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G = C33×C18order 486 = 2·35

Abelian group of type [3,3,3,18]

direct product, abelian, monomial, 3-elementary

Aliases: C33×C18, SmallGroup(486,250)

Series: Derived Chief Lower central Upper central

C1 — C33×C18
C1C3C32C33C34C33×C9 — C33×C18
C1 — C33×C18
C1 — C33×C18

Generators and relations for C33×C18
 G = < a,b,c,d | a3=b3=c3=d18=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, cd=dc >

Subgroups: 792, all normal (8 characteristic)
C1, C2, C3, C3 [×39], C6, C6 [×39], C9 [×27], C32 [×130], C18 [×27], C3×C6 [×130], C3×C9 [×117], C33 [×40], C3×C18 [×117], C32×C6 [×40], C32×C9 [×39], C34, C32×C18 [×39], C33×C6, C33×C9, C33×C18
Quotients: C1, C2, C3 [×40], C6 [×40], C9 [×27], C32 [×130], C18 [×27], C3×C6 [×130], C3×C9 [×117], C33 [×40], C3×C18 [×117], C32×C6 [×40], C32×C9 [×39], C34, C32×C18 [×39], C33×C6, C33×C9, C33×C18

Smallest permutation representation of C33×C18
Regular action on 486 points
Generators in S486
(1 434 165)(2 435 166)(3 436 167)(4 437 168)(5 438 169)(6 439 170)(7 440 171)(8 441 172)(9 442 173)(10 443 174)(11 444 175)(12 445 176)(13 446 177)(14 447 178)(15 448 179)(16 449 180)(17 450 163)(18 433 164)(19 156 310)(20 157 311)(21 158 312)(22 159 313)(23 160 314)(24 161 315)(25 162 316)(26 145 317)(27 146 318)(28 147 319)(29 148 320)(30 149 321)(31 150 322)(32 151 323)(33 152 324)(34 153 307)(35 154 308)(36 155 309)(37 185 250)(38 186 251)(39 187 252)(40 188 235)(41 189 236)(42 190 237)(43 191 238)(44 192 239)(45 193 240)(46 194 241)(47 195 242)(48 196 243)(49 197 244)(50 198 245)(51 181 246)(52 182 247)(53 183 248)(54 184 249)(55 114 399)(56 115 400)(57 116 401)(58 117 402)(59 118 403)(60 119 404)(61 120 405)(62 121 406)(63 122 407)(64 123 408)(65 124 409)(66 125 410)(67 126 411)(68 109 412)(69 110 413)(70 111 414)(71 112 397)(72 113 398)(73 452 282)(74 453 283)(75 454 284)(76 455 285)(77 456 286)(78 457 287)(79 458 288)(80 459 271)(81 460 272)(82 461 273)(83 462 274)(84 463 275)(85 464 276)(86 465 277)(87 466 278)(88 467 279)(89 468 280)(90 451 281)(91 431 385)(92 432 386)(93 415 387)(94 416 388)(95 417 389)(96 418 390)(97 419 391)(98 420 392)(99 421 393)(100 422 394)(101 423 395)(102 424 396)(103 425 379)(104 426 380)(105 427 381)(106 428 382)(107 429 383)(108 430 384)(127 351 472)(128 352 473)(129 353 474)(130 354 475)(131 355 476)(132 356 477)(133 357 478)(134 358 479)(135 359 480)(136 360 481)(137 343 482)(138 344 483)(139 345 484)(140 346 485)(141 347 486)(142 348 469)(143 349 470)(144 350 471)(199 234 333)(200 217 334)(201 218 335)(202 219 336)(203 220 337)(204 221 338)(205 222 339)(206 223 340)(207 224 341)(208 225 342)(209 226 325)(210 227 326)(211 228 327)(212 229 328)(213 230 329)(214 231 330)(215 232 331)(216 233 332)(253 375 293)(254 376 294)(255 377 295)(256 378 296)(257 361 297)(258 362 298)(259 363 299)(260 364 300)(261 365 301)(262 366 302)(263 367 303)(264 368 304)(265 369 305)(266 370 306)(267 371 289)(268 372 290)(269 373 291)(270 374 292)
(1 130 240)(2 131 241)(3 132 242)(4 133 243)(5 134 244)(6 135 245)(7 136 246)(8 137 247)(9 138 248)(10 139 249)(11 140 250)(12 141 251)(13 142 252)(14 143 235)(15 144 236)(16 127 237)(17 128 238)(18 129 239)(19 70 327)(20 71 328)(21 72 329)(22 55 330)(23 56 331)(24 57 332)(25 58 333)(26 59 334)(27 60 335)(28 61 336)(29 62 337)(30 63 338)(31 64 339)(32 65 340)(33 66 341)(34 67 342)(35 68 325)(36 69 326)(37 444 346)(38 445 347)(39 446 348)(40 447 349)(41 448 350)(42 449 351)(43 450 352)(44 433 353)(45 434 354)(46 435 355)(47 436 356)(48 437 357)(49 438 358)(50 439 359)(51 440 360)(52 441 343)(53 442 344)(54 443 345)(73 367 385)(74 368 386)(75 369 387)(76 370 388)(77 371 389)(78 372 390)(79 373 391)(80 374 392)(81 375 393)(82 376 394)(83 377 395)(84 378 396)(85 361 379)(86 362 380)(87 363 381)(88 364 382)(89 365 383)(90 366 384)(91 452 303)(92 453 304)(93 454 305)(94 455 306)(95 456 289)(96 457 290)(97 458 291)(98 459 292)(99 460 293)(100 461 294)(101 462 295)(102 463 296)(103 464 297)(104 465 298)(105 466 299)(106 467 300)(107 468 301)(108 451 302)(109 209 154)(110 210 155)(111 211 156)(112 212 157)(113 213 158)(114 214 159)(115 215 160)(116 216 161)(117 199 162)(118 200 145)(119 201 146)(120 202 147)(121 203 148)(122 204 149)(123 205 150)(124 206 151)(125 207 152)(126 208 153)(163 473 191)(164 474 192)(165 475 193)(166 476 194)(167 477 195)(168 478 196)(169 479 197)(170 480 198)(171 481 181)(172 482 182)(173 483 183)(174 484 184)(175 485 185)(176 486 186)(177 469 187)(178 470 188)(179 471 189)(180 472 190)(217 317 403)(218 318 404)(219 319 405)(220 320 406)(221 321 407)(222 322 408)(223 323 409)(224 324 410)(225 307 411)(226 308 412)(227 309 413)(228 310 414)(229 311 397)(230 312 398)(231 313 399)(232 314 400)(233 315 401)(234 316 402)(253 421 272)(254 422 273)(255 423 274)(256 424 275)(257 425 276)(258 426 277)(259 427 278)(260 428 279)(261 429 280)(262 430 281)(263 431 282)(264 432 283)(265 415 284)(266 416 285)(267 417 286)(268 418 287)(269 419 288)(270 420 271)
(1 214 462)(2 215 463)(3 216 464)(4 199 465)(5 200 466)(6 201 467)(7 202 468)(8 203 451)(9 204 452)(10 205 453)(11 206 454)(12 207 455)(13 208 456)(14 209 457)(15 210 458)(16 211 459)(17 212 460)(18 213 461)(19 374 472)(20 375 473)(21 376 474)(22 377 475)(23 378 476)(24 361 477)(25 362 478)(26 363 479)(27 364 480)(28 365 481)(29 366 482)(30 367 483)(31 368 484)(32 369 485)(33 370 486)(34 371 469)(35 372 470)(36 373 471)(37 409 415)(38 410 416)(39 411 417)(40 412 418)(41 413 419)(42 414 420)(43 397 421)(44 398 422)(45 399 423)(46 400 424)(47 401 425)(48 402 426)(49 403 427)(50 404 428)(51 405 429)(52 406 430)(53 407 431)(54 408 432)(55 395 193)(56 396 194)(57 379 195)(58 380 196)(59 381 197)(60 382 198)(61 383 181)(62 384 182)(63 385 183)(64 386 184)(65 387 185)(66 388 186)(67 389 187)(68 390 188)(69 391 189)(70 392 190)(71 393 191)(72 394 192)(73 173 338)(74 174 339)(75 175 340)(76 176 341)(77 177 342)(78 178 325)(79 179 326)(80 180 327)(81 163 328)(82 164 329)(83 165 330)(84 166 331)(85 167 332)(86 168 333)(87 169 334)(88 170 335)(89 171 336)(90 172 337)(91 248 122)(92 249 123)(93 250 124)(94 251 125)(95 252 126)(96 235 109)(97 236 110)(98 237 111)(99 238 112)(100 239 113)(101 240 114)(102 241 115)(103 242 116)(104 243 117)(105 244 118)(106 245 119)(107 246 120)(108 247 121)(127 156 292)(128 157 293)(129 158 294)(130 159 295)(131 160 296)(132 161 297)(133 162 298)(134 145 299)(135 146 300)(136 147 301)(137 148 302)(138 149 303)(139 150 304)(140 151 305)(141 152 306)(142 153 289)(143 154 290)(144 155 291)(217 278 438)(218 279 439)(219 280 440)(220 281 441)(221 282 442)(222 283 443)(223 284 444)(224 285 445)(225 286 446)(226 287 447)(227 288 448)(228 271 449)(229 272 450)(230 273 433)(231 274 434)(232 275 435)(233 276 436)(234 277 437)(253 352 311)(254 353 312)(255 354 313)(256 355 314)(257 356 315)(258 357 316)(259 358 317)(260 359 318)(261 360 319)(262 343 320)(263 344 321)(264 345 322)(265 346 323)(266 347 324)(267 348 307)(268 349 308)(269 350 309)(270 351 310)
(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)| (1,434,165)(2,435,166)(3,436,167)(4,437,168)(5,438,169)(6,439,170)(7,440,171)(8,441,172)(9,442,173)(10,443,174)(11,444,175)(12,445,176)(13,446,177)(14,447,178)(15,448,179)(16,449,180)(17,450,163)(18,433,164)(19,156,310)(20,157,311)(21,158,312)(22,159,313)(23,160,314)(24,161,315)(25,162,316)(26,145,317)(27,146,318)(28,147,319)(29,148,320)(30,149,321)(31,150,322)(32,151,323)(33,152,324)(34,153,307)(35,154,308)(36,155,309)(37,185,250)(38,186,251)(39,187,252)(40,188,235)(41,189,236)(42,190,237)(43,191,238)(44,192,239)(45,193,240)(46,194,241)(47,195,242)(48,196,243)(49,197,244)(50,198,245)(51,181,246)(52,182,247)(53,183,248)(54,184,249)(55,114,399)(56,115,400)(57,116,401)(58,117,402)(59,118,403)(60,119,404)(61,120,405)(62,121,406)(63,122,407)(64,123,408)(65,124,409)(66,125,410)(67,126,411)(68,109,412)(69,110,413)(70,111,414)(71,112,397)(72,113,398)(73,452,282)(74,453,283)(75,454,284)(76,455,285)(77,456,286)(78,457,287)(79,458,288)(80,459,271)(81,460,272)(82,461,273)(83,462,274)(84,463,275)(85,464,276)(86,465,277)(87,466,278)(88,467,279)(89,468,280)(90,451,281)(91,431,385)(92,432,386)(93,415,387)(94,416,388)(95,417,389)(96,418,390)(97,419,391)(98,420,392)(99,421,393)(100,422,394)(101,423,395)(102,424,396)(103,425,379)(104,426,380)(105,427,381)(106,428,382)(107,429,383)(108,430,384)(127,351,472)(128,352,473)(129,353,474)(130,354,475)(131,355,476)(132,356,477)(133,357,478)(134,358,479)(135,359,480)(136,360,481)(137,343,482)(138,344,483)(139,345,484)(140,346,485)(141,347,486)(142,348,469)(143,349,470)(144,350,471)(199,234,333)(200,217,334)(201,218,335)(202,219,336)(203,220,337)(204,221,338)(205,222,339)(206,223,340)(207,224,341)(208,225,342)(209,226,325)(210,227,326)(211,228,327)(212,229,328)(213,230,329)(214,231,330)(215,232,331)(216,233,332)(253,375,293)(254,376,294)(255,377,295)(256,378,296)(257,361,297)(258,362,298)(259,363,299)(260,364,300)(261,365,301)(262,366,302)(263,367,303)(264,368,304)(265,369,305)(266,370,306)(267,371,289)(268,372,290)(269,373,291)(270,374,292), (1,130,240)(2,131,241)(3,132,242)(4,133,243)(5,134,244)(6,135,245)(7,136,246)(8,137,247)(9,138,248)(10,139,249)(11,140,250)(12,141,251)(13,142,252)(14,143,235)(15,144,236)(16,127,237)(17,128,238)(18,129,239)(19,70,327)(20,71,328)(21,72,329)(22,55,330)(23,56,331)(24,57,332)(25,58,333)(26,59,334)(27,60,335)(28,61,336)(29,62,337)(30,63,338)(31,64,339)(32,65,340)(33,66,341)(34,67,342)(35,68,325)(36,69,326)(37,444,346)(38,445,347)(39,446,348)(40,447,349)(41,448,350)(42,449,351)(43,450,352)(44,433,353)(45,434,354)(46,435,355)(47,436,356)(48,437,357)(49,438,358)(50,439,359)(51,440,360)(52,441,343)(53,442,344)(54,443,345)(73,367,385)(74,368,386)(75,369,387)(76,370,388)(77,371,389)(78,372,390)(79,373,391)(80,374,392)(81,375,393)(82,376,394)(83,377,395)(84,378,396)(85,361,379)(86,362,380)(87,363,381)(88,364,382)(89,365,383)(90,366,384)(91,452,303)(92,453,304)(93,454,305)(94,455,306)(95,456,289)(96,457,290)(97,458,291)(98,459,292)(99,460,293)(100,461,294)(101,462,295)(102,463,296)(103,464,297)(104,465,298)(105,466,299)(106,467,300)(107,468,301)(108,451,302)(109,209,154)(110,210,155)(111,211,156)(112,212,157)(113,213,158)(114,214,159)(115,215,160)(116,216,161)(117,199,162)(118,200,145)(119,201,146)(120,202,147)(121,203,148)(122,204,149)(123,205,150)(124,206,151)(125,207,152)(126,208,153)(163,473,191)(164,474,192)(165,475,193)(166,476,194)(167,477,195)(168,478,196)(169,479,197)(170,480,198)(171,481,181)(172,482,182)(173,483,183)(174,484,184)(175,485,185)(176,486,186)(177,469,187)(178,470,188)(179,471,189)(180,472,190)(217,317,403)(218,318,404)(219,319,405)(220,320,406)(221,321,407)(222,322,408)(223,323,409)(224,324,410)(225,307,411)(226,308,412)(227,309,413)(228,310,414)(229,311,397)(230,312,398)(231,313,399)(232,314,400)(233,315,401)(234,316,402)(253,421,272)(254,422,273)(255,423,274)(256,424,275)(257,425,276)(258,426,277)(259,427,278)(260,428,279)(261,429,280)(262,430,281)(263,431,282)(264,432,283)(265,415,284)(266,416,285)(267,417,286)(268,418,287)(269,419,288)(270,420,271), (1,214,462)(2,215,463)(3,216,464)(4,199,465)(5,200,466)(6,201,467)(7,202,468)(8,203,451)(9,204,452)(10,205,453)(11,206,454)(12,207,455)(13,208,456)(14,209,457)(15,210,458)(16,211,459)(17,212,460)(18,213,461)(19,374,472)(20,375,473)(21,376,474)(22,377,475)(23,378,476)(24,361,477)(25,362,478)(26,363,479)(27,364,480)(28,365,481)(29,366,482)(30,367,483)(31,368,484)(32,369,485)(33,370,486)(34,371,469)(35,372,470)(36,373,471)(37,409,415)(38,410,416)(39,411,417)(40,412,418)(41,413,419)(42,414,420)(43,397,421)(44,398,422)(45,399,423)(46,400,424)(47,401,425)(48,402,426)(49,403,427)(50,404,428)(51,405,429)(52,406,430)(53,407,431)(54,408,432)(55,395,193)(56,396,194)(57,379,195)(58,380,196)(59,381,197)(60,382,198)(61,383,181)(62,384,182)(63,385,183)(64,386,184)(65,387,185)(66,388,186)(67,389,187)(68,390,188)(69,391,189)(70,392,190)(71,393,191)(72,394,192)(73,173,338)(74,174,339)(75,175,340)(76,176,341)(77,177,342)(78,178,325)(79,179,326)(80,180,327)(81,163,328)(82,164,329)(83,165,330)(84,166,331)(85,167,332)(86,168,333)(87,169,334)(88,170,335)(89,171,336)(90,172,337)(91,248,122)(92,249,123)(93,250,124)(94,251,125)(95,252,126)(96,235,109)(97,236,110)(98,237,111)(99,238,112)(100,239,113)(101,240,114)(102,241,115)(103,242,116)(104,243,117)(105,244,118)(106,245,119)(107,246,120)(108,247,121)(127,156,292)(128,157,293)(129,158,294)(130,159,295)(131,160,296)(132,161,297)(133,162,298)(134,145,299)(135,146,300)(136,147,301)(137,148,302)(138,149,303)(139,150,304)(140,151,305)(141,152,306)(142,153,289)(143,154,290)(144,155,291)(217,278,438)(218,279,439)(219,280,440)(220,281,441)(221,282,442)(222,283,443)(223,284,444)(224,285,445)(225,286,446)(226,287,447)(227,288,448)(228,271,449)(229,272,450)(230,273,433)(231,274,434)(232,275,435)(233,276,436)(234,277,437)(253,352,311)(254,353,312)(255,354,313)(256,355,314)(257,356,315)(258,357,316)(259,358,317)(260,359,318)(261,360,319)(262,343,320)(263,344,321)(264,345,322)(265,346,323)(266,347,324)(267,348,307)(268,349,308)(269,350,309)(270,351,310), (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( (1,434,165)(2,435,166)(3,436,167)(4,437,168)(5,438,169)(6,439,170)(7,440,171)(8,441,172)(9,442,173)(10,443,174)(11,444,175)(12,445,176)(13,446,177)(14,447,178)(15,448,179)(16,449,180)(17,450,163)(18,433,164)(19,156,310)(20,157,311)(21,158,312)(22,159,313)(23,160,314)(24,161,315)(25,162,316)(26,145,317)(27,146,318)(28,147,319)(29,148,320)(30,149,321)(31,150,322)(32,151,323)(33,152,324)(34,153,307)(35,154,308)(36,155,309)(37,185,250)(38,186,251)(39,187,252)(40,188,235)(41,189,236)(42,190,237)(43,191,238)(44,192,239)(45,193,240)(46,194,241)(47,195,242)(48,196,243)(49,197,244)(50,198,245)(51,181,246)(52,182,247)(53,183,248)(54,184,249)(55,114,399)(56,115,400)(57,116,401)(58,117,402)(59,118,403)(60,119,404)(61,120,405)(62,121,406)(63,122,407)(64,123,408)(65,124,409)(66,125,410)(67,126,411)(68,109,412)(69,110,413)(70,111,414)(71,112,397)(72,113,398)(73,452,282)(74,453,283)(75,454,284)(76,455,285)(77,456,286)(78,457,287)(79,458,288)(80,459,271)(81,460,272)(82,461,273)(83,462,274)(84,463,275)(85,464,276)(86,465,277)(87,466,278)(88,467,279)(89,468,280)(90,451,281)(91,431,385)(92,432,386)(93,415,387)(94,416,388)(95,417,389)(96,418,390)(97,419,391)(98,420,392)(99,421,393)(100,422,394)(101,423,395)(102,424,396)(103,425,379)(104,426,380)(105,427,381)(106,428,382)(107,429,383)(108,430,384)(127,351,472)(128,352,473)(129,353,474)(130,354,475)(131,355,476)(132,356,477)(133,357,478)(134,358,479)(135,359,480)(136,360,481)(137,343,482)(138,344,483)(139,345,484)(140,346,485)(141,347,486)(142,348,469)(143,349,470)(144,350,471)(199,234,333)(200,217,334)(201,218,335)(202,219,336)(203,220,337)(204,221,338)(205,222,339)(206,223,340)(207,224,341)(208,225,342)(209,226,325)(210,227,326)(211,228,327)(212,229,328)(213,230,329)(214,231,330)(215,232,331)(216,233,332)(253,375,293)(254,376,294)(255,377,295)(256,378,296)(257,361,297)(258,362,298)(259,363,299)(260,364,300)(261,365,301)(262,366,302)(263,367,303)(264,368,304)(265,369,305)(266,370,306)(267,371,289)(268,372,290)(269,373,291)(270,374,292), (1,130,240)(2,131,241)(3,132,242)(4,133,243)(5,134,244)(6,135,245)(7,136,246)(8,137,247)(9,138,248)(10,139,249)(11,140,250)(12,141,251)(13,142,252)(14,143,235)(15,144,236)(16,127,237)(17,128,238)(18,129,239)(19,70,327)(20,71,328)(21,72,329)(22,55,330)(23,56,331)(24,57,332)(25,58,333)(26,59,334)(27,60,335)(28,61,336)(29,62,337)(30,63,338)(31,64,339)(32,65,340)(33,66,341)(34,67,342)(35,68,325)(36,69,326)(37,444,346)(38,445,347)(39,446,348)(40,447,349)(41,448,350)(42,449,351)(43,450,352)(44,433,353)(45,434,354)(46,435,355)(47,436,356)(48,437,357)(49,438,358)(50,439,359)(51,440,360)(52,441,343)(53,442,344)(54,443,345)(73,367,385)(74,368,386)(75,369,387)(76,370,388)(77,371,389)(78,372,390)(79,373,391)(80,374,392)(81,375,393)(82,376,394)(83,377,395)(84,378,396)(85,361,379)(86,362,380)(87,363,381)(88,364,382)(89,365,383)(90,366,384)(91,452,303)(92,453,304)(93,454,305)(94,455,306)(95,456,289)(96,457,290)(97,458,291)(98,459,292)(99,460,293)(100,461,294)(101,462,295)(102,463,296)(103,464,297)(104,465,298)(105,466,299)(106,467,300)(107,468,301)(108,451,302)(109,209,154)(110,210,155)(111,211,156)(112,212,157)(113,213,158)(114,214,159)(115,215,160)(116,216,161)(117,199,162)(118,200,145)(119,201,146)(120,202,147)(121,203,148)(122,204,149)(123,205,150)(124,206,151)(125,207,152)(126,208,153)(163,473,191)(164,474,192)(165,475,193)(166,476,194)(167,477,195)(168,478,196)(169,479,197)(170,480,198)(171,481,181)(172,482,182)(173,483,183)(174,484,184)(175,485,185)(176,486,186)(177,469,187)(178,470,188)(179,471,189)(180,472,190)(217,317,403)(218,318,404)(219,319,405)(220,320,406)(221,321,407)(222,322,408)(223,323,409)(224,324,410)(225,307,411)(226,308,412)(227,309,413)(228,310,414)(229,311,397)(230,312,398)(231,313,399)(232,314,400)(233,315,401)(234,316,402)(253,421,272)(254,422,273)(255,423,274)(256,424,275)(257,425,276)(258,426,277)(259,427,278)(260,428,279)(261,429,280)(262,430,281)(263,431,282)(264,432,283)(265,415,284)(266,416,285)(267,417,286)(268,418,287)(269,419,288)(270,420,271), (1,214,462)(2,215,463)(3,216,464)(4,199,465)(5,200,466)(6,201,467)(7,202,468)(8,203,451)(9,204,452)(10,205,453)(11,206,454)(12,207,455)(13,208,456)(14,209,457)(15,210,458)(16,211,459)(17,212,460)(18,213,461)(19,374,472)(20,375,473)(21,376,474)(22,377,475)(23,378,476)(24,361,477)(25,362,478)(26,363,479)(27,364,480)(28,365,481)(29,366,482)(30,367,483)(31,368,484)(32,369,485)(33,370,486)(34,371,469)(35,372,470)(36,373,471)(37,409,415)(38,410,416)(39,411,417)(40,412,418)(41,413,419)(42,414,420)(43,397,421)(44,398,422)(45,399,423)(46,400,424)(47,401,425)(48,402,426)(49,403,427)(50,404,428)(51,405,429)(52,406,430)(53,407,431)(54,408,432)(55,395,193)(56,396,194)(57,379,195)(58,380,196)(59,381,197)(60,382,198)(61,383,181)(62,384,182)(63,385,183)(64,386,184)(65,387,185)(66,388,186)(67,389,187)(68,390,188)(69,391,189)(70,392,190)(71,393,191)(72,394,192)(73,173,338)(74,174,339)(75,175,340)(76,176,341)(77,177,342)(78,178,325)(79,179,326)(80,180,327)(81,163,328)(82,164,329)(83,165,330)(84,166,331)(85,167,332)(86,168,333)(87,169,334)(88,170,335)(89,171,336)(90,172,337)(91,248,122)(92,249,123)(93,250,124)(94,251,125)(95,252,126)(96,235,109)(97,236,110)(98,237,111)(99,238,112)(100,239,113)(101,240,114)(102,241,115)(103,242,116)(104,243,117)(105,244,118)(106,245,119)(107,246,120)(108,247,121)(127,156,292)(128,157,293)(129,158,294)(130,159,295)(131,160,296)(132,161,297)(133,162,298)(134,145,299)(135,146,300)(136,147,301)(137,148,302)(138,149,303)(139,150,304)(140,151,305)(141,152,306)(142,153,289)(143,154,290)(144,155,291)(217,278,438)(218,279,439)(219,280,440)(220,281,441)(221,282,442)(222,283,443)(223,284,444)(224,285,445)(225,286,446)(226,287,447)(227,288,448)(228,271,449)(229,272,450)(230,273,433)(231,274,434)(232,275,435)(233,276,436)(234,277,437)(253,352,311)(254,353,312)(255,354,313)(256,355,314)(257,356,315)(258,357,316)(259,358,317)(260,359,318)(261,360,319)(262,343,320)(263,344,321)(264,345,322)(265,346,323)(266,347,324)(267,348,307)(268,349,308)(269,350,309)(270,351,310), (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([(1,434,165),(2,435,166),(3,436,167),(4,437,168),(5,438,169),(6,439,170),(7,440,171),(8,441,172),(9,442,173),(10,443,174),(11,444,175),(12,445,176),(13,446,177),(14,447,178),(15,448,179),(16,449,180),(17,450,163),(18,433,164),(19,156,310),(20,157,311),(21,158,312),(22,159,313),(23,160,314),(24,161,315),(25,162,316),(26,145,317),(27,146,318),(28,147,319),(29,148,320),(30,149,321),(31,150,322),(32,151,323),(33,152,324),(34,153,307),(35,154,308),(36,155,309),(37,185,250),(38,186,251),(39,187,252),(40,188,235),(41,189,236),(42,190,237),(43,191,238),(44,192,239),(45,193,240),(46,194,241),(47,195,242),(48,196,243),(49,197,244),(50,198,245),(51,181,246),(52,182,247),(53,183,248),(54,184,249),(55,114,399),(56,115,400),(57,116,401),(58,117,402),(59,118,403),(60,119,404),(61,120,405),(62,121,406),(63,122,407),(64,123,408),(65,124,409),(66,125,410),(67,126,411),(68,109,412),(69,110,413),(70,111,414),(71,112,397),(72,113,398),(73,452,282),(74,453,283),(75,454,284),(76,455,285),(77,456,286),(78,457,287),(79,458,288),(80,459,271),(81,460,272),(82,461,273),(83,462,274),(84,463,275),(85,464,276),(86,465,277),(87,466,278),(88,467,279),(89,468,280),(90,451,281),(91,431,385),(92,432,386),(93,415,387),(94,416,388),(95,417,389),(96,418,390),(97,419,391),(98,420,392),(99,421,393),(100,422,394),(101,423,395),(102,424,396),(103,425,379),(104,426,380),(105,427,381),(106,428,382),(107,429,383),(108,430,384),(127,351,472),(128,352,473),(129,353,474),(130,354,475),(131,355,476),(132,356,477),(133,357,478),(134,358,479),(135,359,480),(136,360,481),(137,343,482),(138,344,483),(139,345,484),(140,346,485),(141,347,486),(142,348,469),(143,349,470),(144,350,471),(199,234,333),(200,217,334),(201,218,335),(202,219,336),(203,220,337),(204,221,338),(205,222,339),(206,223,340),(207,224,341),(208,225,342),(209,226,325),(210,227,326),(211,228,327),(212,229,328),(213,230,329),(214,231,330),(215,232,331),(216,233,332),(253,375,293),(254,376,294),(255,377,295),(256,378,296),(257,361,297),(258,362,298),(259,363,299),(260,364,300),(261,365,301),(262,366,302),(263,367,303),(264,368,304),(265,369,305),(266,370,306),(267,371,289),(268,372,290),(269,373,291),(270,374,292)], [(1,130,240),(2,131,241),(3,132,242),(4,133,243),(5,134,244),(6,135,245),(7,136,246),(8,137,247),(9,138,248),(10,139,249),(11,140,250),(12,141,251),(13,142,252),(14,143,235),(15,144,236),(16,127,237),(17,128,238),(18,129,239),(19,70,327),(20,71,328),(21,72,329),(22,55,330),(23,56,331),(24,57,332),(25,58,333),(26,59,334),(27,60,335),(28,61,336),(29,62,337),(30,63,338),(31,64,339),(32,65,340),(33,66,341),(34,67,342),(35,68,325),(36,69,326),(37,444,346),(38,445,347),(39,446,348),(40,447,349),(41,448,350),(42,449,351),(43,450,352),(44,433,353),(45,434,354),(46,435,355),(47,436,356),(48,437,357),(49,438,358),(50,439,359),(51,440,360),(52,441,343),(53,442,344),(54,443,345),(73,367,385),(74,368,386),(75,369,387),(76,370,388),(77,371,389),(78,372,390),(79,373,391),(80,374,392),(81,375,393),(82,376,394),(83,377,395),(84,378,396),(85,361,379),(86,362,380),(87,363,381),(88,364,382),(89,365,383),(90,366,384),(91,452,303),(92,453,304),(93,454,305),(94,455,306),(95,456,289),(96,457,290),(97,458,291),(98,459,292),(99,460,293),(100,461,294),(101,462,295),(102,463,296),(103,464,297),(104,465,298),(105,466,299),(106,467,300),(107,468,301),(108,451,302),(109,209,154),(110,210,155),(111,211,156),(112,212,157),(113,213,158),(114,214,159),(115,215,160),(116,216,161),(117,199,162),(118,200,145),(119,201,146),(120,202,147),(121,203,148),(122,204,149),(123,205,150),(124,206,151),(125,207,152),(126,208,153),(163,473,191),(164,474,192),(165,475,193),(166,476,194),(167,477,195),(168,478,196),(169,479,197),(170,480,198),(171,481,181),(172,482,182),(173,483,183),(174,484,184),(175,485,185),(176,486,186),(177,469,187),(178,470,188),(179,471,189),(180,472,190),(217,317,403),(218,318,404),(219,319,405),(220,320,406),(221,321,407),(222,322,408),(223,323,409),(224,324,410),(225,307,411),(226,308,412),(227,309,413),(228,310,414),(229,311,397),(230,312,398),(231,313,399),(232,314,400),(233,315,401),(234,316,402),(253,421,272),(254,422,273),(255,423,274),(256,424,275),(257,425,276),(258,426,277),(259,427,278),(260,428,279),(261,429,280),(262,430,281),(263,431,282),(264,432,283),(265,415,284),(266,416,285),(267,417,286),(268,418,287),(269,419,288),(270,420,271)], [(1,214,462),(2,215,463),(3,216,464),(4,199,465),(5,200,466),(6,201,467),(7,202,468),(8,203,451),(9,204,452),(10,205,453),(11,206,454),(12,207,455),(13,208,456),(14,209,457),(15,210,458),(16,211,459),(17,212,460),(18,213,461),(19,374,472),(20,375,473),(21,376,474),(22,377,475),(23,378,476),(24,361,477),(25,362,478),(26,363,479),(27,364,480),(28,365,481),(29,366,482),(30,367,483),(31,368,484),(32,369,485),(33,370,486),(34,371,469),(35,372,470),(36,373,471),(37,409,415),(38,410,416),(39,411,417),(40,412,418),(41,413,419),(42,414,420),(43,397,421),(44,398,422),(45,399,423),(46,400,424),(47,401,425),(48,402,426),(49,403,427),(50,404,428),(51,405,429),(52,406,430),(53,407,431),(54,408,432),(55,395,193),(56,396,194),(57,379,195),(58,380,196),(59,381,197),(60,382,198),(61,383,181),(62,384,182),(63,385,183),(64,386,184),(65,387,185),(66,388,186),(67,389,187),(68,390,188),(69,391,189),(70,392,190),(71,393,191),(72,394,192),(73,173,338),(74,174,339),(75,175,340),(76,176,341),(77,177,342),(78,178,325),(79,179,326),(80,180,327),(81,163,328),(82,164,329),(83,165,330),(84,166,331),(85,167,332),(86,168,333),(87,169,334),(88,170,335),(89,171,336),(90,172,337),(91,248,122),(92,249,123),(93,250,124),(94,251,125),(95,252,126),(96,235,109),(97,236,110),(98,237,111),(99,238,112),(100,239,113),(101,240,114),(102,241,115),(103,242,116),(104,243,117),(105,244,118),(106,245,119),(107,246,120),(108,247,121),(127,156,292),(128,157,293),(129,158,294),(130,159,295),(131,160,296),(132,161,297),(133,162,298),(134,145,299),(135,146,300),(136,147,301),(137,148,302),(138,149,303),(139,150,304),(140,151,305),(141,152,306),(142,153,289),(143,154,290),(144,155,291),(217,278,438),(218,279,439),(219,280,440),(220,281,441),(221,282,442),(222,283,443),(223,284,444),(224,285,445),(225,286,446),(226,287,447),(227,288,448),(228,271,449),(229,272,450),(230,273,433),(231,274,434),(232,275,435),(233,276,436),(234,277,437),(253,352,311),(254,353,312),(255,354,313),(256,355,314),(257,356,315),(258,357,316),(259,358,317),(260,359,318),(261,360,319),(262,343,320),(263,344,321),(264,345,322),(265,346,323),(266,347,324),(267,348,307),(268,349,308),(269,350,309),(270,351,310)], [(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···3CB6A···6CB9A···9FF18A···18FF
order123···36···69···918···18
size111···11···11···11···1

486 irreducible representations

dim11111111
type++
imageC1C2C3C3C6C6C9C18
kernelC33×C18C33×C9C32×C18C33×C6C32×C9C34C32×C6C33
# reps11782782162162

Matrix representation of C33×C18 in GL4(𝔽19) generated by

1000
0700
00110
00011
,
7000
0700
0070
00011
,
7000
01100
0070
0001
,
8000
0900
0090
0009
G:=sub<GL(4,GF(19))| [1,0,0,0,0,7,0,0,0,0,11,0,0,0,0,11],[7,0,0,0,0,7,0,0,0,0,7,0,0,0,0,11],[7,0,0,0,0,11,0,0,0,0,7,0,0,0,0,1],[8,0,0,0,0,9,0,0,0,0,9,0,0,0,0,9] >;

C33×C18 in GAP, Magma, Sage, TeX

C_3^3\times C_{18}
% in TeX

G:=Group("C3^3xC18");
// GroupNames label

G:=SmallGroup(486,250);
// by ID

G=gap.SmallGroup(486,250);
# by ID

G:=PCGroup([6,-2,-3,-3,-3,-3,-3,979]);
// Polycyclic

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

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