C2^2xC3^3:5C4 - GroupNames

G = C₂²×C₃³⋊₅C₄ order 432 = 2⁴·3³

Direct product of C₂² and C₃³⋊₅C₄

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

Aliases: C₂²×C₃³⋊₅C₄, C₆³.₇C₂, C₆²⋊₁₇Dic₃, C₆².₁₆₁D₆, (C₃×C₆²)⋊₁₁C₄, (C₂×C₆²).₃₂S₃, C₃³⋊₂₁(C₂²×C₄), (C₃×C₆²).₇₀C₂², (C₃²×C₆).₁₀₃C₂³, C₂³.₃(C₃³⋊C₂), C₃²⋊₁₁(C₂²×Dic₃), C₆⋊₂(C₂×C₃⋊Dic₃), (C₃²×C₆)⋊₁₅(C₂×C₄), (C₂×C₆)⋊₅(C₃⋊Dic₃), (C₃×C₆)⋊₁₀(C₂×Dic₃), C₆.₄₇(C₂²×C₃⋊S₃), C₃⋊₂(C₂²×C₃⋊Dic₃), (C₂²×C₆).₁₇(C₃⋊S₃), (C₃×C₆).₁₉₂(C₂²×S₃), C₂.₂(C₂²×C₃³⋊C₂), C₂².₁₁(C₂×C₃³⋊C₂), (C₂×C₆).₅₀(C₂×C₃⋊S₃), SmallGroup(432,728)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series

C₁ — C₃³ — C₂²×C₃³⋊₅C₄

Chief series

C₁ — C₃ — C₃² — C₃³ — C₃²×C₆ — C₃³⋊₅C₄ — C₂×C₃³⋊₅C₄ — C₂²×C₃³⋊₅C₄

Lower central

C₃³ — C₂²×C₃³⋊₅C₄

Upper central

C₁ — C₂³

Generators and relations for C₂²×C₃³⋊₅C₄
G = < a,b,c,d,e,f | a²=b²=c³=d³=e³=f⁴=1, ab=ba, ac=ca, ad=da, ae=ea, af=fa, bc=cb, bd=db, be=eb, bf=fb, cd=dc, ce=ec, fcf^-1=c^-1, de=ed, fdf^-1=d^-1, fef^-1=e^-1 >

Subgroups: 2472 in 756 conjugacy classes, 459 normal (7 characteristic)
C₁, C₂, C₂, C₃, C₄, C₂², C₆, C₂×C₄, C₂³, C₃², Dic₃, C₂×C₆, C₂²×C₄, C₃×C₆, C₂×Dic₃, C₂²×C₆, C₃³, C₃⋊Dic₃, C₆², C₂²×Dic₃, C₃²×C₆, C₃²×C₆, C₂×C₃⋊Dic₃, C₂×C₆², C₃³⋊₅C₄, C₃×C₆², C₂²×C₃⋊Dic₃, C₂×C₃³⋊₅C₄, C₆³, C₂²×C₃³⋊₅C₄
Quotients: C₁, C₂, C₄, C₂², S₃, C₂×C₄, C₂³, Dic₃, D₆, C₂²×C₄, C₃⋊S₃, C₂×Dic₃, C₂²×S₃, C₃⋊Dic₃, C₂×C₃⋊S₃, C₂²×Dic₃, C₃³⋊C₂, C₂×C₃⋊Dic₃, C₂²×C₃⋊S₃, C₃³⋊₅C₄, C₂×C₃³⋊C₂, C₂²×C₃⋊Dic₃, C₂×C₃³⋊₅C₄, C₂²×C₃³⋊C₂, C₂²×C₃³⋊₅C₄

Smallest permutation representation of C₂²×C₃³⋊₅C₄
►Regular action on 432 points

Generators in S₄₃₂

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

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

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

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

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

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

120 conjugacy classes

class	1	2A	···	2G	3A	···	3M	4A	···	4H	6A	···	6CM
order	1	2	···	2	3	···	3	4	···	4	6	···	6
size	1	1	···	1	2	···	2	27	···	27	2	···	2

120 irreducible representations

dim	1	1	1	1	2	2	2
type	+	+	+		+	-	+
image	C₁	C₂	C₂	C₄	S₃	Dic₃	D₆
kernel	C₂²×C₃³⋊₅C₄	C₂×C₃³⋊₅C₄	C₆³	C₃×C₆²	C₂×C₆²	C₆²	C₆²
# reps	1	6	1	8	13	52	39

Matrix representation of C₂²×C₃³⋊₅C₄ ►in GL₆(𝔽₁₃)

12	0	0	0	0	0
0	12	0	0	0	0
0	0	1	0	0	0
0	0	0	1	0	0
0	0	0	0	12	0
0	0	0	0	0	12

12	0	0	0	0	0
0	12	0	0	0	0
0	0	1	0	0	0
0	0	0	1	0	0
0	0	0	0	1	0
0	0	0	0	0	1

0	1	0	0	0	0
12	12	0	0	0	0
0	0	9	0	0	0
0	0	8	3	0	0
0	0	0	0	1	0
0	0	0	0	0	1

1	0	0	0	0	0
0	1	0	0	0	0
0	0	9	0	0	0
0	0	8	3	0	0
0	0	0	0	1	0
0	0	0	0	0	1

1	0	0	0	0	0
0	1	0	0	0	0
0	0	3	0	0	0
0	0	5	9	0	0
0	0	0	0	9	0
0	0	0	0	9	3

0	5	0	0	0	0
5	0	0	0	0	0
0	0	7	11	0	0
0	0	12	6	0	0
0	0	0	0	7	4
0	0	0	0	7	6

G:=sub<GL(6,GF(13))| [12,0,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,0,0,12],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,12,0,0,0,0,1,12,0,0,0,0,0,0,9,8,0,0,0,0,0,3,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,9,8,0,0,0,0,0,3,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,3,5,0,0,0,0,0,9,0,0,0,0,0,0,9,9,0,0,0,0,0,3],[0,5,0,0,0,0,5,0,0,0,0,0,0,0,7,12,0,0,0,0,11,6,0,0,0,0,0,0,7,7,0,0,0,0,4,6] >;

C₂²×C₃³⋊₅C₄ in GAP, Magma, Sage, TeX

C_2^2\times C_3^3\rtimes_5C_4

% in TeX

G:=Group("C2^2xC3^3:5C4");

// GroupNames label

G:=SmallGroup(432,728);

// by ID

G=gap.SmallGroup(432,728);

# by ID

G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,56,1124,4037,14118]);

// Polycyclic

G:=Group<a,b,c,d,e,f|a^2=b^2=c^3=d^3=e^3=f^4=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,b*c=c*b,b*d=d*b,b*e=e*b,b*f=f*b,c*d=d*c,c*e=e*c,f*c*f^-1=c^-1,d*e=e*d,f*d*f^-1=d^-1,f*e*f^-1=e^-1>;

// generators/relations

G = C22×C33⋊5C4 order 432 = 24·33

Direct product of C22 and C33⋊5C4

G = C₂²×C₃³⋊₅C₄ order 432 = 2⁴·3³

Direct product of C₂² and C₃³⋊₅C₄