direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C2×C31⋊C8, C62⋊C8, C124.3C4, C4.14D62, C4.3Dic31, C124.14C22, C22.2Dic31, C31⋊2(C2×C8), C62.6(C2×C4), (C2×C62).2C4, (C2×C4).5D31, (C2×C124).6C2, C2.1(C2×Dic31), SmallGroup(496,8)
Series: Derived ►Chief ►Lower central ►Upper central
| C31 — C2×C31⋊C8 |
Generators and relations for C2×C31⋊C8
G = < a,b,c | a2=b31=c8=1, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C2×C31⋊C8
►Regular action on 496 points
Generators in S496
(1 125)(2 126)(3 127)(4 128)(5 129)(6 130)(7 131)(8 132)(9 133)(10 134)(11 135)(12 136)(13 137)(14 138)(15 139)(16 140)(17 141)(18 142)(19 143)(20 144)(21 145)(22 146)(23 147)(24 148)(25 149)(26 150)(27 151)(28 152)(29 153)(30 154)(31 155)(32 156)(33 157)(34 158)(35 159)(36 160)(37 161)(38 162)(39 163)(40 164)(41 165)(42 166)(43 167)(44 168)(45 169)(46 170)(47 171)(48 172)(49 173)(50 174)(51 175)(52 176)(53 177)(54 178)(55 179)(56 180)(57 181)(58 182)(59 183)(60 184)(61 185)(62 186)(63 187)(64 188)(65 189)(66 190)(67 191)(68 192)(69 193)(70 194)(71 195)(72 196)(73 197)(74 198)(75 199)(76 200)(77 201)(78 202)(79 203)(80 204)(81 205)(82 206)(83 207)(84 208)(85 209)(86 210)(87 211)(88 212)(89 213)(90 214)(91 215)(92 216)(93 217)(94 218)(95 219)(96 220)(97 221)(98 222)(99 223)(100 224)(101 225)(102 226)(103 227)(104 228)(105 229)(106 230)(107 231)(108 232)(109 233)(110 234)(111 235)(112 236)(113 237)(114 238)(115 239)(116 240)(117 241)(118 242)(119 243)(120 244)(121 245)(122 246)(123 247)(124 248)(249 375)(250 376)(251 377)(252 378)(253 379)(254 380)(255 381)(256 382)(257 383)(258 384)(259 385)(260 386)(261 387)(262 388)(263 389)(264 390)(265 391)(266 392)(267 393)(268 394)(269 395)(270 396)(271 397)(272 398)(273 399)(274 400)(275 401)(276 402)(277 403)(278 373)(279 374)(280 417)(281 418)(282 419)(283 420)(284 421)(285 422)(286 423)(287 424)(288 425)(289 426)(290 427)(291 428)(292 429)(293 430)(294 431)(295 432)(296 433)(297 434)(298 404)(299 405)(300 406)(301 407)(302 408)(303 409)(304 410)(305 411)(306 412)(307 413)(308 414)(309 415)(310 416)(311 460)(312 461)(313 462)(314 463)(315 464)(316 465)(317 435)(318 436)(319 437)(320 438)(321 439)(322 440)(323 441)(324 442)(325 443)(326 444)(327 445)(328 446)(329 447)(330 448)(331 449)(332 450)(333 451)(334 452)(335 453)(336 454)(337 455)(338 456)(339 457)(340 458)(341 459)(342 472)(343 473)(344 474)(345 475)(346 476)(347 477)(348 478)(349 479)(350 480)(351 481)(352 482)(353 483)(354 484)(355 485)(356 486)(357 487)(358 488)(359 489)(360 490)(361 491)(362 492)(363 493)(364 494)(365 495)(366 496)(367 466)(368 467)(369 468)(370 469)(371 470)(372 471)
(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)
(1 473 94 418 32 451 63 393)(2 472 95 417 33 450 64 392)(3 471 96 416 34 449 65 391)(4 470 97 415 35 448 66 390)(5 469 98 414 36 447 67 389)(6 468 99 413 37 446 68 388)(7 467 100 412 38 445 69 387)(8 466 101 411 39 444 70 386)(9 496 102 410 40 443 71 385)(10 495 103 409 41 442 72 384)(11 494 104 408 42 441 73 383)(12 493 105 407 43 440 74 382)(13 492 106 406 44 439 75 381)(14 491 107 405 45 438 76 380)(15 490 108 404 46 437 77 379)(16 489 109 434 47 436 78 378)(17 488 110 433 48 435 79 377)(18 487 111 432 49 465 80 376)(19 486 112 431 50 464 81 375)(20 485 113 430 51 463 82 374)(21 484 114 429 52 462 83 373)(22 483 115 428 53 461 84 403)(23 482 116 427 54 460 85 402)(24 481 117 426 55 459 86 401)(25 480 118 425 56 458 87 400)(26 479 119 424 57 457 88 399)(27 478 120 423 58 456 89 398)(28 477 121 422 59 455 90 397)(29 476 122 421 60 454 91 396)(30 475 123 420 61 453 92 395)(31 474 124 419 62 452 93 394)(125 343 218 281 156 333 187 267)(126 342 219 280 157 332 188 266)(127 372 220 310 158 331 189 265)(128 371 221 309 159 330 190 264)(129 370 222 308 160 329 191 263)(130 369 223 307 161 328 192 262)(131 368 224 306 162 327 193 261)(132 367 225 305 163 326 194 260)(133 366 226 304 164 325 195 259)(134 365 227 303 165 324 196 258)(135 364 228 302 166 323 197 257)(136 363 229 301 167 322 198 256)(137 362 230 300 168 321 199 255)(138 361 231 299 169 320 200 254)(139 360 232 298 170 319 201 253)(140 359 233 297 171 318 202 252)(141 358 234 296 172 317 203 251)(142 357 235 295 173 316 204 250)(143 356 236 294 174 315 205 249)(144 355 237 293 175 314 206 279)(145 354 238 292 176 313 207 278)(146 353 239 291 177 312 208 277)(147 352 240 290 178 311 209 276)(148 351 241 289 179 341 210 275)(149 350 242 288 180 340 211 274)(150 349 243 287 181 339 212 273)(151 348 244 286 182 338 213 272)(152 347 245 285 183 337 214 271)(153 346 246 284 184 336 215 270)(154 345 247 283 185 335 216 269)(155 344 248 282 186 334 217 268)
G:=sub<Sym(496)| (1,125)(2,126)(3,127)(4,128)(5,129)(6,130)(7,131)(8,132)(9,133)(10,134)(11,135)(12,136)(13,137)(14,138)(15,139)(16,140)(17,141)(18,142)(19,143)(20,144)(21,145)(22,146)(23,147)(24,148)(25,149)(26,150)(27,151)(28,152)(29,153)(30,154)(31,155)(32,156)(33,157)(34,158)(35,159)(36,160)(37,161)(38,162)(39,163)(40,164)(41,165)(42,166)(43,167)(44,168)(45,169)(46,170)(47,171)(48,172)(49,173)(50,174)(51,175)(52,176)(53,177)(54,178)(55,179)(56,180)(57,181)(58,182)(59,183)(60,184)(61,185)(62,186)(63,187)(64,188)(65,189)(66,190)(67,191)(68,192)(69,193)(70,194)(71,195)(72,196)(73,197)(74,198)(75,199)(76,200)(77,201)(78,202)(79,203)(80,204)(81,205)(82,206)(83,207)(84,208)(85,209)(86,210)(87,211)(88,212)(89,213)(90,214)(91,215)(92,216)(93,217)(94,218)(95,219)(96,220)(97,221)(98,222)(99,223)(100,224)(101,225)(102,226)(103,227)(104,228)(105,229)(106,230)(107,231)(108,232)(109,233)(110,234)(111,235)(112,236)(113,237)(114,238)(115,239)(116,240)(117,241)(118,242)(119,243)(120,244)(121,245)(122,246)(123,247)(124,248)(249,375)(250,376)(251,377)(252,378)(253,379)(254,380)(255,381)(256,382)(257,383)(258,384)(259,385)(260,386)(261,387)(262,388)(263,389)(264,390)(265,391)(266,392)(267,393)(268,394)(269,395)(270,396)(271,397)(272,398)(273,399)(274,400)(275,401)(276,402)(277,403)(278,373)(279,374)(280,417)(281,418)(282,419)(283,420)(284,421)(285,422)(286,423)(287,424)(288,425)(289,426)(290,427)(291,428)(292,429)(293,430)(294,431)(295,432)(296,433)(297,434)(298,404)(299,405)(300,406)(301,407)(302,408)(303,409)(304,410)(305,411)(306,412)(307,413)(308,414)(309,415)(310,416)(311,460)(312,461)(313,462)(314,463)(315,464)(316,465)(317,435)(318,436)(319,437)(320,438)(321,439)(322,440)(323,441)(324,442)(325,443)(326,444)(327,445)(328,446)(329,447)(330,448)(331,449)(332,450)(333,451)(334,452)(335,453)(336,454)(337,455)(338,456)(339,457)(340,458)(341,459)(342,472)(343,473)(344,474)(345,475)(346,476)(347,477)(348,478)(349,479)(350,480)(351,481)(352,482)(353,483)(354,484)(355,485)(356,486)(357,487)(358,488)(359,489)(360,490)(361,491)(362,492)(363,493)(364,494)(365,495)(366,496)(367,466)(368,467)(369,468)(370,469)(371,470)(372,471), (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), (1,473,94,418,32,451,63,393)(2,472,95,417,33,450,64,392)(3,471,96,416,34,449,65,391)(4,470,97,415,35,448,66,390)(5,469,98,414,36,447,67,389)(6,468,99,413,37,446,68,388)(7,467,100,412,38,445,69,387)(8,466,101,411,39,444,70,386)(9,496,102,410,40,443,71,385)(10,495,103,409,41,442,72,384)(11,494,104,408,42,441,73,383)(12,493,105,407,43,440,74,382)(13,492,106,406,44,439,75,381)(14,491,107,405,45,438,76,380)(15,490,108,404,46,437,77,379)(16,489,109,434,47,436,78,378)(17,488,110,433,48,435,79,377)(18,487,111,432,49,465,80,376)(19,486,112,431,50,464,81,375)(20,485,113,430,51,463,82,374)(21,484,114,429,52,462,83,373)(22,483,115,428,53,461,84,403)(23,482,116,427,54,460,85,402)(24,481,117,426,55,459,86,401)(25,480,118,425,56,458,87,400)(26,479,119,424,57,457,88,399)(27,478,120,423,58,456,89,398)(28,477,121,422,59,455,90,397)(29,476,122,421,60,454,91,396)(30,475,123,420,61,453,92,395)(31,474,124,419,62,452,93,394)(125,343,218,281,156,333,187,267)(126,342,219,280,157,332,188,266)(127,372,220,310,158,331,189,265)(128,371,221,309,159,330,190,264)(129,370,222,308,160,329,191,263)(130,369,223,307,161,328,192,262)(131,368,224,306,162,327,193,261)(132,367,225,305,163,326,194,260)(133,366,226,304,164,325,195,259)(134,365,227,303,165,324,196,258)(135,364,228,302,166,323,197,257)(136,363,229,301,167,322,198,256)(137,362,230,300,168,321,199,255)(138,361,231,299,169,320,200,254)(139,360,232,298,170,319,201,253)(140,359,233,297,171,318,202,252)(141,358,234,296,172,317,203,251)(142,357,235,295,173,316,204,250)(143,356,236,294,174,315,205,249)(144,355,237,293,175,314,206,279)(145,354,238,292,176,313,207,278)(146,353,239,291,177,312,208,277)(147,352,240,290,178,311,209,276)(148,351,241,289,179,341,210,275)(149,350,242,288,180,340,211,274)(150,349,243,287,181,339,212,273)(151,348,244,286,182,338,213,272)(152,347,245,285,183,337,214,271)(153,346,246,284,184,336,215,270)(154,345,247,283,185,335,216,269)(155,344,248,282,186,334,217,268)>;
G:=Group( (1,125)(2,126)(3,127)(4,128)(5,129)(6,130)(7,131)(8,132)(9,133)(10,134)(11,135)(12,136)(13,137)(14,138)(15,139)(16,140)(17,141)(18,142)(19,143)(20,144)(21,145)(22,146)(23,147)(24,148)(25,149)(26,150)(27,151)(28,152)(29,153)(30,154)(31,155)(32,156)(33,157)(34,158)(35,159)(36,160)(37,161)(38,162)(39,163)(40,164)(41,165)(42,166)(43,167)(44,168)(45,169)(46,170)(47,171)(48,172)(49,173)(50,174)(51,175)(52,176)(53,177)(54,178)(55,179)(56,180)(57,181)(58,182)(59,183)(60,184)(61,185)(62,186)(63,187)(64,188)(65,189)(66,190)(67,191)(68,192)(69,193)(70,194)(71,195)(72,196)(73,197)(74,198)(75,199)(76,200)(77,201)(78,202)(79,203)(80,204)(81,205)(82,206)(83,207)(84,208)(85,209)(86,210)(87,211)(88,212)(89,213)(90,214)(91,215)(92,216)(93,217)(94,218)(95,219)(96,220)(97,221)(98,222)(99,223)(100,224)(101,225)(102,226)(103,227)(104,228)(105,229)(106,230)(107,231)(108,232)(109,233)(110,234)(111,235)(112,236)(113,237)(114,238)(115,239)(116,240)(117,241)(118,242)(119,243)(120,244)(121,245)(122,246)(123,247)(124,248)(249,375)(250,376)(251,377)(252,378)(253,379)(254,380)(255,381)(256,382)(257,383)(258,384)(259,385)(260,386)(261,387)(262,388)(263,389)(264,390)(265,391)(266,392)(267,393)(268,394)(269,395)(270,396)(271,397)(272,398)(273,399)(274,400)(275,401)(276,402)(277,403)(278,373)(279,374)(280,417)(281,418)(282,419)(283,420)(284,421)(285,422)(286,423)(287,424)(288,425)(289,426)(290,427)(291,428)(292,429)(293,430)(294,431)(295,432)(296,433)(297,434)(298,404)(299,405)(300,406)(301,407)(302,408)(303,409)(304,410)(305,411)(306,412)(307,413)(308,414)(309,415)(310,416)(311,460)(312,461)(313,462)(314,463)(315,464)(316,465)(317,435)(318,436)(319,437)(320,438)(321,439)(322,440)(323,441)(324,442)(325,443)(326,444)(327,445)(328,446)(329,447)(330,448)(331,449)(332,450)(333,451)(334,452)(335,453)(336,454)(337,455)(338,456)(339,457)(340,458)(341,459)(342,472)(343,473)(344,474)(345,475)(346,476)(347,477)(348,478)(349,479)(350,480)(351,481)(352,482)(353,483)(354,484)(355,485)(356,486)(357,487)(358,488)(359,489)(360,490)(361,491)(362,492)(363,493)(364,494)(365,495)(366,496)(367,466)(368,467)(369,468)(370,469)(371,470)(372,471), (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), (1,473,94,418,32,451,63,393)(2,472,95,417,33,450,64,392)(3,471,96,416,34,449,65,391)(4,470,97,415,35,448,66,390)(5,469,98,414,36,447,67,389)(6,468,99,413,37,446,68,388)(7,467,100,412,38,445,69,387)(8,466,101,411,39,444,70,386)(9,496,102,410,40,443,71,385)(10,495,103,409,41,442,72,384)(11,494,104,408,42,441,73,383)(12,493,105,407,43,440,74,382)(13,492,106,406,44,439,75,381)(14,491,107,405,45,438,76,380)(15,490,108,404,46,437,77,379)(16,489,109,434,47,436,78,378)(17,488,110,433,48,435,79,377)(18,487,111,432,49,465,80,376)(19,486,112,431,50,464,81,375)(20,485,113,430,51,463,82,374)(21,484,114,429,52,462,83,373)(22,483,115,428,53,461,84,403)(23,482,116,427,54,460,85,402)(24,481,117,426,55,459,86,401)(25,480,118,425,56,458,87,400)(26,479,119,424,57,457,88,399)(27,478,120,423,58,456,89,398)(28,477,121,422,59,455,90,397)(29,476,122,421,60,454,91,396)(30,475,123,420,61,453,92,395)(31,474,124,419,62,452,93,394)(125,343,218,281,156,333,187,267)(126,342,219,280,157,332,188,266)(127,372,220,310,158,331,189,265)(128,371,221,309,159,330,190,264)(129,370,222,308,160,329,191,263)(130,369,223,307,161,328,192,262)(131,368,224,306,162,327,193,261)(132,367,225,305,163,326,194,260)(133,366,226,304,164,325,195,259)(134,365,227,303,165,324,196,258)(135,364,228,302,166,323,197,257)(136,363,229,301,167,322,198,256)(137,362,230,300,168,321,199,255)(138,361,231,299,169,320,200,254)(139,360,232,298,170,319,201,253)(140,359,233,297,171,318,202,252)(141,358,234,296,172,317,203,251)(142,357,235,295,173,316,204,250)(143,356,236,294,174,315,205,249)(144,355,237,293,175,314,206,279)(145,354,238,292,176,313,207,278)(146,353,239,291,177,312,208,277)(147,352,240,290,178,311,209,276)(148,351,241,289,179,341,210,275)(149,350,242,288,180,340,211,274)(150,349,243,287,181,339,212,273)(151,348,244,286,182,338,213,272)(152,347,245,285,183,337,214,271)(153,346,246,284,184,336,215,270)(154,345,247,283,185,335,216,269)(155,344,248,282,186,334,217,268) );
G=PermutationGroup([[(1,125),(2,126),(3,127),(4,128),(5,129),(6,130),(7,131),(8,132),(9,133),(10,134),(11,135),(12,136),(13,137),(14,138),(15,139),(16,140),(17,141),(18,142),(19,143),(20,144),(21,145),(22,146),(23,147),(24,148),(25,149),(26,150),(27,151),(28,152),(29,153),(30,154),(31,155),(32,156),(33,157),(34,158),(35,159),(36,160),(37,161),(38,162),(39,163),(40,164),(41,165),(42,166),(43,167),(44,168),(45,169),(46,170),(47,171),(48,172),(49,173),(50,174),(51,175),(52,176),(53,177),(54,178),(55,179),(56,180),(57,181),(58,182),(59,183),(60,184),(61,185),(62,186),(63,187),(64,188),(65,189),(66,190),(67,191),(68,192),(69,193),(70,194),(71,195),(72,196),(73,197),(74,198),(75,199),(76,200),(77,201),(78,202),(79,203),(80,204),(81,205),(82,206),(83,207),(84,208),(85,209),(86,210),(87,211),(88,212),(89,213),(90,214),(91,215),(92,216),(93,217),(94,218),(95,219),(96,220),(97,221),(98,222),(99,223),(100,224),(101,225),(102,226),(103,227),(104,228),(105,229),(106,230),(107,231),(108,232),(109,233),(110,234),(111,235),(112,236),(113,237),(114,238),(115,239),(116,240),(117,241),(118,242),(119,243),(120,244),(121,245),(122,246),(123,247),(124,248),(249,375),(250,376),(251,377),(252,378),(253,379),(254,380),(255,381),(256,382),(257,383),(258,384),(259,385),(260,386),(261,387),(262,388),(263,389),(264,390),(265,391),(266,392),(267,393),(268,394),(269,395),(270,396),(271,397),(272,398),(273,399),(274,400),(275,401),(276,402),(277,403),(278,373),(279,374),(280,417),(281,418),(282,419),(283,420),(284,421),(285,422),(286,423),(287,424),(288,425),(289,426),(290,427),(291,428),(292,429),(293,430),(294,431),(295,432),(296,433),(297,434),(298,404),(299,405),(300,406),(301,407),(302,408),(303,409),(304,410),(305,411),(306,412),(307,413),(308,414),(309,415),(310,416),(311,460),(312,461),(313,462),(314,463),(315,464),(316,465),(317,435),(318,436),(319,437),(320,438),(321,439),(322,440),(323,441),(324,442),(325,443),(326,444),(327,445),(328,446),(329,447),(330,448),(331,449),(332,450),(333,451),(334,452),(335,453),(336,454),(337,455),(338,456),(339,457),(340,458),(341,459),(342,472),(343,473),(344,474),(345,475),(346,476),(347,477),(348,478),(349,479),(350,480),(351,481),(352,482),(353,483),(354,484),(355,485),(356,486),(357,487),(358,488),(359,489),(360,490),(361,491),(362,492),(363,493),(364,494),(365,495),(366,496),(367,466),(368,467),(369,468),(370,469),(371,470),(372,471)], [(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)], [(1,473,94,418,32,451,63,393),(2,472,95,417,33,450,64,392),(3,471,96,416,34,449,65,391),(4,470,97,415,35,448,66,390),(5,469,98,414,36,447,67,389),(6,468,99,413,37,446,68,388),(7,467,100,412,38,445,69,387),(8,466,101,411,39,444,70,386),(9,496,102,410,40,443,71,385),(10,495,103,409,41,442,72,384),(11,494,104,408,42,441,73,383),(12,493,105,407,43,440,74,382),(13,492,106,406,44,439,75,381),(14,491,107,405,45,438,76,380),(15,490,108,404,46,437,77,379),(16,489,109,434,47,436,78,378),(17,488,110,433,48,435,79,377),(18,487,111,432,49,465,80,376),(19,486,112,431,50,464,81,375),(20,485,113,430,51,463,82,374),(21,484,114,429,52,462,83,373),(22,483,115,428,53,461,84,403),(23,482,116,427,54,460,85,402),(24,481,117,426,55,459,86,401),(25,480,118,425,56,458,87,400),(26,479,119,424,57,457,88,399),(27,478,120,423,58,456,89,398),(28,477,121,422,59,455,90,397),(29,476,122,421,60,454,91,396),(30,475,123,420,61,453,92,395),(31,474,124,419,62,452,93,394),(125,343,218,281,156,333,187,267),(126,342,219,280,157,332,188,266),(127,372,220,310,158,331,189,265),(128,371,221,309,159,330,190,264),(129,370,222,308,160,329,191,263),(130,369,223,307,161,328,192,262),(131,368,224,306,162,327,193,261),(132,367,225,305,163,326,194,260),(133,366,226,304,164,325,195,259),(134,365,227,303,165,324,196,258),(135,364,228,302,166,323,197,257),(136,363,229,301,167,322,198,256),(137,362,230,300,168,321,199,255),(138,361,231,299,169,320,200,254),(139,360,232,298,170,319,201,253),(140,359,233,297,171,318,202,252),(141,358,234,296,172,317,203,251),(142,357,235,295,173,316,204,250),(143,356,236,294,174,315,205,249),(144,355,237,293,175,314,206,279),(145,354,238,292,176,313,207,278),(146,353,239,291,177,312,208,277),(147,352,240,290,178,311,209,276),(148,351,241,289,179,341,210,275),(149,350,242,288,180,340,211,274),(150,349,243,287,181,339,212,273),(151,348,244,286,182,338,213,272),(152,347,245,285,183,337,214,271),(153,346,246,284,184,336,215,270),(154,345,247,283,185,335,216,269),(155,344,248,282,186,334,217,268)]])
136 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 8A | ··· | 8H | 31A | ··· | 31O | 62A | ··· | 62AS | 124A | ··· | 124BH |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 8 | ··· | 8 | 31 | ··· | 31 | 62 | ··· | 62 | 124 | ··· | 124 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 31 | ··· | 31 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
136 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | - | ||||
| image | C1 | C2 | C2 | C4 | C4 | C8 | D31 | Dic31 | D62 | Dic31 | C31⋊C8 |
| kernel | C2×C31⋊C8 | C31⋊C8 | C2×C124 | C124 | C2×C62 | C62 | C2×C4 | C4 | C4 | C22 | C2 |
| # reps | 1 | 2 | 1 | 2 | 2 | 8 | 15 | 15 | 15 | 15 | 60 |
Matrix representation of C2×C31⋊C8 ►in GL3(𝔽1489) generated by
| 1488 | 0 | 0 |
| 0 | 1488 | 0 |
| 0 | 0 | 1488 |
| 1 | 0 | 0 |
| 0 | 668 | 1488 |
| 0 | 1 | 0 |
| 15 | 0 | 0 |
| 0 | 469 | 253 |
| 0 | 855 | 1020 |
G:=sub<GL(3,GF(1489))| [1488,0,0,0,1488,0,0,0,1488],[1,0,0,0,668,1,0,1488,0],[15,0,0,0,469,855,0,253,1020] >;
C2×C31⋊C8 in GAP, Magma, Sage, TeX
C_2\times C_{31}\rtimes C_8 % in TeX
G:=Group("C2xC31:C8"); // GroupNames label
G:=SmallGroup(496,8);
// by ID
G=gap.SmallGroup(496,8);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-31,20,42,12004]);
// Polycyclic
G:=Group<a,b,c|a^2=b^31=c^8=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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