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G = C13×Dic9order 468 = 22·32·13

Direct product of C13 and Dic9

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

Aliases: C13×Dic9, C9⋊C52, C1175C4, C18.C26, C78.5S3, C26.2D9, C234.3C2, C39.3Dic3, C2.(C13×D9), C6.1(S3×C13), C3.(Dic3×C13), SmallGroup(468,3)

Series: Derived Chief Lower central Upper central

C1C9 — C13×Dic9
C1C3C9C18C234 — C13×Dic9
C9 — C13×Dic9
C1C26

Generators and relations for C13×Dic9
 G = < a,b,c | a13=b18=1, c2=b9, ab=ba, ac=ca, cbc-1=b-1 >

9C4
3Dic3
9C52
3Dic3×C13

Smallest permutation representation of C13×Dic9
Regular action on 468 points
Generators in S468
(1 231 199 195 166 145 134 112 94 73 58 51 19)(2 232 200 196 167 146 135 113 95 74 59 52 20)(3 233 201 197 168 147 136 114 96 75 60 53 21)(4 234 202 198 169 148 137 115 97 76 61 54 22)(5 217 203 181 170 149 138 116 98 77 62 37 23)(6 218 204 182 171 150 139 117 99 78 63 38 24)(7 219 205 183 172 151 140 118 100 79 64 39 25)(8 220 206 184 173 152 141 119 101 80 65 40 26)(9 221 207 185 174 153 142 120 102 81 66 41 27)(10 222 208 186 175 154 143 121 103 82 67 42 28)(11 223 209 187 176 155 144 122 104 83 68 43 29)(12 224 210 188 177 156 127 123 105 84 69 44 30)(13 225 211 189 178 157 128 124 106 85 70 45 31)(14 226 212 190 179 158 129 125 107 86 71 46 32)(15 227 213 191 180 159 130 126 108 87 72 47 33)(16 228 214 192 163 160 131 109 91 88 55 48 34)(17 229 215 193 164 161 132 110 92 89 56 49 35)(18 230 216 194 165 162 133 111 93 90 57 50 36)(235 460 440 427 406 393 362 360 342 320 290 283 262)(236 461 441 428 407 394 363 343 325 321 291 284 263)(237 462 442 429 408 395 364 344 326 322 292 285 264)(238 463 443 430 409 396 365 345 327 323 293 286 265)(239 464 444 431 410 379 366 346 328 324 294 287 266)(240 465 445 432 411 380 367 347 329 307 295 288 267)(241 466 446 415 412 381 368 348 330 308 296 271 268)(242 467 447 416 413 382 369 349 331 309 297 272 269)(243 468 448 417 414 383 370 350 332 310 298 273 270)(244 451 449 418 397 384 371 351 333 311 299 274 253)(245 452 450 419 398 385 372 352 334 312 300 275 254)(246 453 433 420 399 386 373 353 335 313 301 276 255)(247 454 434 421 400 387 374 354 336 314 302 277 256)(248 455 435 422 401 388 375 355 337 315 303 278 257)(249 456 436 423 402 389 376 356 338 316 304 279 258)(250 457 437 424 403 390 377 357 339 317 305 280 259)(251 458 438 425 404 391 378 358 340 318 306 281 260)(252 459 439 426 405 392 361 359 341 319 289 282 261)
(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)
(1 243 10 252)(2 242 11 251)(3 241 12 250)(4 240 13 249)(5 239 14 248)(6 238 15 247)(7 237 16 246)(8 236 17 245)(9 235 18 244)(19 270 28 261)(20 269 29 260)(21 268 30 259)(22 267 31 258)(23 266 32 257)(24 265 33 256)(25 264 34 255)(26 263 35 254)(27 262 36 253)(37 287 46 278)(38 286 47 277)(39 285 48 276)(40 284 49 275)(41 283 50 274)(42 282 51 273)(43 281 52 272)(44 280 53 271)(45 279 54 288)(55 301 64 292)(56 300 65 291)(57 299 66 290)(58 298 67 289)(59 297 68 306)(60 296 69 305)(61 295 70 304)(62 294 71 303)(63 293 72 302)(73 310 82 319)(74 309 83 318)(75 308 84 317)(76 307 85 316)(77 324 86 315)(78 323 87 314)(79 322 88 313)(80 321 89 312)(81 320 90 311)(91 335 100 326)(92 334 101 325)(93 333 102 342)(94 332 103 341)(95 331 104 340)(96 330 105 339)(97 329 106 338)(98 328 107 337)(99 327 108 336)(109 353 118 344)(110 352 119 343)(111 351 120 360)(112 350 121 359)(113 349 122 358)(114 348 123 357)(115 347 124 356)(116 346 125 355)(117 345 126 354)(127 377 136 368)(128 376 137 367)(129 375 138 366)(130 374 139 365)(131 373 140 364)(132 372 141 363)(133 371 142 362)(134 370 143 361)(135 369 144 378)(145 383 154 392)(146 382 155 391)(147 381 156 390)(148 380 157 389)(149 379 158 388)(150 396 159 387)(151 395 160 386)(152 394 161 385)(153 393 162 384)(163 399 172 408)(164 398 173 407)(165 397 174 406)(166 414 175 405)(167 413 176 404)(168 412 177 403)(169 411 178 402)(170 410 179 401)(171 409 180 400)(181 431 190 422)(182 430 191 421)(183 429 192 420)(184 428 193 419)(185 427 194 418)(186 426 195 417)(187 425 196 416)(188 424 197 415)(189 423 198 432)(199 448 208 439)(200 447 209 438)(201 446 210 437)(202 445 211 436)(203 444 212 435)(204 443 213 434)(205 442 214 433)(206 441 215 450)(207 440 216 449)(217 464 226 455)(218 463 227 454)(219 462 228 453)(220 461 229 452)(221 460 230 451)(222 459 231 468)(223 458 232 467)(224 457 233 466)(225 456 234 465)

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

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

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

156 conjugacy classes

class 1  2  3 4A4B 6 9A9B9C13A···13L18A18B18C26A···26L39A···39L52A···52X78A···78L117A···117AJ234A···234AJ
order12344699913···1318181826···2639···3952···5278···78117···117234···234
size1129922221···12221···12···29···92···22···22···2

156 irreducible representations

dim11111122222222
type+++-+-
imageC1C2C4C13C26C52S3Dic3D9Dic9S3×C13Dic3×C13C13×D9C13×Dic9
kernelC13×Dic9C234C117Dic9C18C9C78C39C26C13C6C3C2C1
# reps112121224113312123636

Matrix representation of C13×Dic9 in GL3(𝔽937) generated by

100
06760
00676
,
93600
0465262
0675203
,
19600
0501889
0388436
G:=sub<GL(3,GF(937))| [1,0,0,0,676,0,0,0,676],[936,0,0,0,465,675,0,262,203],[196,0,0,0,501,388,0,889,436] >;

C13×Dic9 in GAP, Magma, Sage, TeX

C_{13}\times {\rm Dic}_9
% in TeX

G:=Group("C13xDic9");
// GroupNames label

G:=SmallGroup(468,3);
// by ID

G=gap.SmallGroup(468,3);
# by ID

G:=PCGroup([5,-2,-13,-2,-3,-3,130,5203,138,7804]);
// Polycyclic

G:=Group<a,b,c|a^13=b^18=1,c^2=b^9,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

Export

Subgroup lattice of C13×Dic9 in TeX

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