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G = C4⋊C4×C33order 432 = 24·33

Direct product of C33 and C4⋊C4

direct product, metabelian, nilpotent (class 2), monomial

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2 — C4⋊C4×C33
 Chief series C1 — C2 — C22 — C2×C6 — C62 — C3×C62 — C3×C6×C12 — C4⋊C4×C33
 Lower central C1 — C2 — C4⋊C4×C33
 Upper central C1 — C3×C62 — C4⋊C4×C33

Generators and relations for C4⋊C4×C33
G = < a,b,c,d,e | a3=b3=c3=d4=e4=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >

Subgroups: 420 in 364 conjugacy classes, 308 normal (14 characteristic)
C1, C2, C3, C4, C4, C22, C6, C2×C4, C2×C4, C32, C12, C12, C2×C6, C4⋊C4, C3×C6, C2×C12, C33, C3×C12, C3×C12, C62, C3×C4⋊C4, C32×C6, C6×C12, C32×C12, C32×C12, C3×C62, C32×C4⋊C4, C3×C6×C12, C3×C6×C12, C4⋊C4×C33
Quotients: C1, C2, C3, C4, C22, C6, C2×C4, D4, Q8, C32, C12, C2×C6, C4⋊C4, C3×C6, C2×C12, C3×D4, C3×Q8, C33, C3×C12, C62, C3×C4⋊C4, C32×C6, C6×C12, D4×C32, Q8×C32, C32×C12, C3×C62, C32×C4⋊C4, C3×C6×C12, D4×C33, Q8×C33, C4⋊C4×C33

Smallest permutation representation of C4⋊C4×C33
Regular action on 432 points
Generators in S432
(1 220 191)(2 217 192)(3 218 189)(4 219 190)(5 57 138)(6 58 139)(7 59 140)(8 60 137)(9 162 29)(10 163 30)(11 164 31)(12 161 32)(13 41 146)(14 42 147)(15 43 148)(16 44 145)(17 158 25)(18 159 26)(19 160 27)(20 157 28)(21 49 130)(22 50 131)(23 51 132)(24 52 129)(33 114 53)(34 115 54)(35 116 55)(36 113 56)(37 118 45)(38 119 46)(39 120 47)(40 117 48)(61 214 81)(62 215 82)(63 216 83)(64 213 84)(65 93 198)(66 94 199)(67 95 200)(68 96 197)(69 210 77)(70 211 78)(71 212 79)(72 209 80)(73 101 182)(74 102 183)(75 103 184)(76 104 181)(85 166 105)(86 167 106)(87 168 107)(88 165 108)(89 170 97)(90 171 98)(91 172 99)(92 169 100)(109 405 274)(110 406 275)(111 407 276)(112 408 273)(121 149 141)(122 150 142)(123 151 143)(124 152 144)(125 153 133)(126 154 134)(127 155 135)(128 156 136)(173 201 193)(174 202 194)(175 203 195)(176 204 196)(177 205 185)(178 206 186)(179 207 187)(180 208 188)(221 376 356)(222 373 353)(223 374 354)(224 375 355)(225 368 360)(226 365 357)(227 366 358)(228 367 359)(229 257 249)(230 258 250)(231 259 251)(232 260 252)(233 261 241)(234 262 242)(235 263 243)(236 264 244)(237 344 372)(238 341 369)(239 342 370)(240 343 371)(245 328 380)(246 325 377)(247 326 378)(248 327 379)(253 336 364)(254 333 361)(255 334 362)(256 335 363)(265 348 340)(266 345 337)(267 346 338)(268 347 339)(269 352 332)(270 349 329)(271 350 330)(272 351 331)(277 432 297)(278 429 298)(279 430 299)(280 431 300)(281 309 416)(282 310 413)(283 311 414)(284 312 415)(285 428 293)(286 425 294)(287 426 295)(288 427 296)(289 317 400)(290 318 397)(291 319 398)(292 320 399)(301 384 321)(302 381 322)(303 382 323)(304 383 324)(305 388 313)(306 385 314)(307 386 315)(308 387 316)(389 417 409)(390 418 410)(391 419 411)(392 420 412)(393 421 401)(394 422 402)(395 423 403)(396 424 404)
(1 70 171)(2 71 172)(3 72 169)(4 69 170)(5 17 118)(6 18 119)(7 19 120)(8 20 117)(9 21 122)(10 22 123)(11 23 124)(12 24 121)(13 114 126)(14 115 127)(15 116 128)(16 113 125)(25 37 138)(26 38 139)(27 39 140)(28 40 137)(29 130 142)(30 131 143)(31 132 144)(32 129 141)(33 134 146)(34 135 147)(35 136 148)(36 133 145)(41 53 154)(42 54 155)(43 55 156)(44 56 153)(45 57 158)(46 58 159)(47 59 160)(48 60 157)(49 150 162)(50 151 163)(51 152 164)(52 149 161)(61 73 174)(62 74 175)(63 75 176)(64 76 173)(65 166 178)(66 167 179)(67 168 180)(68 165 177)(77 89 190)(78 90 191)(79 91 192)(80 92 189)(81 182 194)(82 183 195)(83 184 196)(84 181 193)(85 186 198)(86 187 199)(87 188 200)(88 185 197)(93 105 206)(94 106 207)(95 107 208)(96 108 205)(97 219 210)(98 220 211)(99 217 212)(100 218 209)(101 202 214)(102 203 215)(103 204 216)(104 201 213)(109 425 314)(110 426 315)(111 427 316)(112 428 313)(221 233 336)(222 234 333)(223 235 334)(224 236 335)(225 328 340)(226 325 337)(227 326 338)(228 327 339)(229 332 344)(230 329 341)(231 330 342)(232 331 343)(237 249 352)(238 250 349)(239 251 350)(240 252 351)(241 253 356)(242 254 353)(243 255 354)(244 256 355)(245 348 360)(246 345 357)(247 346 358)(248 347 359)(257 269 372)(258 270 369)(259 271 370)(260 272 371)(261 364 376)(262 361 373)(263 362 374)(264 363 375)(265 368 380)(266 365 377)(267 366 378)(268 367 379)(273 285 388)(274 286 385)(275 287 386)(276 288 387)(277 289 392)(278 290 389)(279 291 390)(280 292 391)(281 384 396)(282 381 393)(283 382 394)(284 383 395)(293 305 408)(294 306 405)(295 307 406)(296 308 407)(297 400 412)(298 397 409)(299 398 410)(300 399 411)(301 404 416)(302 401 413)(303 402 414)(304 403 415)(309 321 424)(310 322 421)(311 323 422)(312 324 423)(317 420 432)(318 417 429)(319 418 430)(320 419 431)
(1 62 167)(2 63 168)(3 64 165)(4 61 166)(5 9 114)(6 10 115)(7 11 116)(8 12 113)(13 118 122)(14 119 123)(15 120 124)(16 117 121)(17 21 126)(18 22 127)(19 23 128)(20 24 125)(25 130 134)(26 131 135)(27 132 136)(28 129 133)(29 33 138)(30 34 139)(31 35 140)(32 36 137)(37 142 146)(38 143 147)(39 144 148)(40 141 145)(41 45 150)(42 46 151)(43 47 152)(44 48 149)(49 154 158)(50 155 159)(51 156 160)(52 153 157)(53 57 162)(54 58 163)(55 59 164)(56 60 161)(65 170 174)(66 171 175)(67 172 176)(68 169 173)(69 73 178)(70 74 179)(71 75 180)(72 76 177)(77 182 186)(78 183 187)(79 184 188)(80 181 185)(81 85 190)(82 86 191)(83 87 192)(84 88 189)(89 194 198)(90 195 199)(91 196 200)(92 193 197)(93 97 202)(94 98 203)(95 99 204)(96 100 201)(101 206 210)(102 207 211)(103 208 212)(104 205 209)(105 219 214)(106 220 215)(107 217 216)(108 218 213)(109 429 322)(110 430 323)(111 431 324)(112 432 321)(221 328 332)(222 325 329)(223 326 330)(224 327 331)(225 229 336)(226 230 333)(227 231 334)(228 232 335)(233 340 344)(234 337 341)(235 338 342)(236 339 343)(237 241 348)(238 242 345)(239 243 346)(240 244 347)(245 352 356)(246 349 353)(247 350 354)(248 351 355)(249 253 360)(250 254 357)(251 255 358)(252 256 359)(257 364 368)(258 361 365)(259 362 366)(260 363 367)(261 265 372)(262 266 369)(263 267 370)(264 268 371)(269 376 380)(270 373 377)(271 374 378)(272 375 379)(273 277 384)(274 278 381)(275 279 382)(276 280 383)(281 388 392)(282 385 389)(283 386 390)(284 387 391)(285 289 396)(286 290 393)(287 291 394)(288 292 395)(293 400 404)(294 397 401)(295 398 402)(296 399 403)(297 301 408)(298 302 405)(299 303 406)(300 304 407)(305 412 416)(306 409 413)(307 410 414)(308 411 415)(309 313 420)(310 314 417)(311 315 418)(312 316 419)(317 424 428)(318 421 425)(319 422 426)(320 423 427)
(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)
(1 326 8 274)(2 325 5 273)(3 328 6 276)(4 327 7 275)(9 277 63 329)(10 280 64 332)(11 279 61 331)(12 278 62 330)(13 281 67 333)(14 284 68 336)(15 283 65 335)(16 282 66 334)(17 285 71 337)(18 288 72 340)(19 287 69 339)(20 286 70 338)(21 289 75 341)(22 292 76 344)(23 291 73 343)(24 290 74 342)(25 293 79 345)(26 296 80 348)(27 295 77 347)(28 294 78 346)(29 297 83 349)(30 300 84 352)(31 299 81 351)(32 298 82 350)(33 301 87 353)(34 304 88 356)(35 303 85 355)(36 302 86 354)(37 305 91 357)(38 308 92 360)(39 307 89 359)(40 306 90 358)(41 309 95 361)(42 312 96 364)(43 311 93 363)(44 310 94 362)(45 313 99 365)(46 316 100 368)(47 315 97 367)(48 314 98 366)(49 317 103 369)(50 320 104 372)(51 319 101 371)(52 318 102 370)(53 321 107 373)(54 324 108 376)(55 323 105 375)(56 322 106 374)(57 112 217 377)(58 111 218 380)(59 110 219 379)(60 109 220 378)(113 381 167 223)(114 384 168 222)(115 383 165 221)(116 382 166 224)(117 385 171 227)(118 388 172 226)(119 387 169 225)(120 386 170 228)(121 389 175 231)(122 392 176 230)(123 391 173 229)(124 390 174 232)(125 393 179 235)(126 396 180 234)(127 395 177 233)(128 394 178 236)(129 397 183 239)(130 400 184 238)(131 399 181 237)(132 398 182 240)(133 401 187 243)(134 404 188 242)(135 403 185 241)(136 402 186 244)(137 405 191 247)(138 408 192 246)(139 407 189 245)(140 406 190 248)(141 409 195 251)(142 412 196 250)(143 411 193 249)(144 410 194 252)(145 413 199 255)(146 416 200 254)(147 415 197 253)(148 414 198 256)(149 417 203 259)(150 420 204 258)(151 419 201 257)(152 418 202 260)(153 421 207 263)(154 424 208 262)(155 423 205 261)(156 422 206 264)(157 425 211 267)(158 428 212 266)(159 427 209 265)(160 426 210 268)(161 429 215 271)(162 432 216 270)(163 431 213 269)(164 430 214 272)

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

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

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

270 conjugacy classes

 class 1 2A 2B 2C 3A ··· 3Z 4A ··· 4F 6A ··· 6BZ 12A ··· 12EZ order 1 2 2 2 3 ··· 3 4 ··· 4 6 ··· 6 12 ··· 12 size 1 1 1 1 1 ··· 1 2 ··· 2 1 ··· 1 2 ··· 2

270 irreducible representations

 dim 1 1 1 1 1 1 2 2 2 2 type + + + - image C1 C2 C3 C4 C6 C12 D4 Q8 C3×D4 C3×Q8 kernel C4⋊C4×C33 C3×C6×C12 C32×C4⋊C4 C32×C12 C6×C12 C3×C12 C32×C6 C32×C6 C3×C6 C3×C6 # reps 1 3 26 4 78 104 1 1 26 26

Matrix representation of C4⋊C4×C33 in GL5(𝔽13)

 1 0 0 0 0 0 9 0 0 0 0 0 3 0 0 0 0 0 9 0 0 0 0 0 9
,
 1 0 0 0 0 0 1 0 0 0 0 0 9 0 0 0 0 0 1 0 0 0 0 0 1
,
 1 0 0 0 0 0 9 0 0 0 0 0 9 0 0 0 0 0 1 0 0 0 0 0 1
,
 1 0 0 0 0 0 12 0 0 0 0 0 12 0 0 0 0 0 5 0 0 0 0 0 8
,
 5 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 12 0

G:=sub<GL(5,GF(13))| [1,0,0,0,0,0,9,0,0,0,0,0,3,0,0,0,0,0,9,0,0,0,0,0,9],[1,0,0,0,0,0,1,0,0,0,0,0,9,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,9,0,0,0,0,0,9,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,12,0,0,0,0,0,12,0,0,0,0,0,5,0,0,0,0,0,8],[5,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,1,0] >;

C4⋊C4×C33 in GAP, Magma, Sage, TeX

C_4\rtimes C_4\times C_3^3
% in TeX

G:=Group("C4:C4xC3^3");
// GroupNames label

G:=SmallGroup(432,514);
// by ID

G=gap.SmallGroup(432,514);
# by ID

G:=PCGroup([7,-2,-2,-3,-3,-3,-2,-2,1512,1541,764]);
// Polycyclic

G:=Group<a,b,c,d,e|a^3=b^3=c^3=d^4=e^4=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations

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