direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: C17×Dic7, C7⋊C68, C119⋊5C4, C14.C34, C34.2D7, C238.3C2, C2.(D7×C17), SmallGroup(476,1)
Series: Derived ►Chief ►Lower central ►Upper central
| C7 — C17×Dic7 |
Generators and relations for C17×Dic7
G = < a,b,c | a17=b14=1, c2=b7, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C17×Dic7
►Regular action on 476 points
Generators in S476
(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)
(1 340 412 97 234 120 107 153 462 448 168 294 203 371)(2 324 413 98 235 121 108 137 463 449 169 295 204 372)(3 325 414 99 236 122 109 138 464 450 170 296 188 373)(4 326 415 100 237 123 110 139 465 451 154 297 189 374)(5 327 416 101 238 124 111 140 466 452 155 298 190 358)(6 328 417 102 222 125 112 141 467 453 156 299 191 359)(7 329 418 86 223 126 113 142 468 454 157 300 192 360)(8 330 419 87 224 127 114 143 469 455 158 301 193 361)(9 331 420 88 225 128 115 144 470 456 159 302 194 362)(10 332 421 89 226 129 116 145 471 457 160 303 195 363)(11 333 422 90 227 130 117 146 472 458 161 304 196 364)(12 334 423 91 228 131 118 147 473 459 162 305 197 365)(13 335 424 92 229 132 119 148 474 443 163 306 198 366)(14 336 425 93 230 133 103 149 475 444 164 290 199 367)(15 337 409 94 231 134 104 150 476 445 165 291 200 368)(16 338 410 95 232 135 105 151 460 446 166 292 201 369)(17 339 411 96 233 136 106 152 461 447 167 293 202 370)(18 254 323 217 434 403 38 63 261 181 390 346 82 283)(19 255 307 218 435 404 39 64 262 182 391 347 83 284)(20 239 308 219 436 405 40 65 263 183 375 348 84 285)(21 240 309 220 437 406 41 66 264 184 376 349 85 286)(22 241 310 221 438 407 42 67 265 185 377 350 69 287)(23 242 311 205 439 408 43 68 266 186 378 351 70 288)(24 243 312 206 440 392 44 52 267 187 379 352 71 289)(25 244 313 207 441 393 45 53 268 171 380 353 72 273)(26 245 314 208 442 394 46 54 269 172 381 354 73 274)(27 246 315 209 426 395 47 55 270 173 382 355 74 275)(28 247 316 210 427 396 48 56 271 174 383 356 75 276)(29 248 317 211 428 397 49 57 272 175 384 357 76 277)(30 249 318 212 429 398 50 58 256 176 385 341 77 278)(31 250 319 213 430 399 51 59 257 177 386 342 78 279)(32 251 320 214 431 400 35 60 258 178 387 343 79 280)(33 252 321 215 432 401 36 61 259 179 388 344 80 281)(34 253 322 216 433 402 37 62 260 180 389 345 81 282)
(1 353 153 441)(2 354 137 442)(3 355 138 426)(4 356 139 427)(5 357 140 428)(6 341 141 429)(7 342 142 430)(8 343 143 431)(9 344 144 432)(10 345 145 433)(11 346 146 434)(12 347 147 435)(13 348 148 436)(14 349 149 437)(15 350 150 438)(16 351 151 439)(17 352 152 440)(18 227 63 304)(19 228 64 305)(20 229 65 306)(21 230 66 290)(22 231 67 291)(23 232 68 292)(24 233 52 293)(25 234 53 294)(26 235 54 295)(27 236 55 296)(28 237 56 297)(29 238 57 298)(30 222 58 299)(31 223 59 300)(32 224 60 301)(33 225 61 302)(34 226 62 303)(35 193 280 127)(36 194 281 128)(37 195 282 129)(38 196 283 130)(39 197 284 131)(40 198 285 132)(41 199 286 133)(42 200 287 134)(43 201 288 135)(44 202 289 136)(45 203 273 120)(46 204 274 121)(47 188 275 122)(48 189 276 123)(49 190 277 124)(50 191 278 125)(51 192 279 126)(69 104 407 368)(70 105 408 369)(71 106 392 370)(72 107 393 371)(73 108 394 372)(74 109 395 373)(75 110 396 374)(76 111 397 358)(77 112 398 359)(78 113 399 360)(79 114 400 361)(80 115 401 362)(81 116 402 363)(82 117 403 364)(83 118 404 365)(84 119 405 366)(85 103 406 367)(86 257 157 250)(87 258 158 251)(88 259 159 252)(89 260 160 253)(90 261 161 254)(91 262 162 255)(92 263 163 239)(93 264 164 240)(94 265 165 241)(95 266 166 242)(96 267 167 243)(97 268 168 244)(98 269 169 245)(99 270 170 246)(100 271 154 247)(101 272 155 248)(102 256 156 249)(171 448 313 412)(172 449 314 413)(173 450 315 414)(174 451 316 415)(175 452 317 416)(176 453 318 417)(177 454 319 418)(178 455 320 419)(179 456 321 420)(180 457 322 421)(181 458 323 422)(182 459 307 423)(183 443 308 424)(184 444 309 425)(185 445 310 409)(186 446 311 410)(187 447 312 411)(205 338 378 460)(206 339 379 461)(207 340 380 462)(208 324 381 463)(209 325 382 464)(210 326 383 465)(211 327 384 466)(212 328 385 467)(213 329 386 468)(214 330 387 469)(215 331 388 470)(216 332 389 471)(217 333 390 472)(218 334 391 473)(219 335 375 474)(220 336 376 475)(221 337 377 476)
G:=sub<Sym(476)| (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), (1,340,412,97,234,120,107,153,462,448,168,294,203,371)(2,324,413,98,235,121,108,137,463,449,169,295,204,372)(3,325,414,99,236,122,109,138,464,450,170,296,188,373)(4,326,415,100,237,123,110,139,465,451,154,297,189,374)(5,327,416,101,238,124,111,140,466,452,155,298,190,358)(6,328,417,102,222,125,112,141,467,453,156,299,191,359)(7,329,418,86,223,126,113,142,468,454,157,300,192,360)(8,330,419,87,224,127,114,143,469,455,158,301,193,361)(9,331,420,88,225,128,115,144,470,456,159,302,194,362)(10,332,421,89,226,129,116,145,471,457,160,303,195,363)(11,333,422,90,227,130,117,146,472,458,161,304,196,364)(12,334,423,91,228,131,118,147,473,459,162,305,197,365)(13,335,424,92,229,132,119,148,474,443,163,306,198,366)(14,336,425,93,230,133,103,149,475,444,164,290,199,367)(15,337,409,94,231,134,104,150,476,445,165,291,200,368)(16,338,410,95,232,135,105,151,460,446,166,292,201,369)(17,339,411,96,233,136,106,152,461,447,167,293,202,370)(18,254,323,217,434,403,38,63,261,181,390,346,82,283)(19,255,307,218,435,404,39,64,262,182,391,347,83,284)(20,239,308,219,436,405,40,65,263,183,375,348,84,285)(21,240,309,220,437,406,41,66,264,184,376,349,85,286)(22,241,310,221,438,407,42,67,265,185,377,350,69,287)(23,242,311,205,439,408,43,68,266,186,378,351,70,288)(24,243,312,206,440,392,44,52,267,187,379,352,71,289)(25,244,313,207,441,393,45,53,268,171,380,353,72,273)(26,245,314,208,442,394,46,54,269,172,381,354,73,274)(27,246,315,209,426,395,47,55,270,173,382,355,74,275)(28,247,316,210,427,396,48,56,271,174,383,356,75,276)(29,248,317,211,428,397,49,57,272,175,384,357,76,277)(30,249,318,212,429,398,50,58,256,176,385,341,77,278)(31,250,319,213,430,399,51,59,257,177,386,342,78,279)(32,251,320,214,431,400,35,60,258,178,387,343,79,280)(33,252,321,215,432,401,36,61,259,179,388,344,80,281)(34,253,322,216,433,402,37,62,260,180,389,345,81,282), (1,353,153,441)(2,354,137,442)(3,355,138,426)(4,356,139,427)(5,357,140,428)(6,341,141,429)(7,342,142,430)(8,343,143,431)(9,344,144,432)(10,345,145,433)(11,346,146,434)(12,347,147,435)(13,348,148,436)(14,349,149,437)(15,350,150,438)(16,351,151,439)(17,352,152,440)(18,227,63,304)(19,228,64,305)(20,229,65,306)(21,230,66,290)(22,231,67,291)(23,232,68,292)(24,233,52,293)(25,234,53,294)(26,235,54,295)(27,236,55,296)(28,237,56,297)(29,238,57,298)(30,222,58,299)(31,223,59,300)(32,224,60,301)(33,225,61,302)(34,226,62,303)(35,193,280,127)(36,194,281,128)(37,195,282,129)(38,196,283,130)(39,197,284,131)(40,198,285,132)(41,199,286,133)(42,200,287,134)(43,201,288,135)(44,202,289,136)(45,203,273,120)(46,204,274,121)(47,188,275,122)(48,189,276,123)(49,190,277,124)(50,191,278,125)(51,192,279,126)(69,104,407,368)(70,105,408,369)(71,106,392,370)(72,107,393,371)(73,108,394,372)(74,109,395,373)(75,110,396,374)(76,111,397,358)(77,112,398,359)(78,113,399,360)(79,114,400,361)(80,115,401,362)(81,116,402,363)(82,117,403,364)(83,118,404,365)(84,119,405,366)(85,103,406,367)(86,257,157,250)(87,258,158,251)(88,259,159,252)(89,260,160,253)(90,261,161,254)(91,262,162,255)(92,263,163,239)(93,264,164,240)(94,265,165,241)(95,266,166,242)(96,267,167,243)(97,268,168,244)(98,269,169,245)(99,270,170,246)(100,271,154,247)(101,272,155,248)(102,256,156,249)(171,448,313,412)(172,449,314,413)(173,450,315,414)(174,451,316,415)(175,452,317,416)(176,453,318,417)(177,454,319,418)(178,455,320,419)(179,456,321,420)(180,457,322,421)(181,458,323,422)(182,459,307,423)(183,443,308,424)(184,444,309,425)(185,445,310,409)(186,446,311,410)(187,447,312,411)(205,338,378,460)(206,339,379,461)(207,340,380,462)(208,324,381,463)(209,325,382,464)(210,326,383,465)(211,327,384,466)(212,328,385,467)(213,329,386,468)(214,330,387,469)(215,331,388,470)(216,332,389,471)(217,333,390,472)(218,334,391,473)(219,335,375,474)(220,336,376,475)(221,337,377,476)>;
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), (1,340,412,97,234,120,107,153,462,448,168,294,203,371)(2,324,413,98,235,121,108,137,463,449,169,295,204,372)(3,325,414,99,236,122,109,138,464,450,170,296,188,373)(4,326,415,100,237,123,110,139,465,451,154,297,189,374)(5,327,416,101,238,124,111,140,466,452,155,298,190,358)(6,328,417,102,222,125,112,141,467,453,156,299,191,359)(7,329,418,86,223,126,113,142,468,454,157,300,192,360)(8,330,419,87,224,127,114,143,469,455,158,301,193,361)(9,331,420,88,225,128,115,144,470,456,159,302,194,362)(10,332,421,89,226,129,116,145,471,457,160,303,195,363)(11,333,422,90,227,130,117,146,472,458,161,304,196,364)(12,334,423,91,228,131,118,147,473,459,162,305,197,365)(13,335,424,92,229,132,119,148,474,443,163,306,198,366)(14,336,425,93,230,133,103,149,475,444,164,290,199,367)(15,337,409,94,231,134,104,150,476,445,165,291,200,368)(16,338,410,95,232,135,105,151,460,446,166,292,201,369)(17,339,411,96,233,136,106,152,461,447,167,293,202,370)(18,254,323,217,434,403,38,63,261,181,390,346,82,283)(19,255,307,218,435,404,39,64,262,182,391,347,83,284)(20,239,308,219,436,405,40,65,263,183,375,348,84,285)(21,240,309,220,437,406,41,66,264,184,376,349,85,286)(22,241,310,221,438,407,42,67,265,185,377,350,69,287)(23,242,311,205,439,408,43,68,266,186,378,351,70,288)(24,243,312,206,440,392,44,52,267,187,379,352,71,289)(25,244,313,207,441,393,45,53,268,171,380,353,72,273)(26,245,314,208,442,394,46,54,269,172,381,354,73,274)(27,246,315,209,426,395,47,55,270,173,382,355,74,275)(28,247,316,210,427,396,48,56,271,174,383,356,75,276)(29,248,317,211,428,397,49,57,272,175,384,357,76,277)(30,249,318,212,429,398,50,58,256,176,385,341,77,278)(31,250,319,213,430,399,51,59,257,177,386,342,78,279)(32,251,320,214,431,400,35,60,258,178,387,343,79,280)(33,252,321,215,432,401,36,61,259,179,388,344,80,281)(34,253,322,216,433,402,37,62,260,180,389,345,81,282), (1,353,153,441)(2,354,137,442)(3,355,138,426)(4,356,139,427)(5,357,140,428)(6,341,141,429)(7,342,142,430)(8,343,143,431)(9,344,144,432)(10,345,145,433)(11,346,146,434)(12,347,147,435)(13,348,148,436)(14,349,149,437)(15,350,150,438)(16,351,151,439)(17,352,152,440)(18,227,63,304)(19,228,64,305)(20,229,65,306)(21,230,66,290)(22,231,67,291)(23,232,68,292)(24,233,52,293)(25,234,53,294)(26,235,54,295)(27,236,55,296)(28,237,56,297)(29,238,57,298)(30,222,58,299)(31,223,59,300)(32,224,60,301)(33,225,61,302)(34,226,62,303)(35,193,280,127)(36,194,281,128)(37,195,282,129)(38,196,283,130)(39,197,284,131)(40,198,285,132)(41,199,286,133)(42,200,287,134)(43,201,288,135)(44,202,289,136)(45,203,273,120)(46,204,274,121)(47,188,275,122)(48,189,276,123)(49,190,277,124)(50,191,278,125)(51,192,279,126)(69,104,407,368)(70,105,408,369)(71,106,392,370)(72,107,393,371)(73,108,394,372)(74,109,395,373)(75,110,396,374)(76,111,397,358)(77,112,398,359)(78,113,399,360)(79,114,400,361)(80,115,401,362)(81,116,402,363)(82,117,403,364)(83,118,404,365)(84,119,405,366)(85,103,406,367)(86,257,157,250)(87,258,158,251)(88,259,159,252)(89,260,160,253)(90,261,161,254)(91,262,162,255)(92,263,163,239)(93,264,164,240)(94,265,165,241)(95,266,166,242)(96,267,167,243)(97,268,168,244)(98,269,169,245)(99,270,170,246)(100,271,154,247)(101,272,155,248)(102,256,156,249)(171,448,313,412)(172,449,314,413)(173,450,315,414)(174,451,316,415)(175,452,317,416)(176,453,318,417)(177,454,319,418)(178,455,320,419)(179,456,321,420)(180,457,322,421)(181,458,323,422)(182,459,307,423)(183,443,308,424)(184,444,309,425)(185,445,310,409)(186,446,311,410)(187,447,312,411)(205,338,378,460)(206,339,379,461)(207,340,380,462)(208,324,381,463)(209,325,382,464)(210,326,383,465)(211,327,384,466)(212,328,385,467)(213,329,386,468)(214,330,387,469)(215,331,388,470)(216,332,389,471)(217,333,390,472)(218,334,391,473)(219,335,375,474)(220,336,376,475)(221,337,377,476) );
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)], [(1,340,412,97,234,120,107,153,462,448,168,294,203,371),(2,324,413,98,235,121,108,137,463,449,169,295,204,372),(3,325,414,99,236,122,109,138,464,450,170,296,188,373),(4,326,415,100,237,123,110,139,465,451,154,297,189,374),(5,327,416,101,238,124,111,140,466,452,155,298,190,358),(6,328,417,102,222,125,112,141,467,453,156,299,191,359),(7,329,418,86,223,126,113,142,468,454,157,300,192,360),(8,330,419,87,224,127,114,143,469,455,158,301,193,361),(9,331,420,88,225,128,115,144,470,456,159,302,194,362),(10,332,421,89,226,129,116,145,471,457,160,303,195,363),(11,333,422,90,227,130,117,146,472,458,161,304,196,364),(12,334,423,91,228,131,118,147,473,459,162,305,197,365),(13,335,424,92,229,132,119,148,474,443,163,306,198,366),(14,336,425,93,230,133,103,149,475,444,164,290,199,367),(15,337,409,94,231,134,104,150,476,445,165,291,200,368),(16,338,410,95,232,135,105,151,460,446,166,292,201,369),(17,339,411,96,233,136,106,152,461,447,167,293,202,370),(18,254,323,217,434,403,38,63,261,181,390,346,82,283),(19,255,307,218,435,404,39,64,262,182,391,347,83,284),(20,239,308,219,436,405,40,65,263,183,375,348,84,285),(21,240,309,220,437,406,41,66,264,184,376,349,85,286),(22,241,310,221,438,407,42,67,265,185,377,350,69,287),(23,242,311,205,439,408,43,68,266,186,378,351,70,288),(24,243,312,206,440,392,44,52,267,187,379,352,71,289),(25,244,313,207,441,393,45,53,268,171,380,353,72,273),(26,245,314,208,442,394,46,54,269,172,381,354,73,274),(27,246,315,209,426,395,47,55,270,173,382,355,74,275),(28,247,316,210,427,396,48,56,271,174,383,356,75,276),(29,248,317,211,428,397,49,57,272,175,384,357,76,277),(30,249,318,212,429,398,50,58,256,176,385,341,77,278),(31,250,319,213,430,399,51,59,257,177,386,342,78,279),(32,251,320,214,431,400,35,60,258,178,387,343,79,280),(33,252,321,215,432,401,36,61,259,179,388,344,80,281),(34,253,322,216,433,402,37,62,260,180,389,345,81,282)], [(1,353,153,441),(2,354,137,442),(3,355,138,426),(4,356,139,427),(5,357,140,428),(6,341,141,429),(7,342,142,430),(8,343,143,431),(9,344,144,432),(10,345,145,433),(11,346,146,434),(12,347,147,435),(13,348,148,436),(14,349,149,437),(15,350,150,438),(16,351,151,439),(17,352,152,440),(18,227,63,304),(19,228,64,305),(20,229,65,306),(21,230,66,290),(22,231,67,291),(23,232,68,292),(24,233,52,293),(25,234,53,294),(26,235,54,295),(27,236,55,296),(28,237,56,297),(29,238,57,298),(30,222,58,299),(31,223,59,300),(32,224,60,301),(33,225,61,302),(34,226,62,303),(35,193,280,127),(36,194,281,128),(37,195,282,129),(38,196,283,130),(39,197,284,131),(40,198,285,132),(41,199,286,133),(42,200,287,134),(43,201,288,135),(44,202,289,136),(45,203,273,120),(46,204,274,121),(47,188,275,122),(48,189,276,123),(49,190,277,124),(50,191,278,125),(51,192,279,126),(69,104,407,368),(70,105,408,369),(71,106,392,370),(72,107,393,371),(73,108,394,372),(74,109,395,373),(75,110,396,374),(76,111,397,358),(77,112,398,359),(78,113,399,360),(79,114,400,361),(80,115,401,362),(81,116,402,363),(82,117,403,364),(83,118,404,365),(84,119,405,366),(85,103,406,367),(86,257,157,250),(87,258,158,251),(88,259,159,252),(89,260,160,253),(90,261,161,254),(91,262,162,255),(92,263,163,239),(93,264,164,240),(94,265,165,241),(95,266,166,242),(96,267,167,243),(97,268,168,244),(98,269,169,245),(99,270,170,246),(100,271,154,247),(101,272,155,248),(102,256,156,249),(171,448,313,412),(172,449,314,413),(173,450,315,414),(174,451,316,415),(175,452,317,416),(176,453,318,417),(177,454,319,418),(178,455,320,419),(179,456,321,420),(180,457,322,421),(181,458,323,422),(182,459,307,423),(183,443,308,424),(184,444,309,425),(185,445,310,409),(186,446,311,410),(187,447,312,411),(205,338,378,460),(206,339,379,461),(207,340,380,462),(208,324,381,463),(209,325,382,464),(210,326,383,465),(211,327,384,466),(212,328,385,467),(213,329,386,468),(214,330,387,469),(215,331,388,470),(216,332,389,471),(217,333,390,472),(218,334,391,473),(219,335,375,474),(220,336,376,475),(221,337,377,476)]])
170 conjugacy classes
| class | 1 | 2 | 4A | 4B | 7A | 7B | 7C | 14A | 14B | 14C | 17A | ··· | 17P | 34A | ··· | 34P | 68A | ··· | 68AF | 119A | ··· | 119AV | 238A | ··· | 238AV |
| order | 1 | 2 | 4 | 4 | 7 | 7 | 7 | 14 | 14 | 14 | 17 | ··· | 17 | 34 | ··· | 34 | 68 | ··· | 68 | 119 | ··· | 119 | 238 | ··· | 238 |
| size | 1 | 1 | 7 | 7 | 2 | 2 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 7 | ··· | 7 | 2 | ··· | 2 | 2 | ··· | 2 |
170 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | ||||||
| image | C1 | C2 | C4 | C17 | C34 | C68 | D7 | Dic7 | D7×C17 | C17×Dic7 |
| kernel | C17×Dic7 | C238 | C119 | Dic7 | C14 | C7 | C34 | C17 | C2 | C1 |
| # reps | 1 | 1 | 2 | 16 | 16 | 32 | 3 | 3 | 48 | 48 |
Matrix representation of C17×Dic7 ►in GL3(𝔽953) generated by
| 1 | 0 | 0 |
| 0 | 802 | 0 |
| 0 | 0 | 802 |
| 952 | 0 | 0 |
| 0 | 952 | 1 |
| 0 | 497 | 455 |
| 442 | 0 | 0 |
| 0 | 879 | 40 |
| 0 | 697 | 74 |
G:=sub<GL(3,GF(953))| [1,0,0,0,802,0,0,0,802],[952,0,0,0,952,497,0,1,455],[442,0,0,0,879,697,0,40,74] >;
C17×Dic7 in GAP, Magma, Sage, TeX
C_{17}\times {\rm Dic}_7 % in TeX
G:=Group("C17xDic7"); // GroupNames label
G:=SmallGroup(476,1);
// by ID
G=gap.SmallGroup(476,1);
# by ID
G:=PCGroup([4,-2,-17,-2,-7,136,6531]);
// Polycyclic
G:=Group<a,b,c|a^17=b^14=1,c^2=b^7,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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