Copied to
clipboard

G = C3×C9×C18order 486 = 2·35

Abelian group of type [3,9,18]

direct product, abelian, monomial, 3-elementary

Aliases: C3×C9×C18, SmallGroup(486,190)

Series: Derived Chief Lower central Upper central

C1 — C3×C9×C18
C1C3C32C33C32×C9C3×C92 — C3×C9×C18
C1 — C3×C9×C18
C1 — C3×C9×C18

Generators and relations for C3×C9×C18
 G = < a,b,c | a3=b9=c18=1, ab=ba, ac=ca, bc=cb >

Subgroups: 252, all normal (8 characteristic)
C1, C2, C3 [×13], C6 [×13], C9 [×36], C32, C32 [×12], C18 [×36], C3×C6, C3×C6 [×12], C3×C9 [×48], C33, C3×C18 [×48], C32×C6, C92 [×9], C32×C9 [×4], C9×C18 [×9], C32×C18 [×4], C3×C92, C3×C9×C18
Quotients: C1, C2, C3 [×13], C6 [×13], C9 [×36], C32 [×13], C18 [×36], C3×C6 [×13], C3×C9 [×48], C33, C3×C18 [×48], C32×C6, C92 [×9], C32×C9 [×4], C9×C18 [×9], C32×C18 [×4], C3×C92, C3×C9×C18

Smallest permutation representation of C3×C9×C18
Regular action on 486 points
Generators in S486
(1 108 433)(2 91 434)(3 92 435)(4 93 436)(5 94 437)(6 95 438)(7 96 439)(8 97 440)(9 98 441)(10 99 442)(11 100 443)(12 101 444)(13 102 445)(14 103 446)(15 104 447)(16 105 448)(17 106 449)(18 107 450)(19 118 158)(20 119 159)(21 120 160)(22 121 161)(23 122 162)(24 123 145)(25 124 146)(26 125 147)(27 126 148)(28 109 149)(29 110 150)(30 111 151)(31 112 152)(32 113 153)(33 114 154)(34 115 155)(35 116 156)(36 117 157)(37 234 237)(38 217 238)(39 218 239)(40 219 240)(41 220 241)(42 221 242)(43 222 243)(44 223 244)(45 224 245)(46 225 246)(47 226 247)(48 227 248)(49 228 249)(50 229 250)(51 230 251)(52 231 252)(53 232 235)(54 233 236)(55 455 399)(56 456 400)(57 457 401)(58 458 402)(59 459 403)(60 460 404)(61 461 405)(62 462 406)(63 463 407)(64 464 408)(65 465 409)(66 466 410)(67 467 411)(68 468 412)(69 451 413)(70 452 414)(71 453 397)(72 454 398)(73 323 396)(74 324 379)(75 307 380)(76 308 381)(77 309 382)(78 310 383)(79 311 384)(80 312 385)(81 313 386)(82 314 387)(83 315 388)(84 316 389)(85 317 390)(86 318 391)(87 319 392)(88 320 393)(89 321 394)(90 322 395)(127 371 163)(128 372 164)(129 373 165)(130 374 166)(131 375 167)(132 376 168)(133 377 169)(134 378 170)(135 361 171)(136 362 172)(137 363 173)(138 364 174)(139 365 175)(140 366 176)(141 367 177)(142 368 178)(143 369 179)(144 370 180)(181 469 428)(182 470 429)(183 471 430)(184 472 431)(185 473 432)(186 474 415)(187 475 416)(188 476 417)(189 477 418)(190 478 419)(191 479 420)(192 480 421)(193 481 422)(194 482 423)(195 483 424)(196 484 425)(197 485 426)(198 486 427)(199 257 285)(200 258 286)(201 259 287)(202 260 288)(203 261 271)(204 262 272)(205 263 273)(206 264 274)(207 265 275)(208 266 276)(209 267 277)(210 268 278)(211 269 279)(212 270 280)(213 253 281)(214 254 282)(215 255 283)(216 256 284)(289 342 358)(290 325 359)(291 326 360)(292 327 343)(293 328 344)(294 329 345)(295 330 346)(296 331 347)(297 332 348)(298 333 349)(299 334 350)(300 335 351)(301 336 352)(302 337 353)(303 338 354)(304 339 355)(305 340 356)(306 341 357)
(1 75 192 164 402 210 156 236 334)(2 76 193 165 403 211 157 237 335)(3 77 194 166 404 212 158 238 336)(4 78 195 167 405 213 159 239 337)(5 79 196 168 406 214 160 240 338)(6 80 197 169 407 215 161 241 339)(7 81 198 170 408 216 162 242 340)(8 82 181 171 409 199 145 243 341)(9 83 182 172 410 200 146 244 342)(10 84 183 173 411 201 147 245 325)(11 85 184 174 412 202 148 246 326)(12 86 185 175 413 203 149 247 327)(13 87 186 176 414 204 150 248 328)(14 88 187 177 397 205 151 249 329)(15 89 188 178 398 206 152 250 330)(16 90 189 179 399 207 153 251 331)(17 73 190 180 400 208 154 252 332)(18 74 191 163 401 209 155 235 333)(19 38 352 92 309 482 130 60 270)(20 39 353 93 310 483 131 61 253)(21 40 354 94 311 484 132 62 254)(22 41 355 95 312 485 133 63 255)(23 42 356 96 313 486 134 64 256)(24 43 357 97 314 469 135 65 257)(25 44 358 98 315 470 136 66 258)(26 45 359 99 316 471 137 67 259)(27 46 360 100 317 472 138 68 260)(28 47 343 101 318 473 139 69 261)(29 48 344 102 319 474 140 70 262)(30 49 345 103 320 475 141 71 263)(31 50 346 104 321 476 142 72 264)(32 51 347 105 322 477 143 55 265)(33 52 348 106 323 478 144 56 266)(34 53 349 107 324 479 127 57 267)(35 54 350 108 307 480 128 58 268)(36 37 351 91 308 481 129 59 269)(109 226 292 444 391 432 365 451 271)(110 227 293 445 392 415 366 452 272)(111 228 294 446 393 416 367 453 273)(112 229 295 447 394 417 368 454 274)(113 230 296 448 395 418 369 455 275)(114 231 297 449 396 419 370 456 276)(115 232 298 450 379 420 371 457 277)(116 233 299 433 380 421 372 458 278)(117 234 300 434 381 422 373 459 279)(118 217 301 435 382 423 374 460 280)(119 218 302 436 383 424 375 461 281)(120 219 303 437 384 425 376 462 282)(121 220 304 438 385 426 377 463 283)(122 221 305 439 386 427 378 464 284)(123 222 306 440 387 428 361 465 285)(124 223 289 441 388 429 362 466 286)(125 224 290 442 389 430 363 467 287)(126 225 291 443 390 431 364 468 288)
(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)(469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486)

G:=sub<Sym(486)| (1,108,433)(2,91,434)(3,92,435)(4,93,436)(5,94,437)(6,95,438)(7,96,439)(8,97,440)(9,98,441)(10,99,442)(11,100,443)(12,101,444)(13,102,445)(14,103,446)(15,104,447)(16,105,448)(17,106,449)(18,107,450)(19,118,158)(20,119,159)(21,120,160)(22,121,161)(23,122,162)(24,123,145)(25,124,146)(26,125,147)(27,126,148)(28,109,149)(29,110,150)(30,111,151)(31,112,152)(32,113,153)(33,114,154)(34,115,155)(35,116,156)(36,117,157)(37,234,237)(38,217,238)(39,218,239)(40,219,240)(41,220,241)(42,221,242)(43,222,243)(44,223,244)(45,224,245)(46,225,246)(47,226,247)(48,227,248)(49,228,249)(50,229,250)(51,230,251)(52,231,252)(53,232,235)(54,233,236)(55,455,399)(56,456,400)(57,457,401)(58,458,402)(59,459,403)(60,460,404)(61,461,405)(62,462,406)(63,463,407)(64,464,408)(65,465,409)(66,466,410)(67,467,411)(68,468,412)(69,451,413)(70,452,414)(71,453,397)(72,454,398)(73,323,396)(74,324,379)(75,307,380)(76,308,381)(77,309,382)(78,310,383)(79,311,384)(80,312,385)(81,313,386)(82,314,387)(83,315,388)(84,316,389)(85,317,390)(86,318,391)(87,319,392)(88,320,393)(89,321,394)(90,322,395)(127,371,163)(128,372,164)(129,373,165)(130,374,166)(131,375,167)(132,376,168)(133,377,169)(134,378,170)(135,361,171)(136,362,172)(137,363,173)(138,364,174)(139,365,175)(140,366,176)(141,367,177)(142,368,178)(143,369,179)(144,370,180)(181,469,428)(182,470,429)(183,471,430)(184,472,431)(185,473,432)(186,474,415)(187,475,416)(188,476,417)(189,477,418)(190,478,419)(191,479,420)(192,480,421)(193,481,422)(194,482,423)(195,483,424)(196,484,425)(197,485,426)(198,486,427)(199,257,285)(200,258,286)(201,259,287)(202,260,288)(203,261,271)(204,262,272)(205,263,273)(206,264,274)(207,265,275)(208,266,276)(209,267,277)(210,268,278)(211,269,279)(212,270,280)(213,253,281)(214,254,282)(215,255,283)(216,256,284)(289,342,358)(290,325,359)(291,326,360)(292,327,343)(293,328,344)(294,329,345)(295,330,346)(296,331,347)(297,332,348)(298,333,349)(299,334,350)(300,335,351)(301,336,352)(302,337,353)(303,338,354)(304,339,355)(305,340,356)(306,341,357), (1,75,192,164,402,210,156,236,334)(2,76,193,165,403,211,157,237,335)(3,77,194,166,404,212,158,238,336)(4,78,195,167,405,213,159,239,337)(5,79,196,168,406,214,160,240,338)(6,80,197,169,407,215,161,241,339)(7,81,198,170,408,216,162,242,340)(8,82,181,171,409,199,145,243,341)(9,83,182,172,410,200,146,244,342)(10,84,183,173,411,201,147,245,325)(11,85,184,174,412,202,148,246,326)(12,86,185,175,413,203,149,247,327)(13,87,186,176,414,204,150,248,328)(14,88,187,177,397,205,151,249,329)(15,89,188,178,398,206,152,250,330)(16,90,189,179,399,207,153,251,331)(17,73,190,180,400,208,154,252,332)(18,74,191,163,401,209,155,235,333)(19,38,352,92,309,482,130,60,270)(20,39,353,93,310,483,131,61,253)(21,40,354,94,311,484,132,62,254)(22,41,355,95,312,485,133,63,255)(23,42,356,96,313,486,134,64,256)(24,43,357,97,314,469,135,65,257)(25,44,358,98,315,470,136,66,258)(26,45,359,99,316,471,137,67,259)(27,46,360,100,317,472,138,68,260)(28,47,343,101,318,473,139,69,261)(29,48,344,102,319,474,140,70,262)(30,49,345,103,320,475,141,71,263)(31,50,346,104,321,476,142,72,264)(32,51,347,105,322,477,143,55,265)(33,52,348,106,323,478,144,56,266)(34,53,349,107,324,479,127,57,267)(35,54,350,108,307,480,128,58,268)(36,37,351,91,308,481,129,59,269)(109,226,292,444,391,432,365,451,271)(110,227,293,445,392,415,366,452,272)(111,228,294,446,393,416,367,453,273)(112,229,295,447,394,417,368,454,274)(113,230,296,448,395,418,369,455,275)(114,231,297,449,396,419,370,456,276)(115,232,298,450,379,420,371,457,277)(116,233,299,433,380,421,372,458,278)(117,234,300,434,381,422,373,459,279)(118,217,301,435,382,423,374,460,280)(119,218,302,436,383,424,375,461,281)(120,219,303,437,384,425,376,462,282)(121,220,304,438,385,426,377,463,283)(122,221,305,439,386,427,378,464,284)(123,222,306,440,387,428,361,465,285)(124,223,289,441,388,429,362,466,286)(125,224,290,442,389,430,363,467,287)(126,225,291,443,390,431,364,468,288), (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)(469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486)>;

G:=Group( (1,108,433)(2,91,434)(3,92,435)(4,93,436)(5,94,437)(6,95,438)(7,96,439)(8,97,440)(9,98,441)(10,99,442)(11,100,443)(12,101,444)(13,102,445)(14,103,446)(15,104,447)(16,105,448)(17,106,449)(18,107,450)(19,118,158)(20,119,159)(21,120,160)(22,121,161)(23,122,162)(24,123,145)(25,124,146)(26,125,147)(27,126,148)(28,109,149)(29,110,150)(30,111,151)(31,112,152)(32,113,153)(33,114,154)(34,115,155)(35,116,156)(36,117,157)(37,234,237)(38,217,238)(39,218,239)(40,219,240)(41,220,241)(42,221,242)(43,222,243)(44,223,244)(45,224,245)(46,225,246)(47,226,247)(48,227,248)(49,228,249)(50,229,250)(51,230,251)(52,231,252)(53,232,235)(54,233,236)(55,455,399)(56,456,400)(57,457,401)(58,458,402)(59,459,403)(60,460,404)(61,461,405)(62,462,406)(63,463,407)(64,464,408)(65,465,409)(66,466,410)(67,467,411)(68,468,412)(69,451,413)(70,452,414)(71,453,397)(72,454,398)(73,323,396)(74,324,379)(75,307,380)(76,308,381)(77,309,382)(78,310,383)(79,311,384)(80,312,385)(81,313,386)(82,314,387)(83,315,388)(84,316,389)(85,317,390)(86,318,391)(87,319,392)(88,320,393)(89,321,394)(90,322,395)(127,371,163)(128,372,164)(129,373,165)(130,374,166)(131,375,167)(132,376,168)(133,377,169)(134,378,170)(135,361,171)(136,362,172)(137,363,173)(138,364,174)(139,365,175)(140,366,176)(141,367,177)(142,368,178)(143,369,179)(144,370,180)(181,469,428)(182,470,429)(183,471,430)(184,472,431)(185,473,432)(186,474,415)(187,475,416)(188,476,417)(189,477,418)(190,478,419)(191,479,420)(192,480,421)(193,481,422)(194,482,423)(195,483,424)(196,484,425)(197,485,426)(198,486,427)(199,257,285)(200,258,286)(201,259,287)(202,260,288)(203,261,271)(204,262,272)(205,263,273)(206,264,274)(207,265,275)(208,266,276)(209,267,277)(210,268,278)(211,269,279)(212,270,280)(213,253,281)(214,254,282)(215,255,283)(216,256,284)(289,342,358)(290,325,359)(291,326,360)(292,327,343)(293,328,344)(294,329,345)(295,330,346)(296,331,347)(297,332,348)(298,333,349)(299,334,350)(300,335,351)(301,336,352)(302,337,353)(303,338,354)(304,339,355)(305,340,356)(306,341,357), (1,75,192,164,402,210,156,236,334)(2,76,193,165,403,211,157,237,335)(3,77,194,166,404,212,158,238,336)(4,78,195,167,405,213,159,239,337)(5,79,196,168,406,214,160,240,338)(6,80,197,169,407,215,161,241,339)(7,81,198,170,408,216,162,242,340)(8,82,181,171,409,199,145,243,341)(9,83,182,172,410,200,146,244,342)(10,84,183,173,411,201,147,245,325)(11,85,184,174,412,202,148,246,326)(12,86,185,175,413,203,149,247,327)(13,87,186,176,414,204,150,248,328)(14,88,187,177,397,205,151,249,329)(15,89,188,178,398,206,152,250,330)(16,90,189,179,399,207,153,251,331)(17,73,190,180,400,208,154,252,332)(18,74,191,163,401,209,155,235,333)(19,38,352,92,309,482,130,60,270)(20,39,353,93,310,483,131,61,253)(21,40,354,94,311,484,132,62,254)(22,41,355,95,312,485,133,63,255)(23,42,356,96,313,486,134,64,256)(24,43,357,97,314,469,135,65,257)(25,44,358,98,315,470,136,66,258)(26,45,359,99,316,471,137,67,259)(27,46,360,100,317,472,138,68,260)(28,47,343,101,318,473,139,69,261)(29,48,344,102,319,474,140,70,262)(30,49,345,103,320,475,141,71,263)(31,50,346,104,321,476,142,72,264)(32,51,347,105,322,477,143,55,265)(33,52,348,106,323,478,144,56,266)(34,53,349,107,324,479,127,57,267)(35,54,350,108,307,480,128,58,268)(36,37,351,91,308,481,129,59,269)(109,226,292,444,391,432,365,451,271)(110,227,293,445,392,415,366,452,272)(111,228,294,446,393,416,367,453,273)(112,229,295,447,394,417,368,454,274)(113,230,296,448,395,418,369,455,275)(114,231,297,449,396,419,370,456,276)(115,232,298,450,379,420,371,457,277)(116,233,299,433,380,421,372,458,278)(117,234,300,434,381,422,373,459,279)(118,217,301,435,382,423,374,460,280)(119,218,302,436,383,424,375,461,281)(120,219,303,437,384,425,376,462,282)(121,220,304,438,385,426,377,463,283)(122,221,305,439,386,427,378,464,284)(123,222,306,440,387,428,361,465,285)(124,223,289,441,388,429,362,466,286)(125,224,290,442,389,430,363,467,287)(126,225,291,443,390,431,364,468,288), (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)(469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486) );

G=PermutationGroup([(1,108,433),(2,91,434),(3,92,435),(4,93,436),(5,94,437),(6,95,438),(7,96,439),(8,97,440),(9,98,441),(10,99,442),(11,100,443),(12,101,444),(13,102,445),(14,103,446),(15,104,447),(16,105,448),(17,106,449),(18,107,450),(19,118,158),(20,119,159),(21,120,160),(22,121,161),(23,122,162),(24,123,145),(25,124,146),(26,125,147),(27,126,148),(28,109,149),(29,110,150),(30,111,151),(31,112,152),(32,113,153),(33,114,154),(34,115,155),(35,116,156),(36,117,157),(37,234,237),(38,217,238),(39,218,239),(40,219,240),(41,220,241),(42,221,242),(43,222,243),(44,223,244),(45,224,245),(46,225,246),(47,226,247),(48,227,248),(49,228,249),(50,229,250),(51,230,251),(52,231,252),(53,232,235),(54,233,236),(55,455,399),(56,456,400),(57,457,401),(58,458,402),(59,459,403),(60,460,404),(61,461,405),(62,462,406),(63,463,407),(64,464,408),(65,465,409),(66,466,410),(67,467,411),(68,468,412),(69,451,413),(70,452,414),(71,453,397),(72,454,398),(73,323,396),(74,324,379),(75,307,380),(76,308,381),(77,309,382),(78,310,383),(79,311,384),(80,312,385),(81,313,386),(82,314,387),(83,315,388),(84,316,389),(85,317,390),(86,318,391),(87,319,392),(88,320,393),(89,321,394),(90,322,395),(127,371,163),(128,372,164),(129,373,165),(130,374,166),(131,375,167),(132,376,168),(133,377,169),(134,378,170),(135,361,171),(136,362,172),(137,363,173),(138,364,174),(139,365,175),(140,366,176),(141,367,177),(142,368,178),(143,369,179),(144,370,180),(181,469,428),(182,470,429),(183,471,430),(184,472,431),(185,473,432),(186,474,415),(187,475,416),(188,476,417),(189,477,418),(190,478,419),(191,479,420),(192,480,421),(193,481,422),(194,482,423),(195,483,424),(196,484,425),(197,485,426),(198,486,427),(199,257,285),(200,258,286),(201,259,287),(202,260,288),(203,261,271),(204,262,272),(205,263,273),(206,264,274),(207,265,275),(208,266,276),(209,267,277),(210,268,278),(211,269,279),(212,270,280),(213,253,281),(214,254,282),(215,255,283),(216,256,284),(289,342,358),(290,325,359),(291,326,360),(292,327,343),(293,328,344),(294,329,345),(295,330,346),(296,331,347),(297,332,348),(298,333,349),(299,334,350),(300,335,351),(301,336,352),(302,337,353),(303,338,354),(304,339,355),(305,340,356),(306,341,357)], [(1,75,192,164,402,210,156,236,334),(2,76,193,165,403,211,157,237,335),(3,77,194,166,404,212,158,238,336),(4,78,195,167,405,213,159,239,337),(5,79,196,168,406,214,160,240,338),(6,80,197,169,407,215,161,241,339),(7,81,198,170,408,216,162,242,340),(8,82,181,171,409,199,145,243,341),(9,83,182,172,410,200,146,244,342),(10,84,183,173,411,201,147,245,325),(11,85,184,174,412,202,148,246,326),(12,86,185,175,413,203,149,247,327),(13,87,186,176,414,204,150,248,328),(14,88,187,177,397,205,151,249,329),(15,89,188,178,398,206,152,250,330),(16,90,189,179,399,207,153,251,331),(17,73,190,180,400,208,154,252,332),(18,74,191,163,401,209,155,235,333),(19,38,352,92,309,482,130,60,270),(20,39,353,93,310,483,131,61,253),(21,40,354,94,311,484,132,62,254),(22,41,355,95,312,485,133,63,255),(23,42,356,96,313,486,134,64,256),(24,43,357,97,314,469,135,65,257),(25,44,358,98,315,470,136,66,258),(26,45,359,99,316,471,137,67,259),(27,46,360,100,317,472,138,68,260),(28,47,343,101,318,473,139,69,261),(29,48,344,102,319,474,140,70,262),(30,49,345,103,320,475,141,71,263),(31,50,346,104,321,476,142,72,264),(32,51,347,105,322,477,143,55,265),(33,52,348,106,323,478,144,56,266),(34,53,349,107,324,479,127,57,267),(35,54,350,108,307,480,128,58,268),(36,37,351,91,308,481,129,59,269),(109,226,292,444,391,432,365,451,271),(110,227,293,445,392,415,366,452,272),(111,228,294,446,393,416,367,453,273),(112,229,295,447,394,417,368,454,274),(113,230,296,448,395,418,369,455,275),(114,231,297,449,396,419,370,456,276),(115,232,298,450,379,420,371,457,277),(116,233,299,433,380,421,372,458,278),(117,234,300,434,381,422,373,459,279),(118,217,301,435,382,423,374,460,280),(119,218,302,436,383,424,375,461,281),(120,219,303,437,384,425,376,462,282),(121,220,304,438,385,426,377,463,283),(122,221,305,439,386,427,378,464,284),(123,222,306,440,387,428,361,465,285),(124,223,289,441,388,429,362,466,286),(125,224,290,442,389,430,363,467,287),(126,225,291,443,390,431,364,468,288)], [(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),(469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486)])

486 conjugacy classes

class 1  2 3A···3Z6A···6Z9A···9HH18A···18HH
order123···36···69···918···18
size111···11···11···11···1

486 irreducible representations

dim11111111
type++
imageC1C2C3C3C6C6C9C18
kernelC3×C9×C18C3×C92C9×C18C32×C18C92C32×C9C3×C18C3×C9
# reps11188188216216

Matrix representation of C3×C9×C18 in GL3(𝔽19) generated by

1100
010
007
,
600
090
006
,
1600
0130
0013
G:=sub<GL(3,GF(19))| [11,0,0,0,1,0,0,0,7],[6,0,0,0,9,0,0,0,6],[16,0,0,0,13,0,0,0,13] >;

C3×C9×C18 in GAP, Magma, Sage, TeX

C_3\times C_9\times C_{18}
% in TeX

G:=Group("C3xC9xC18");
// GroupNames label

G:=SmallGroup(486,190);
// by ID

G=gap.SmallGroup(486,190);
# by ID

G:=PCGroup([6,-2,-3,-3,-3,-3,-3,331,500]);
// Polycyclic

G:=Group<a,b,c|a^3=b^9=c^18=1,a*b=b*a,a*c=c*a,b*c=c*b>;
// generators/relations

׿
×
𝔽