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G = C17×Dic7order 476 = 22·7·17

Direct product of C17 and Dic7

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

Aliases: C17×Dic7, C7⋊C68, C1195C4, C14.C34, C34.2D7, C238.3C2, C2.(D7×C17), SmallGroup(476,1)

Series: Derived Chief Lower central Upper central

C1C7 — C17×Dic7
C1C7C14C238 — C17×Dic7
C7 — C17×Dic7
C1C34

Generators and relations for C17×Dic7
 G = < a,b,c | a17=b14=1, c2=b7, ab=ba, ac=ca, cbc-1=b-1 >

7C4
7C68

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

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

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

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

170 conjugacy classes

class 1  2 4A4B7A7B7C14A14B14C17A···17P34A···34P68A···68AF119A···119AV238A···238AV
order124477714141417···1734···3468···68119···119238···238
size11772222221···11···17···72···22···2

170 irreducible representations

dim1111112222
type+++-
imageC1C2C4C17C34C68D7Dic7D7×C17C17×Dic7
kernelC17×Dic7C238C119Dic7C14C7C34C17C2C1
# reps112161632334848

Matrix representation of C17×Dic7 in GL3(𝔽953) generated by

100
08020
00802
,
95200
09521
0497455
,
44200
087940
069774
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

Export

Subgroup lattice of C17×Dic7 in TeX

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