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G = C22×C6×C18order 432 = 24·33

Abelian group of type [2,2,6,18]

direct product, abelian, monomial

Aliases: C22×C6×C18, SmallGroup(432,562)

Series: Derived Chief Lower central Upper central

C1 — C22×C6×C18
C1C3C32C3×C9C3×C18C6×C18C2×C6×C18 — C22×C6×C18
C1 — C22×C6×C18
C1 — C22×C6×C18

Generators and relations for C22×C6×C18
 G = < a,b,c,d | a2=b2=c6=d18=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, cd=dc >

Subgroups: 670, all normal (8 characteristic)
C1, C2 [×15], C3, C3 [×3], C22 [×35], C6 [×60], C23 [×15], C9 [×3], C32, C2×C6 [×140], C24, C18 [×45], C3×C6 [×15], C22×C6 [×60], C3×C9, C2×C18 [×105], C62 [×35], C23×C6, C23×C6 [×3], C3×C18 [×15], C22×C18 [×45], C2×C62 [×15], C6×C18 [×35], C23×C18 [×3], C22×C62, C2×C6×C18 [×15], C22×C6×C18
Quotients: C1, C2 [×15], C3 [×4], C22 [×35], C6 [×60], C23 [×15], C9 [×3], C32, C2×C6 [×140], C24, C18 [×45], C3×C6 [×15], C22×C6 [×60], C3×C9, C2×C18 [×105], C62 [×35], C23×C6 [×4], C3×C18 [×15], C22×C18 [×45], C2×C62 [×15], C6×C18 [×35], C23×C18 [×3], C22×C62, C2×C6×C18 [×15], C22×C6×C18

Smallest permutation representation of C22×C6×C18
Regular action on 432 points
Generators in S432
(1 162)(2 145)(3 146)(4 147)(5 148)(6 149)(7 150)(8 151)(9 152)(10 153)(11 154)(12 155)(13 156)(14 157)(15 158)(16 159)(17 160)(18 161)(19 205)(20 206)(21 207)(22 208)(23 209)(24 210)(25 211)(26 212)(27 213)(28 214)(29 215)(30 216)(31 199)(32 200)(33 201)(34 202)(35 203)(36 204)(37 273)(38 274)(39 275)(40 276)(41 277)(42 278)(43 279)(44 280)(45 281)(46 282)(47 283)(48 284)(49 285)(50 286)(51 287)(52 288)(53 271)(54 272)(55 314)(56 315)(57 316)(58 317)(59 318)(60 319)(61 320)(62 321)(63 322)(64 323)(65 324)(66 307)(67 308)(68 309)(69 310)(70 311)(71 312)(72 313)(73 334)(74 335)(75 336)(76 337)(77 338)(78 339)(79 340)(80 341)(81 342)(82 325)(83 326)(84 327)(85 328)(86 329)(87 330)(88 331)(89 332)(90 333)(91 370)(92 371)(93 372)(94 373)(95 374)(96 375)(97 376)(98 377)(99 378)(100 361)(101 362)(102 363)(103 364)(104 365)(105 366)(106 367)(107 368)(108 369)(109 423)(110 424)(111 425)(112 426)(113 427)(114 428)(115 429)(116 430)(117 431)(118 432)(119 415)(120 416)(121 417)(122 418)(123 419)(124 420)(125 421)(126 422)(127 224)(128 225)(129 226)(130 227)(131 228)(132 229)(133 230)(134 231)(135 232)(136 233)(137 234)(138 217)(139 218)(140 219)(141 220)(142 221)(143 222)(144 223)(163 184)(164 185)(165 186)(166 187)(167 188)(168 189)(169 190)(170 191)(171 192)(172 193)(173 194)(174 195)(175 196)(176 197)(177 198)(178 181)(179 182)(180 183)(235 391)(236 392)(237 393)(238 394)(239 395)(240 396)(241 379)(242 380)(243 381)(244 382)(245 383)(246 384)(247 385)(248 386)(249 387)(250 388)(251 389)(252 390)(253 357)(254 358)(255 359)(256 360)(257 343)(258 344)(259 345)(260 346)(261 347)(262 348)(263 349)(264 350)(265 351)(266 352)(267 353)(268 354)(269 355)(270 356)(289 403)(290 404)(291 405)(292 406)(293 407)(294 408)(295 409)(296 410)(297 411)(298 412)(299 413)(300 414)(301 397)(302 398)(303 399)(304 400)(305 401)(306 402)
(1 282)(2 283)(3 284)(4 285)(5 286)(6 287)(7 288)(8 271)(9 272)(10 273)(11 274)(12 275)(13 276)(14 277)(15 278)(16 279)(17 280)(18 281)(19 175)(20 176)(21 177)(22 178)(23 179)(24 180)(25 163)(26 164)(27 165)(28 166)(29 167)(30 168)(31 169)(32 170)(33 171)(34 172)(35 173)(36 174)(37 153)(38 154)(39 155)(40 156)(41 157)(42 158)(43 159)(44 160)(45 161)(46 162)(47 145)(48 146)(49 147)(50 148)(51 149)(52 150)(53 151)(54 152)(55 414)(56 397)(57 398)(58 399)(59 400)(60 401)(61 402)(62 403)(63 404)(64 405)(65 406)(66 407)(67 408)(68 409)(69 410)(70 411)(71 412)(72 413)(73 144)(74 127)(75 128)(76 129)(77 130)(78 131)(79 132)(80 133)(81 134)(82 135)(83 136)(84 137)(85 138)(86 139)(87 140)(88 141)(89 142)(90 143)(91 238)(92 239)(93 240)(94 241)(95 242)(96 243)(97 244)(98 245)(99 246)(100 247)(101 248)(102 249)(103 250)(104 251)(105 252)(106 235)(107 236)(108 237)(109 253)(110 254)(111 255)(112 256)(113 257)(114 258)(115 259)(116 260)(117 261)(118 262)(119 263)(120 264)(121 265)(122 266)(123 267)(124 268)(125 269)(126 270)(181 208)(182 209)(183 210)(184 211)(185 212)(186 213)(187 214)(188 215)(189 216)(190 199)(191 200)(192 201)(193 202)(194 203)(195 204)(196 205)(197 206)(198 207)(217 328)(218 329)(219 330)(220 331)(221 332)(222 333)(223 334)(224 335)(225 336)(226 337)(227 338)(228 339)(229 340)(230 341)(231 342)(232 325)(233 326)(234 327)(289 321)(290 322)(291 323)(292 324)(293 307)(294 308)(295 309)(296 310)(297 311)(298 312)(299 313)(300 314)(301 315)(302 316)(303 317)(304 318)(305 319)(306 320)(343 427)(344 428)(345 429)(346 430)(347 431)(348 432)(349 415)(350 416)(351 417)(352 418)(353 419)(354 420)(355 421)(356 422)(357 423)(358 424)(359 425)(360 426)(361 385)(362 386)(363 387)(364 388)(365 389)(366 390)(367 391)(368 392)(369 393)(370 394)(371 395)(372 396)(373 379)(374 380)(375 381)(376 382)(377 383)(378 384)
(1 192 377 356 309 223)(2 193 378 357 310 224)(3 194 361 358 311 225)(4 195 362 359 312 226)(5 196 363 360 313 227)(6 197 364 343 314 228)(7 198 365 344 315 229)(8 181 366 345 316 230)(9 182 367 346 317 231)(10 183 368 347 318 232)(11 184 369 348 319 233)(12 185 370 349 320 234)(13 186 371 350 321 217)(14 187 372 351 322 218)(15 188 373 352 323 219)(16 189 374 353 324 220)(17 190 375 354 307 221)(18 191 376 355 308 222)(19 249 112 413 77 50)(20 250 113 414 78 51)(21 251 114 397 79 52)(22 252 115 398 80 53)(23 235 116 399 81 54)(24 236 117 400 82 37)(25 237 118 401 83 38)(26 238 119 402 84 39)(27 239 120 403 85 40)(28 240 121 404 86 41)(29 241 122 405 87 42)(30 242 123 406 88 43)(31 243 124 407 89 44)(32 244 125 408 90 45)(33 245 126 409 73 46)(34 246 109 410 74 47)(35 247 110 411 75 48)(36 248 111 412 76 49)(55 131 149 176 103 257)(56 132 150 177 104 258)(57 133 151 178 105 259)(58 134 152 179 106 260)(59 135 153 180 107 261)(60 136 154 163 108 262)(61 137 155 164 91 263)(62 138 156 165 92 264)(63 139 157 166 93 265)(64 140 158 167 94 266)(65 141 159 168 95 267)(66 142 160 169 96 268)(67 143 161 170 97 269)(68 144 162 171 98 270)(69 127 145 172 99 253)(70 128 146 173 100 254)(71 129 147 174 101 255)(72 130 148 175 102 256)(199 381 420 293 332 280)(200 382 421 294 333 281)(201 383 422 295 334 282)(202 384 423 296 335 283)(203 385 424 297 336 284)(204 386 425 298 337 285)(205 387 426 299 338 286)(206 388 427 300 339 287)(207 389 428 301 340 288)(208 390 429 302 341 271)(209 391 430 303 342 272)(210 392 431 304 325 273)(211 393 432 305 326 274)(212 394 415 306 327 275)(213 395 416 289 328 276)(214 396 417 290 329 277)(215 379 418 291 330 278)(216 380 419 292 331 279)
(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)

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

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

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

432 conjugacy classes

class 1 2A···2O3A···3H6A···6DP9A···9R18A···18JJ
order12···23···36···69···918···18
size11···11···11···11···11···1

432 irreducible representations

dim11111111
type++
imageC1C2C3C3C6C6C9C18
kernelC22×C6×C18C2×C6×C18C23×C18C22×C62C22×C18C2×C62C23×C6C22×C6
# reps11562903018270

Matrix representation of C22×C6×C18 in GL4(𝔽19) generated by

18000
01800
00180
0001
,
18000
01800
0010
00018
,
7000
01100
00110
0008
,
9000
0200
00170
0001
G:=sub<GL(4,GF(19))| [18,0,0,0,0,18,0,0,0,0,18,0,0,0,0,1],[18,0,0,0,0,18,0,0,0,0,1,0,0,0,0,18],[7,0,0,0,0,11,0,0,0,0,11,0,0,0,0,8],[9,0,0,0,0,2,0,0,0,0,17,0,0,0,0,1] >;

C22×C6×C18 in GAP, Magma, Sage, TeX

C_2^2\times C_6\times C_{18}
% in TeX

G:=Group("C2^2xC6xC18");
// GroupNames label

G:=SmallGroup(432,562);
// by ID

G=gap.SmallGroup(432,562);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,347]);
// Polycyclic

G:=Group<a,b,c,d|a^2=b^2=c^6=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

׿
×
𝔽