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G = C9×Dic13order 468 = 22·32·13

Direct product of C9 and Dic13

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

Aliases: C9×Dic13, C1174C4, C135C36, C78.10C6, C234.2C2, C39.5C12, C26.3C18, C18.2D13, C2.(C9×D13), C6.2(C3×D13), C3.(C3×Dic13), (C3×Dic13).2C3, SmallGroup(468,4)

Series: Derived Chief Lower central Upper central

C1C13 — C9×Dic13
C1C13C39C78C234 — C9×Dic13
C13 — C9×Dic13
C1C18

Generators and relations for C9×Dic13
 G = < a,b,c | a9=b26=1, c2=b13, ab=ba, ac=ca, cbc-1=b-1 >

13C4
13C12
13C36

Smallest permutation representation of C9×Dic13
Regular action on 468 points
Generators in S468
(1 380 329 459 424 42 183 165 394)(2 381 330 460 425 43 184 166 395)(3 382 331 461 426 44 185 167 396)(4 383 332 462 427 45 186 168 397)(5 384 333 463 428 46 187 169 398)(6 385 334 464 429 47 188 170 399)(7 386 335 465 430 48 189 171 400)(8 387 336 466 431 49 190 172 401)(9 388 337 467 432 50 191 173 402)(10 389 338 468 433 51 192 174 403)(11 390 313 443 434 52 193 175 404)(12 365 314 444 435 27 194 176 405)(13 366 315 445 436 28 195 177 406)(14 367 316 446 437 29 196 178 407)(15 368 317 447 438 30 197 179 408)(16 369 318 448 439 31 198 180 409)(17 370 319 449 440 32 199 181 410)(18 371 320 450 441 33 200 182 411)(19 372 321 451 442 34 201 157 412)(20 373 322 452 417 35 202 158 413)(21 374 323 453 418 36 203 159 414)(22 375 324 454 419 37 204 160 415)(23 376 325 455 420 38 205 161 416)(24 377 326 456 421 39 206 162 391)(25 378 327 457 422 40 207 163 392)(26 379 328 458 423 41 208 164 393)(53 90 138 107 340 220 265 290 246)(54 91 139 108 341 221 266 291 247)(55 92 140 109 342 222 267 292 248)(56 93 141 110 343 223 268 293 249)(57 94 142 111 344 224 269 294 250)(58 95 143 112 345 225 270 295 251)(59 96 144 113 346 226 271 296 252)(60 97 145 114 347 227 272 297 253)(61 98 146 115 348 228 273 298 254)(62 99 147 116 349 229 274 299 255)(63 100 148 117 350 230 275 300 256)(64 101 149 118 351 231 276 301 257)(65 102 150 119 352 232 277 302 258)(66 103 151 120 353 233 278 303 259)(67 104 152 121 354 234 279 304 260)(68 79 153 122 355 209 280 305 235)(69 80 154 123 356 210 281 306 236)(70 81 155 124 357 211 282 307 237)(71 82 156 125 358 212 283 308 238)(72 83 131 126 359 213 284 309 239)(73 84 132 127 360 214 285 310 240)(74 85 133 128 361 215 286 311 241)(75 86 134 129 362 216 261 312 242)(76 87 135 130 363 217 262 287 243)(77 88 136 105 364 218 263 288 244)(78 89 137 106 339 219 264 289 245)
(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)
(1 343 14 356)(2 342 15 355)(3 341 16 354)(4 340 17 353)(5 339 18 352)(6 364 19 351)(7 363 20 350)(8 362 21 349)(9 361 22 348)(10 360 23 347)(11 359 24 346)(12 358 25 345)(13 357 26 344)(27 71 40 58)(28 70 41 57)(29 69 42 56)(30 68 43 55)(31 67 44 54)(32 66 45 53)(33 65 46 78)(34 64 47 77)(35 63 48 76)(36 62 49 75)(37 61 50 74)(38 60 51 73)(39 59 52 72)(79 184 92 197)(80 183 93 196)(81 208 94 195)(82 207 95 194)(83 206 96 193)(84 205 97 192)(85 204 98 191)(86 203 99 190)(87 202 100 189)(88 201 101 188)(89 200 102 187)(90 199 103 186)(91 198 104 185)(105 412 118 399)(106 411 119 398)(107 410 120 397)(108 409 121 396)(109 408 122 395)(110 407 123 394)(111 406 124 393)(112 405 125 392)(113 404 126 391)(114 403 127 416)(115 402 128 415)(116 401 129 414)(117 400 130 413)(131 162 144 175)(132 161 145 174)(133 160 146 173)(134 159 147 172)(135 158 148 171)(136 157 149 170)(137 182 150 169)(138 181 151 168)(139 180 152 167)(140 179 153 166)(141 178 154 165)(142 177 155 164)(143 176 156 163)(209 381 222 368)(210 380 223 367)(211 379 224 366)(212 378 225 365)(213 377 226 390)(214 376 227 389)(215 375 228 388)(216 374 229 387)(217 373 230 386)(218 372 231 385)(219 371 232 384)(220 370 233 383)(221 369 234 382)(235 425 248 438)(236 424 249 437)(237 423 250 436)(238 422 251 435)(239 421 252 434)(240 420 253 433)(241 419 254 432)(242 418 255 431)(243 417 256 430)(244 442 257 429)(245 441 258 428)(246 440 259 427)(247 439 260 426)(261 323 274 336)(262 322 275 335)(263 321 276 334)(264 320 277 333)(265 319 278 332)(266 318 279 331)(267 317 280 330)(268 316 281 329)(269 315 282 328)(270 314 283 327)(271 313 284 326)(272 338 285 325)(273 337 286 324)(287 452 300 465)(288 451 301 464)(289 450 302 463)(290 449 303 462)(291 448 304 461)(292 447 305 460)(293 446 306 459)(294 445 307 458)(295 444 308 457)(296 443 309 456)(297 468 310 455)(298 467 311 454)(299 466 312 453)

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

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

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

144 conjugacy classes

class 1  2 3A3B4A4B6A6B9A···9F12A12B12C12D13A···13F18A···18F26A···26F36A···36L39A···39L78A···78L117A···117AJ234A···234AJ
order123344669···91212121213···1318···1826···2636···3639···3978···78117···117234···234
size11111313111···1131313132···21···12···213···132···22···22···22···2

144 irreducible representations

dim111111111222222
type+++-
imageC1C2C3C4C6C9C12C18C36D13Dic13C3×D13C3×Dic13C9×D13C9×Dic13
kernelC9×Dic13C234C3×Dic13C117C78Dic13C39C26C13C18C9C6C3C2C1
# reps11222646126612123636

Matrix representation of C9×Dic13 in GL3(𝔽937) generated by

100
09240
00924
,
93600
001
0936150
,
74100
0207367
0496730
G:=sub<GL(3,GF(937))| [1,0,0,0,924,0,0,0,924],[936,0,0,0,0,936,0,1,150],[741,0,0,0,207,496,0,367,730] >;

C9×Dic13 in GAP, Magma, Sage, TeX

C_9\times {\rm Dic}_{13}
% in TeX

G:=Group("C9xDic13");
// GroupNames label

G:=SmallGroup(468,4);
// by ID

G=gap.SmallGroup(468,4);
# by ID

G:=PCGroup([5,-2,-3,-2,-3,-13,30,66,10804]);
// Polycyclic

G:=Group<a,b,c|a^9=b^26=1,c^2=b^13,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

Export

Subgroup lattice of C9×Dic13 in TeX

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