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G = C7×Dic17order 476 = 22·7·17

Direct product of C7 and Dic17

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

Aliases: C7×Dic17, C172C28, C1194C4, C34.C14, C238.2C2, C14.2D17, C2.(C7×D17), SmallGroup(476,2)

Series: Derived Chief Lower central Upper central

C1C17 — C7×Dic17
C1C17C34C238 — C7×Dic17
C17 — C7×Dic17
C1C14

Generators and relations for C7×Dic17
 G = < a,b,c | a7=b34=1, c2=b17, ab=ba, ac=ca, cbc-1=b-1 >

17C4
17C28

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

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

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

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

140 conjugacy classes

class 1  2 4A4B7A···7F14A···14F17A···17H28A···28L34A···34H119A···119AV238A···238AV
order12447···714···1417···1728···2834···34119···119238···238
size1117171···11···12···217···172···22···22···2

140 irreducible representations

dim1111112222
type+++-
imageC1C2C4C7C14C28D17Dic17C7×D17C7×Dic17
kernelC7×Dic17C238C119Dic17C34C17C14C7C2C1
# reps1126612884848

Matrix representation of C7×Dic17 in GL2(𝔽953) generated by

4310
0431
,
0952
1883
,
195947
302758
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

Export

Subgroup lattice of C7×Dic17 in TeX

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