65,389,153,265)(17,481,224,357,120,419,168,295,33,450,199,326,66,388,154,264)(18,480,225,356,121,418,169,294,34,449,200,325,67,387,155,263)(19,479,226,355,122,417,170,293,35,448,201,324,68,386,125,262)(20,478,227,354,123,416,171,292,36,447,202,323,69,385,126,261)(21,477,228,353,124,415,172,291,37,446,203,322,70,384,127,260)(22,476,229,352,94,414,173,290,38,445,204,321,71,383,128,259)(23,475,230,351,95,413,174,289,39,444,205,320,72,382,129,258)(24,474,231,350,96,412,175,288,40,443,206,319,73,381,130,257)(25,473,232,349,97,411,176,287,41,442,207,318,74,380,131,256)(26,472,233,348,98,410,177,286,42,441,208,317,75,379,132,255)(27,471,234,347,99,409,178,285,43,440,209,316,76,378,133,254)(28,470,235,346,100,408,179,284,44,439,210,315,77,377,134,253)(29,469,236,345,101,407,180,283,45,438,211,314,78,376,135,252)(30,468,237,344,102,406,181,282,46,437,212,313,79,375,136,251)(31,467,238,343,103,405,182,281,47,436,213,312,80,374,137,250) );

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)], [(1,466,239,342,104,404,183,280,48,435,214,311,81,373,138,249),(2,496,240,372,105,434,184,310,49,465,215,341,82,403,139,279),(3,495,241,371,106,433,185,309,50,464,216,340,83,402,140,278),(4,494,242,370,107,432,186,308,51,463,217,339,84,401,141,277),(5,493,243,369,108,431,156,307,52,462,187,338,85,400,142,276),(6,492,244,368,109,430,157,306,53,461,188,337,86,399,143,275),(7,491,245,367,110,429,158,305,54,460,189,336,87,398,144,274),(8,490,246,366,111,428,159,304,55,459,190,335,88,397,145,273),(9,489,247,365,112,427,160,303,56,458,191,334,89,396,146,272),(10,488,248,364,113,426,161,302,57,457,192,333,90,395,147,271),(11,487,218,363,114,425,162,301,58,456,193,332,91,394,148,270),(12,486,219,362,115,424,163,300,59,455,194,331,92,393,149,269),(13,485,220,361,116,423,164,299,60,454,195,330,93,392,150,268),(14,484,221,360,117,422,165,298,61,453,196,329,63,391,151,267),(15,483,222,359,118,421,166,297,62,452,197,328,64,390,152,266),(16,482,223,358,119,420,167,296,32,451,198,327,65,389,153,265),(17,481,224,357,120,419,168,295,33,450,199,326,66,388,154,264),(18,480,225,356,121,418,169,294,34,449,200,325,67,387,155,263),(19,479,226,355,122,417,170,293,35,448,201,324,68,386,125,262),(20,478,227,354,123,416,171,292,36,447,202,323,69,385,126,261),(21,477,228,353,124,415,172,291,37,446,203,322,70,384,127,260),(22,476,229,352,94,414,173,290,38,445,204,321,71,383,128,259),(23,475,230,351,95,413,174,289,39,444,205,320,72,382,129,258),(24,474,231,350,96,412,175,288,40,443,206,319,73,381,130,257),(25,473,232,349,97,411,176,287,41,442,207,318,74,380,131,256),(26,472,233,348,98,410,177,286,42,441,208,317,75,379,132,255),(27,471,234,347,99,409,178,285,43,440,209,316,76,378,133,254),(28,470,235,346,100,408,179,284,44,439,210,315,77,377,134,253),(29,469,236,345,101,407,180,283,45,438,211,314,78,376,135,252),(30,468,237,344,102,406,181,282,46,437,212,313,79,375,136,251),(31,467,238,343,103,405,182,281,47,436,213,312,80,374,137,250)])

136 conjugacy classes

class 1  2 4A4B8A8B8C8D16A···16H31A···31O62A···62O124A···124AD248A···248BH
order1244888816···1631···3162···62124···124248···248
size1111111131···312···22···22···22···2

136 irreducible representations

dim111112222
type+++-
imageC1C2C4C8C16D31Dic31C31⋊C8C31⋊C16
kernelC31⋊C16C248C124C62C31C8C4C2C1
# reps1124815153060

Matrix representation of C31⋊C16 in GL2(𝔽1489) generated by

01
1488246
,
1080566
1204409
G:=sub<GL(2,GF(1489))| [0,1488,1,246],[1080,1204,566,409] >;

C31⋊C16 in GAP, Magma, Sage, TeX

C_{31}\rtimes C_{16}
% in TeX

G:=Group("C31:C16");
// GroupNames label

G:=SmallGroup(496,1);
// by ID

G=gap.SmallGroup(496,1);
# by ID

G:=PCGroup([5,-2,-2,-2,-2,-31,10,26,42,12004]);
// Polycyclic

G:=Group<a,b|a^31=b^16=1,b*a*b^-1=a^-1>;
// generators/relations

Export

Subgroup lattice of C31⋊C16 in TeX

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