direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: C7×Dic17, C17⋊2C28, C119⋊4C4, C34.C14, C238.2C2, C14.2D17, C2.(C7×D17), SmallGroup(476,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C17 — C7×Dic17 |
Generators and relations for C7×Dic17
G = < a,b,c | a7=b34=1, c2=b17, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C7×Dic17
►Regular action on 476 points
Generators in S476
(1 229 190 150 130 81 36)(2 230 191 151 131 82 37)(3 231 192 152 132 83 38)(4 232 193 153 133 84 39)(5 233 194 154 134 85 40)(6 234 195 155 135 86 41)(7 235 196 156 136 87 42)(8 236 197 157 103 88 43)(9 237 198 158 104 89 44)(10 238 199 159 105 90 45)(11 205 200 160 106 91 46)(12 206 201 161 107 92 47)(13 207 202 162 108 93 48)(14 208 203 163 109 94 49)(15 209 204 164 110 95 50)(16 210 171 165 111 96 51)(17 211 172 166 112 97 52)(18 212 173 167 113 98 53)(19 213 174 168 114 99 54)(20 214 175 169 115 100 55)(21 215 176 170 116 101 56)(22 216 177 137 117 102 57)(23 217 178 138 118 69 58)(24 218 179 139 119 70 59)(25 219 180 140 120 71 60)(26 220 181 141 121 72 61)(27 221 182 142 122 73 62)(28 222 183 143 123 74 63)(29 223 184 144 124 75 64)(30 224 185 145 125 76 65)(31 225 186 146 126 77 66)(32 226 187 147 127 78 67)(33 227 188 148 128 79 68)(34 228 189 149 129 80 35)(239 443 426 392 358 324 273)(240 444 427 393 359 325 274)(241 445 428 394 360 326 275)(242 446 429 395 361 327 276)(243 447 430 396 362 328 277)(244 448 431 397 363 329 278)(245 449 432 398 364 330 279)(246 450 433 399 365 331 280)(247 451 434 400 366 332 281)(248 452 435 401 367 333 282)(249 453 436 402 368 334 283)(250 454 437 403 369 335 284)(251 455 438 404 370 336 285)(252 456 439 405 371 337 286)(253 457 440 406 372 338 287)(254 458 441 407 373 339 288)(255 459 442 408 374 340 289)(256 460 409 375 341 307 290)(257 461 410 376 342 308 291)(258 462 411 377 343 309 292)(259 463 412 378 344 310 293)(260 464 413 379 345 311 294)(261 465 414 380 346 312 295)(262 466 415 381 347 313 296)(263 467 416 382 348 314 297)(264 468 417 383 349 315 298)(265 469 418 384 350 316 299)(266 470 419 385 351 317 300)(267 471 420 386 352 318 301)(268 472 421 387 353 319 302)(269 473 422 388 354 320 303)(270 474 423 389 355 321 304)(271 475 424 390 356 322 305)(272 476 425 391 357 323 306)
(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)
(1 239 18 256)(2 272 19 255)(3 271 20 254)(4 270 21 253)(5 269 22 252)(6 268 23 251)(7 267 24 250)(8 266 25 249)(9 265 26 248)(10 264 27 247)(11 263 28 246)(12 262 29 245)(13 261 30 244)(14 260 31 243)(15 259 32 242)(16 258 33 241)(17 257 34 240)(35 274 52 291)(36 273 53 290)(37 306 54 289)(38 305 55 288)(39 304 56 287)(40 303 57 286)(41 302 58 285)(42 301 59 284)(43 300 60 283)(44 299 61 282)(45 298 62 281)(46 297 63 280)(47 296 64 279)(48 295 65 278)(49 294 66 277)(50 293 67 276)(51 292 68 275)(69 336 86 319)(70 335 87 318)(71 334 88 317)(72 333 89 316)(73 332 90 315)(74 331 91 314)(75 330 92 313)(76 329 93 312)(77 328 94 311)(78 327 95 310)(79 326 96 309)(80 325 97 308)(81 324 98 307)(82 323 99 340)(83 322 100 339)(84 321 101 338)(85 320 102 337)(103 351 120 368)(104 350 121 367)(105 349 122 366)(106 348 123 365)(107 347 124 364)(108 346 125 363)(109 345 126 362)(110 344 127 361)(111 343 128 360)(112 342 129 359)(113 341 130 358)(114 374 131 357)(115 373 132 356)(116 372 133 355)(117 371 134 354)(118 370 135 353)(119 369 136 352)(137 405 154 388)(138 404 155 387)(139 403 156 386)(140 402 157 385)(141 401 158 384)(142 400 159 383)(143 399 160 382)(144 398 161 381)(145 397 162 380)(146 396 163 379)(147 395 164 378)(148 394 165 377)(149 393 166 376)(150 392 167 375)(151 391 168 408)(152 390 169 407)(153 389 170 406)(171 411 188 428)(172 410 189 427)(173 409 190 426)(174 442 191 425)(175 441 192 424)(176 440 193 423)(177 439 194 422)(178 438 195 421)(179 437 196 420)(180 436 197 419)(181 435 198 418)(182 434 199 417)(183 433 200 416)(184 432 201 415)(185 431 202 414)(186 430 203 413)(187 429 204 412)(205 467 222 450)(206 466 223 449)(207 465 224 448)(208 464 225 447)(209 463 226 446)(210 462 227 445)(211 461 228 444)(212 460 229 443)(213 459 230 476)(214 458 231 475)(215 457 232 474)(216 456 233 473)(217 455 234 472)(218 454 235 471)(219 453 236 470)(220 452 237 469)(221 451 238 468)
G:=sub<Sym(476)| (1,229,190,150,130,81,36)(2,230,191,151,131,82,37)(3,231,192,152,132,83,38)(4,232,193,153,133,84,39)(5,233,194,154,134,85,40)(6,234,195,155,135,86,41)(7,235,196,156,136,87,42)(8,236,197,157,103,88,43)(9,237,198,158,104,89,44)(10,238,199,159,105,90,45)(11,205,200,160,106,91,46)(12,206,201,161,107,92,47)(13,207,202,162,108,93,48)(14,208,203,163,109,94,49)(15,209,204,164,110,95,50)(16,210,171,165,111,96,51)(17,211,172,166,112,97,52)(18,212,173,167,113,98,53)(19,213,174,168,114,99,54)(20,214,175,169,115,100,55)(21,215,176,170,116,101,56)(22,216,177,137,117,102,57)(23,217,178,138,118,69,58)(24,218,179,139,119,70,59)(25,219,180,140,120,71,60)(26,220,181,141,121,72,61)(27,221,182,142,122,73,62)(28,222,183,143,123,74,63)(29,223,184,144,124,75,64)(30,224,185,145,125,76,65)(31,225,186,146,126,77,66)(32,226,187,147,127,78,67)(33,227,188,148,128,79,68)(34,228,189,149,129,80,35)(239,443,426,392,358,324,273)(240,444,427,393,359,325,274)(241,445,428,394,360,326,275)(242,446,429,395,361,327,276)(243,447,430,396,362,328,277)(244,448,431,397,363,329,278)(245,449,432,398,364,330,279)(246,450,433,399,365,331,280)(247,451,434,400,366,332,281)(248,452,435,401,367,333,282)(249,453,436,402,368,334,283)(250,454,437,403,369,335,284)(251,455,438,404,370,336,285)(252,456,439,405,371,337,286)(253,457,440,406,372,338,287)(254,458,441,407,373,339,288)(255,459,442,408,374,340,289)(256,460,409,375,341,307,290)(257,461,410,376,342,308,291)(258,462,411,377,343,309,292)(259,463,412,378,344,310,293)(260,464,413,379,345,311,294)(261,465,414,380,346,312,295)(262,466,415,381,347,313,296)(263,467,416,382,348,314,297)(264,468,417,383,349,315,298)(265,469,418,384,350,316,299)(266,470,419,385,351,317,300)(267,471,420,386,352,318,301)(268,472,421,387,353,319,302)(269,473,422,388,354,320,303)(270,474,423,389,355,321,304)(271,475,424,390,356,322,305)(272,476,425,391,357,323,306), (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), (1,239,18,256)(2,272,19,255)(3,271,20,254)(4,270,21,253)(5,269,22,252)(6,268,23,251)(7,267,24,250)(8,266,25,249)(9,265,26,248)(10,264,27,247)(11,263,28,246)(12,262,29,245)(13,261,30,244)(14,260,31,243)(15,259,32,242)(16,258,33,241)(17,257,34,240)(35,274,52,291)(36,273,53,290)(37,306,54,289)(38,305,55,288)(39,304,56,287)(40,303,57,286)(41,302,58,285)(42,301,59,284)(43,300,60,283)(44,299,61,282)(45,298,62,281)(46,297,63,280)(47,296,64,279)(48,295,65,278)(49,294,66,277)(50,293,67,276)(51,292,68,275)(69,336,86,319)(70,335,87,318)(71,334,88,317)(72,333,89,316)(73,332,90,315)(74,331,91,314)(75,330,92,313)(76,329,93,312)(77,328,94,311)(78,327,95,310)(79,326,96,309)(80,325,97,308)(81,324,98,307)(82,323,99,340)(83,322,100,339)(84,321,101,338)(85,320,102,337)(103,351,120,368)(104,350,121,367)(105,349,122,366)(106,348,123,365)(107,347,124,364)(108,346,125,363)(109,345,126,362)(110,344,127,361)(111,343,128,360)(112,342,129,359)(113,341,130,358)(114,374,131,357)(115,373,132,356)(116,372,133,355)(117,371,134,354)(118,370,135,353)(119,369,136,352)(137,405,154,388)(138,404,155,387)(139,403,156,386)(140,402,157,385)(141,401,158,384)(142,400,159,383)(143,399,160,382)(144,398,161,381)(145,397,162,380)(146,396,163,379)(147,395,164,378)(148,394,165,377)(149,393,166,376)(150,392,167,375)(151,391,168,408)(152,390,169,407)(153,389,170,406)(171,411,188,428)(172,410,189,427)(173,409,190,426)(174,442,191,425)(175,441,192,424)(176,440,193,423)(177,439,194,422)(178,438,195,421)(179,437,196,420)(180,436,197,419)(181,435,198,418)(182,434,199,417)(183,433,200,416)(184,432,201,415)(185,431,202,414)(186,430,203,413)(187,429,204,412)(205,467,222,450)(206,466,223,449)(207,465,224,448)(208,464,225,447)(209,463,226,446)(210,462,227,445)(211,461,228,444)(212,460,229,443)(213,459,230,476)(214,458,231,475)(215,457,232,474)(216,456,233,473)(217,455,234,472)(218,454,235,471)(219,453,236,470)(220,452,237,469)(221,451,238,468)>;
G:=Group( (1,229,190,150,130,81,36)(2,230,191,151,131,82,37)(3,231,192,152,132,83,38)(4,232,193,153,133,84,39)(5,233,194,154,134,85,40)(6,234,195,155,135,86,41)(7,235,196,156,136,87,42)(8,236,197,157,103,88,43)(9,237,198,158,104,89,44)(10,238,199,159,105,90,45)(11,205,200,160,106,91,46)(12,206,201,161,107,92,47)(13,207,202,162,108,93,48)(14,208,203,163,109,94,49)(15,209,204,164,110,95,50)(16,210,171,165,111,96,51)(17,211,172,166,112,97,52)(18,212,173,167,113,98,53)(19,213,174,168,114,99,54)(20,214,175,169,115,100,55)(21,215,176,170,116,101,56)(22,216,177,137,117,102,57)(23,217,178,138,118,69,58)(24,218,179,139,119,70,59)(25,219,180,140,120,71,60)(26,220,181,141,121,72,61)(27,221,182,142,122,73,62)(28,222,183,143,123,74,63)(29,223,184,144,124,75,64)(30,224,185,145,125,76,65)(31,225,186,146,126,77,66)(32,226,187,147,127,78,67)(33,227,188,148,128,79,68)(34,228,189,149,129,80,35)(239,443,426,392,358,324,273)(240,444,427,393,359,325,274)(241,445,428,394,360,326,275)(242,446,429,395,361,327,276)(243,447,430,396,362,328,277)(244,448,431,397,363,329,278)(245,449,432,398,364,330,279)(246,450,433,399,365,331,280)(247,451,434,400,366,332,281)(248,452,435,401,367,333,282)(249,453,436,402,368,334,283)(250,454,437,403,369,335,284)(251,455,438,404,370,336,285)(252,456,439,405,371,337,286)(253,457,440,406,372,338,287)(254,458,441,407,373,339,288)(255,459,442,408,374,340,289)(256,460,409,375,341,307,290)(257,461,410,376,342,308,291)(258,462,411,377,343,309,292)(259,463,412,378,344,310,293)(260,464,413,379,345,311,294)(261,465,414,380,346,312,295)(262,466,415,381,347,313,296)(263,467,416,382,348,314,297)(264,468,417,383,349,315,298)(265,469,418,384,350,316,299)(266,470,419,385,351,317,300)(267,471,420,386,352,318,301)(268,472,421,387,353,319,302)(269,473,422,388,354,320,303)(270,474,423,389,355,321,304)(271,475,424,390,356,322,305)(272,476,425,391,357,323,306), (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), (1,239,18,256)(2,272,19,255)(3,271,20,254)(4,270,21,253)(5,269,22,252)(6,268,23,251)(7,267,24,250)(8,266,25,249)(9,265,26,248)(10,264,27,247)(11,263,28,246)(12,262,29,245)(13,261,30,244)(14,260,31,243)(15,259,32,242)(16,258,33,241)(17,257,34,240)(35,274,52,291)(36,273,53,290)(37,306,54,289)(38,305,55,288)(39,304,56,287)(40,303,57,286)(41,302,58,285)(42,301,59,284)(43,300,60,283)(44,299,61,282)(45,298,62,281)(46,297,63,280)(47,296,64,279)(48,295,65,278)(49,294,66,277)(50,293,67,276)(51,292,68,275)(69,336,86,319)(70,335,87,318)(71,334,88,317)(72,333,89,316)(73,332,90,315)(74,331,91,314)(75,330,92,313)(76,329,93,312)(77,328,94,311)(78,327,95,310)(79,326,96,309)(80,325,97,308)(81,324,98,307)(82,323,99,340)(83,322,100,339)(84,321,101,338)(85,320,102,337)(103,351,120,368)(104,350,121,367)(105,349,122,366)(106,348,123,365)(107,347,124,364)(108,346,125,363)(109,345,126,362)(110,344,127,361)(111,343,128,360)(112,342,129,359)(113,341,130,358)(114,374,131,357)(115,373,132,356)(116,372,133,355)(117,371,134,354)(118,370,135,353)(119,369,136,352)(137,405,154,388)(138,404,155,387)(139,403,156,386)(140,402,157,385)(141,401,158,384)(142,400,159,383)(143,399,160,382)(144,398,161,381)(145,397,162,380)(146,396,163,379)(147,395,164,378)(148,394,165,377)(149,393,166,376)(150,392,167,375)(151,391,168,408)(152,390,169,407)(153,389,170,406)(171,411,188,428)(172,410,189,427)(173,409,190,426)(174,442,191,425)(175,441,192,424)(176,440,193,423)(177,439,194,422)(178,438,195,421)(179,437,196,420)(180,436,197,419)(181,435,198,418)(182,434,199,417)(183,433,200,416)(184,432,201,415)(185,431,202,414)(186,430,203,413)(187,429,204,412)(205,467,222,450)(206,466,223,449)(207,465,224,448)(208,464,225,447)(209,463,226,446)(210,462,227,445)(211,461,228,444)(212,460,229,443)(213,459,230,476)(214,458,231,475)(215,457,232,474)(216,456,233,473)(217,455,234,472)(218,454,235,471)(219,453,236,470)(220,452,237,469)(221,451,238,468) );
G=PermutationGroup([[(1,229,190,150,130,81,36),(2,230,191,151,131,82,37),(3,231,192,152,132,83,38),(4,232,193,153,133,84,39),(5,233,194,154,134,85,40),(6,234,195,155,135,86,41),(7,235,196,156,136,87,42),(8,236,197,157,103,88,43),(9,237,198,158,104,89,44),(10,238,199,159,105,90,45),(11,205,200,160,106,91,46),(12,206,201,161,107,92,47),(13,207,202,162,108,93,48),(14,208,203,163,109,94,49),(15,209,204,164,110,95,50),(16,210,171,165,111,96,51),(17,211,172,166,112,97,52),(18,212,173,167,113,98,53),(19,213,174,168,114,99,54),(20,214,175,169,115,100,55),(21,215,176,170,116,101,56),(22,216,177,137,117,102,57),(23,217,178,138,118,69,58),(24,218,179,139,119,70,59),(25,219,180,140,120,71,60),(26,220,181,141,121,72,61),(27,221,182,142,122,73,62),(28,222,183,143,123,74,63),(29,223,184,144,124,75,64),(30,224,185,145,125,76,65),(31,225,186,146,126,77,66),(32,226,187,147,127,78,67),(33,227,188,148,128,79,68),(34,228,189,149,129,80,35),(239,443,426,392,358,324,273),(240,444,427,393,359,325,274),(241,445,428,394,360,326,275),(242,446,429,395,361,327,276),(243,447,430,396,362,328,277),(244,448,431,397,363,329,278),(245,449,432,398,364,330,279),(246,450,433,399,365,331,280),(247,451,434,400,366,332,281),(248,452,435,401,367,333,282),(249,453,436,402,368,334,283),(250,454,437,403,369,335,284),(251,455,438,404,370,336,285),(252,456,439,405,371,337,286),(253,457,440,406,372,338,287),(254,458,441,407,373,339,288),(255,459,442,408,374,340,289),(256,460,409,375,341,307,290),(257,461,410,376,342,308,291),(258,462,411,377,343,309,292),(259,463,412,378,344,310,293),(260,464,413,379,345,311,294),(261,465,414,380,346,312,295),(262,466,415,381,347,313,296),(263,467,416,382,348,314,297),(264,468,417,383,349,315,298),(265,469,418,384,350,316,299),(266,470,419,385,351,317,300),(267,471,420,386,352,318,301),(268,472,421,387,353,319,302),(269,473,422,388,354,320,303),(270,474,423,389,355,321,304),(271,475,424,390,356,322,305),(272,476,425,391,357,323,306)], [(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)], [(1,239,18,256),(2,272,19,255),(3,271,20,254),(4,270,21,253),(5,269,22,252),(6,268,23,251),(7,267,24,250),(8,266,25,249),(9,265,26,248),(10,264,27,247),(11,263,28,246),(12,262,29,245),(13,261,30,244),(14,260,31,243),(15,259,32,242),(16,258,33,241),(17,257,34,240),(35,274,52,291),(36,273,53,290),(37,306,54,289),(38,305,55,288),(39,304,56,287),(40,303,57,286),(41,302,58,285),(42,301,59,284),(43,300,60,283),(44,299,61,282),(45,298,62,281),(46,297,63,280),(47,296,64,279),(48,295,65,278),(49,294,66,277),(50,293,67,276),(51,292,68,275),(69,336,86,319),(70,335,87,318),(71,334,88,317),(72,333,89,316),(73,332,90,315),(74,331,91,314),(75,330,92,313),(76,329,93,312),(77,328,94,311),(78,327,95,310),(79,326,96,309),(80,325,97,308),(81,324,98,307),(82,323,99,340),(83,322,100,339),(84,321,101,338),(85,320,102,337),(103,351,120,368),(104,350,121,367),(105,349,122,366),(106,348,123,365),(107,347,124,364),(108,346,125,363),(109,345,126,362),(110,344,127,361),(111,343,128,360),(112,342,129,359),(113,341,130,358),(114,374,131,357),(115,373,132,356),(116,372,133,355),(117,371,134,354),(118,370,135,353),(119,369,136,352),(137,405,154,388),(138,404,155,387),(139,403,156,386),(140,402,157,385),(141,401,158,384),(142,400,159,383),(143,399,160,382),(144,398,161,381),(145,397,162,380),(146,396,163,379),(147,395,164,378),(148,394,165,377),(149,393,166,376),(150,392,167,375),(151,391,168,408),(152,390,169,407),(153,389,170,406),(171,411,188,428),(172,410,189,427),(173,409,190,426),(174,442,191,425),(175,441,192,424),(176,440,193,423),(177,439,194,422),(178,438,195,421),(179,437,196,420),(180,436,197,419),(181,435,198,418),(182,434,199,417),(183,433,200,416),(184,432,201,415),(185,431,202,414),(186,430,203,413),(187,429,204,412),(205,467,222,450),(206,466,223,449),(207,465,224,448),(208,464,225,447),(209,463,226,446),(210,462,227,445),(211,461,228,444),(212,460,229,443),(213,459,230,476),(214,458,231,475),(215,457,232,474),(216,456,233,473),(217,455,234,472),(218,454,235,471),(219,453,236,470),(220,452,237,469),(221,451,238,468)]])
140 conjugacy classes
| class | 1 | 2 | 4A | 4B | 7A | ··· | 7F | 14A | ··· | 14F | 17A | ··· | 17H | 28A | ··· | 28L | 34A | ··· | 34H | 119A | ··· | 119AV | 238A | ··· | 238AV |
| order | 1 | 2 | 4 | 4 | 7 | ··· | 7 | 14 | ··· | 14 | 17 | ··· | 17 | 28 | ··· | 28 | 34 | ··· | 34 | 119 | ··· | 119 | 238 | ··· | 238 |
| size | 1 | 1 | 17 | 17 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 17 | ··· | 17 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
140 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | ||||||
| image | C1 | C2 | C4 | C7 | C14 | C28 | D17 | Dic17 | C7×D17 | C7×Dic17 |
| kernel | C7×Dic17 | C238 | C119 | Dic17 | C34 | C17 | C14 | C7 | C2 | C1 |
| # reps | 1 | 1 | 2 | 6 | 6 | 12 | 8 | 8 | 48 | 48 |
Matrix representation of C7×Dic17 ►in GL2(𝔽953) generated by
| 431 | 0 |
| 0 | 431 |
| 0 | 952 |
| 1 | 883 |
| 195 | 947 |
| 302 | 758 |
G:=sub<GL(2,GF(953))| [431,0,0,431],[0,1,952,883],[195,302,947,758] >;
C7×Dic17 in GAP, Magma, Sage, TeX
C_7\times {\rm Dic}_{17} % in TeX
G:=Group("C7xDic17"); // GroupNames label
G:=SmallGroup(476,2);
// by ID
G=gap.SmallGroup(476,2);
# by ID
G:=PCGroup([4,-2,-7,-2,-17,56,7171]);
// Polycyclic
G:=Group<a,b,c|a^7=b^34=1,c^2=b^17,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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