Copied to
clipboard

G = C4×C33⋊5C4  order 432 = 24·33

Direct product of C4 and C33⋊5C4

direct product, metabelian, supersoluble, monomial, A-group

Aliases: C4×C33⋊5C4, C33⋊9C42, C62.145D6, (C6×C12).55S3, (C32×C12)⋊10C4, C12⋊2(C3⋊Dic3), (C3×C12)⋊10Dic3, C32⋊10(C4×Dic3), (C3×C62).51C22, C6.14(C4×C3⋊S3), (C3×C6×C12).18C2, C3⋊2(C4×C3⋊Dic3), (C3×C6).82(C4×S3), C6.14(C2×C3⋊Dic3), C2.2(C4×C33⋊C2), C2.2(C2×C33⋊5C4), (C2×C12).19(C3⋊S3), (C32×C6).61(C2×C4), (C2×C33⋊5C4).9C2, (C3×C6).73(C2×Dic3), (C2×C4).6(C33⋊C2), C22.3(C2×C33⋊C2), (C2×C6).40(C2×C3⋊S3), SmallGroup(432,503)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C33 — C4×C33⋊5C4
Chief series
C1 — C3 — C32 — C33 — C32×C6 — C3×C62 — C2×C33⋊5C4 — C4×C33⋊5C4
Lower central
C33 — C4×C33⋊5C4
Upper central
C1 — C2×C4

Generators and relations for C4×C33⋊5C4
 G = < a,b,c,d,e | a4=b3=c3=d3=e4=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, ebe-1=b-1, cd=dc, ece-1=c-1, ede-1=d-1 >

Subgroups: 1512 in 420 conjugacy classes, 231 normal (9 characteristic)
C1, C2, C2, C3, C4, C4, C22, C6, C2×C4, C2×C4, C32, Dic3, C12, C2×C6, C42, C3×C6, C2×Dic3, C2×C12, C33, C3⋊Dic3, C3×C12, C62, C4×Dic3, C32×C6, C32×C6, C2×C3⋊Dic3, C6×C12, C33⋊5C4, C32×C12, C3×C62, C4×C3⋊Dic3, C2×C33⋊5C4, C3×C6×C12, C4×C33⋊5C4
Quotients: C1, C2, C4, C22, S3, C2×C4, Dic3, D6, C42, C3⋊S3, C4×S3, C2×Dic3, C3⋊Dic3, C2×C3⋊S3, C4×Dic3, C33⋊C2, C4×C3⋊S3, C2×C3⋊Dic3, C33⋊5C4, C2×C33⋊C2, C4×C3⋊Dic3, C4×C33⋊C2, C2×C33⋊5C4, C4×C33⋊5C4

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

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

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

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

120 conjugacy classes

class 1 2A2B2C3A···3M4A4B4C4D4E···4L6A···6AM12A···12AZ
order12223···344444···46···612···12
size11112···2111127···272···22···2

120 irreducible representations

dim111112222
type++++-+
imageC1C2C2C4C4S3Dic3D6C4×S3
kernelC4×C33⋊5C4C2×C33⋊5C4C3×C6×C12C33⋊5C4C32×C12C6×C12C3×C12C62C3×C6
# reps1218413261352

Matrix representation of C4×C33⋊5C4 ►in GL6(𝔽13)

500000
050000
005000
000500
0000120
0000012
,
010000
12120000
000100
00121200
000010
000001
,
010000
12120000
00121200
001000
00001212
000010
,
010000
12120000
000100
00121200
000001
00001212
,
2110000
9110000
001000
00121200
000008
000080

G:=sub<GL(6,GF(13))| [5,0,0,0,0,0,0,5,0,0,0,0,0,0,5,0,0,0,0,0,0,5,0,0,0,0,0,0,12,0,0,0,0,0,0,12],[0,12,0,0,0,0,1,12,0,0,0,0,0,0,0,12,0,0,0,0,1,12,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,12,0,0,0,0,1,12,0,0,0,0,0,0,12,1,0,0,0,0,12,0,0,0,0,0,0,0,12,1,0,0,0,0,12,0],[0,12,0,0,0,0,1,12,0,0,0,0,0,0,0,12,0,0,0,0,1,12,0,0,0,0,0,0,0,12,0,0,0,0,1,12],[2,9,0,0,0,0,11,11,0,0,0,0,0,0,1,12,0,0,0,0,0,12,0,0,0,0,0,0,0,8,0,0,0,0,8,0] >;
 

C4×C33⋊5C4 in GAP, Magma, Sage, TeX 

C_4\times C_3^3\rtimes_5C_4
 
% in TeX
 
G:=Group("C4xC3^3:5C4");
 
// GroupNames label
 
G:=SmallGroup(432,503);
 
// by ID
 
G=gap.SmallGroup(432,503);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,28,64,1124,4037,14118]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e|a^4=b^3=c^3=d^3=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,e*b*e^-1=b^-1,c*d=d*c,e*c*e^-1=c^-1,e*d*e^-1=d^-1>;
 
// generators/relations
 

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁