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## G = C3×C42.D5order 480 = 25·3·5

### Direct product of C3 and C42.D5

Series: Derived Chief Lower central Upper central

 Derived series C1 — C10 — C3×C42.D5
 Chief series C1 — C5 — C10 — C2×C10 — C2×C20 — C2×C60 — C6×C5⋊2C8 — C3×C42.D5
 Lower central C5 — C10 — C3×C42.D5
 Upper central C1 — C2×C12 — C4×C12

Generators and relations for C3×C42.D5
G = < a,b,c,d,e | a3=b4=c4=d5=1, e2=c, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, ebe-1=bc2, cd=dc, ce=ec, ede-1=d-1 >

Subgroups: 144 in 80 conjugacy classes, 58 normal (22 characteristic)
C1, C2, C2, C3, C4, C4, C22, C5, C6, C6, C8, C2×C4, C2×C4, C10, C10, C12, C12, C2×C6, C15, C42, C2×C8, C20, C20, C2×C10, C24, C2×C12, C2×C12, C30, C30, C8⋊C4, C52C8, C2×C20, C2×C20, C4×C12, C2×C24, C60, C60, C2×C30, C2×C52C8, C4×C20, C3×C8⋊C4, C3×C52C8, C2×C60, C2×C60, C42.D5, C6×C52C8, C4×C60, C3×C42.D5
Quotients: C1, C2, C3, C4, C22, C6, C2×C4, D5, C12, C2×C6, C42, M4(2), Dic5, D10, C2×C12, C3×D5, C8⋊C4, C4×D5, C2×Dic5, C4×C12, C3×M4(2), C3×Dic5, C6×D5, C4.Dic5, C4×Dic5, C3×C8⋊C4, D5×C12, C6×Dic5, C42.D5, C3×C4.Dic5, C12×Dic5, C3×C42.D5

Smallest permutation representation of C3×C42.D5
Regular action on 480 points
Generators in S480
(1 303 66)(2 304 67)(3 297 68)(4 298 69)(5 299 70)(6 300 71)(7 301 72)(8 302 65)(9 340 100)(10 341 101)(11 342 102)(12 343 103)(13 344 104)(14 337 97)(15 338 98)(16 339 99)(17 451 207)(18 452 208)(19 453 201)(20 454 202)(21 455 203)(22 456 204)(23 449 205)(24 450 206)(25 238 471)(26 239 472)(27 240 465)(28 233 466)(29 234 467)(30 235 468)(31 236 469)(32 237 470)(33 73 306)(34 74 307)(35 75 308)(36 76 309)(37 77 310)(38 78 311)(39 79 312)(40 80 305)(41 81 293)(42 82 294)(43 83 295)(44 84 296)(45 85 289)(46 86 290)(47 87 291)(48 88 292)(49 275 315)(50 276 316)(51 277 317)(52 278 318)(53 279 319)(54 280 320)(55 273 313)(56 274 314)(57 282 322)(58 283 323)(59 284 324)(60 285 325)(61 286 326)(62 287 327)(63 288 328)(64 281 321)(89 129 355)(90 130 356)(91 131 357)(92 132 358)(93 133 359)(94 134 360)(95 135 353)(96 136 354)(105 368 253)(106 361 254)(107 362 255)(108 363 256)(109 364 249)(110 365 250)(111 366 251)(112 367 252)(113 335 146)(114 336 147)(115 329 148)(116 330 149)(117 331 150)(118 332 151)(119 333 152)(120 334 145)(121 349 389)(122 350 390)(123 351 391)(124 352 392)(125 345 385)(126 346 386)(127 347 387)(128 348 388)(137 177 402)(138 178 403)(139 179 404)(140 180 405)(141 181 406)(142 182 407)(143 183 408)(144 184 401)(153 193 426)(154 194 427)(155 195 428)(156 196 429)(157 197 430)(158 198 431)(159 199 432)(160 200 425)(161 373 413)(162 374 414)(163 375 415)(164 376 416)(165 369 409)(166 370 410)(167 371 411)(168 372 412)(169 395 435)(170 396 436)(171 397 437)(172 398 438)(173 399 439)(174 400 440)(175 393 433)(176 394 434)(185 382 422)(186 383 423)(187 384 424)(188 377 417)(189 378 418)(190 379 419)(191 380 420)(192 381 421)(209 270 475)(210 271 476)(211 272 477)(212 265 478)(213 266 479)(214 267 480)(215 268 473)(216 269 474)(217 442 245)(218 443 246)(219 444 247)(220 445 248)(221 446 241)(222 447 242)(223 448 243)(224 441 244)(225 264 462)(226 257 463)(227 258 464)(228 259 457)(229 260 458)(230 261 459)(231 262 460)(232 263 461)
(1 467 154 106)(2 472 155 111)(3 469 156 108)(4 466 157 105)(5 471 158 110)(6 468 159 107)(7 465 160 112)(8 470 153 109)(9 325 263 421)(10 322 264 418)(11 327 257 423)(12 324 258 420)(13 321 259 417)(14 326 260 422)(15 323 261 419)(16 328 262 424)(17 415 385 76)(18 412 386 73)(19 409 387 78)(20 414 388 75)(21 411 389 80)(22 416 390 77)(23 413 391 74)(24 410 392 79)(25 198 365 299)(26 195 366 304)(27 200 367 301)(28 197 368 298)(29 194 361 303)(30 199 362 300)(31 196 363 297)(32 193 364 302)(33 208 372 346)(34 205 373 351)(35 202 374 348)(36 207 375 345)(37 204 376 350)(38 201 369 347)(39 206 370 352)(40 203 371 349)(41 216 398 329)(42 213 399 334)(43 210 400 331)(44 215 393 336)(45 212 394 333)(46 209 395 330)(47 214 396 335)(48 211 397 332)(49 218 403 355)(50 223 404 360)(51 220 405 357)(52 217 406 354)(53 222 407 359)(54 219 408 356)(55 224 401 353)(56 221 402 358)(57 462 189 341)(58 459 190 338)(59 464 191 343)(60 461 192 340)(61 458 185 337)(62 463 186 342)(63 460 187 339)(64 457 188 344)(65 237 426 249)(66 234 427 254)(67 239 428 251)(68 236 429 256)(69 233 430 253)(70 238 431 250)(71 235 432 255)(72 240 425 252)(81 269 438 148)(82 266 439 145)(83 271 440 150)(84 268 433 147)(85 265 434 152)(86 270 435 149)(87 267 436 146)(88 272 437 151)(89 275 443 138)(90 280 444 143)(91 277 445 140)(92 274 446 137)(93 279 447 142)(94 276 448 139)(95 273 441 144)(96 278 442 141)(97 286 229 382)(98 283 230 379)(99 288 231 384)(100 285 232 381)(101 282 225 378)(102 287 226 383)(103 284 227 380)(104 281 228 377)(113 291 480 170)(114 296 473 175)(115 293 474 172)(116 290 475 169)(117 295 476 174)(118 292 477 171)(119 289 478 176)(120 294 479 173)(121 305 455 167)(122 310 456 164)(123 307 449 161)(124 312 450 166)(125 309 451 163)(126 306 452 168)(127 311 453 165)(128 308 454 162)(129 315 246 178)(130 320 247 183)(131 317 248 180)(132 314 241 177)(133 319 242 182)(134 316 243 179)(135 313 244 184)(136 318 245 181)
(1 3 5 7)(2 4 6 8)(9 11 13 15)(10 12 14 16)(17 19 21 23)(18 20 22 24)(25 27 29 31)(26 28 30 32)(33 35 37 39)(34 36 38 40)(41 43 45 47)(42 44 46 48)(49 51 53 55)(50 52 54 56)(57 59 61 63)(58 60 62 64)(65 67 69 71)(66 68 70 72)(73 75 77 79)(74 76 78 80)(81 83 85 87)(82 84 86 88)(89 91 93 95)(90 92 94 96)(97 99 101 103)(98 100 102 104)(105 107 109 111)(106 108 110 112)(113 115 117 119)(114 116 118 120)(121 123 125 127)(122 124 126 128)(129 131 133 135)(130 132 134 136)(137 139 141 143)(138 140 142 144)(145 147 149 151)(146 148 150 152)(153 155 157 159)(154 156 158 160)(161 163 165 167)(162 164 166 168)(169 171 173 175)(170 172 174 176)(177 179 181 183)(178 180 182 184)(185 187 189 191)(186 188 190 192)(193 195 197 199)(194 196 198 200)(201 203 205 207)(202 204 206 208)(209 211 213 215)(210 212 214 216)(217 219 221 223)(218 220 222 224)(225 227 229 231)(226 228 230 232)(233 235 237 239)(234 236 238 240)(241 243 245 247)(242 244 246 248)(249 251 253 255)(250 252 254 256)(257 259 261 263)(258 260 262 264)(265 267 269 271)(266 268 270 272)(273 275 277 279)(274 276 278 280)(281 283 285 287)(282 284 286 288)(289 291 293 295)(290 292 294 296)(297 299 301 303)(298 300 302 304)(305 307 309 311)(306 308 310 312)(313 315 317 319)(314 316 318 320)(321 323 325 327)(322 324 326 328)(329 331 333 335)(330 332 334 336)(337 339 341 343)(338 340 342 344)(345 347 349 351)(346 348 350 352)(353 355 357 359)(354 356 358 360)(361 363 365 367)(362 364 366 368)(369 371 373 375)(370 372 374 376)(377 379 381 383)(378 380 382 384)(385 387 389 391)(386 388 390 392)(393 395 397 399)(394 396 398 400)(401 403 405 407)(402 404 406 408)(409 411 413 415)(410 412 414 416)(417 419 421 423)(418 420 422 424)(425 427 429 431)(426 428 430 432)(433 435 437 439)(434 436 438 440)(441 443 445 447)(442 444 446 448)(449 451 453 455)(450 452 454 456)(457 459 461 463)(458 460 462 464)(465 467 469 471)(466 468 470 472)(473 475 477 479)(474 476 478 480)
(1 372 383 42 273)(2 274 43 384 373)(3 374 377 44 275)(4 276 45 378 375)(5 376 379 46 277)(6 278 47 380 369)(7 370 381 48 279)(8 280 41 382 371)(9 272 242 27 392)(10 385 28 243 265)(11 266 244 29 386)(12 387 30 245 267)(13 268 246 31 388)(14 389 32 247 269)(15 270 248 25 390)(16 391 26 241 271)(17 368 134 152 264)(18 257 145 135 361)(19 362 136 146 258)(20 259 147 129 363)(21 364 130 148 260)(22 261 149 131 365)(23 366 132 150 262)(24 263 151 133 367)(33 287 399 144 154)(34 155 137 400 288)(35 281 393 138 156)(36 157 139 394 282)(37 283 395 140 158)(38 159 141 396 284)(39 285 397 142 160)(40 153 143 398 286)(49 68 162 188 296)(50 289 189 163 69)(51 70 164 190 290)(52 291 191 165 71)(53 72 166 192 292)(54 293 185 167 65)(55 66 168 186 294)(56 295 187 161 67)(57 309 430 404 176)(58 169 405 431 310)(59 311 432 406 170)(60 171 407 425 312)(61 305 426 408 172)(62 173 401 427 306)(63 307 428 402 174)(64 175 403 429 308)(73 327 439 184 194)(74 195 177 440 328)(75 321 433 178 196)(76 197 179 434 322)(77 323 435 180 198)(78 199 181 436 324)(79 325 437 182 200)(80 193 183 438 326)(81 422 411 302 320)(82 313 303 412 423)(83 424 413 304 314)(84 315 297 414 417)(85 418 415 298 316)(86 317 299 416 419)(87 420 409 300 318)(88 319 301 410 421)(89 108 202 228 336)(90 329 229 203 109)(91 110 204 230 330)(92 331 231 205 111)(93 112 206 232 332)(94 333 225 207 105)(95 106 208 226 334)(96 335 227 201 107)(97 349 470 444 216)(98 209 445 471 350)(99 351 472 446 210)(100 211 447 465 352)(101 345 466 448 212)(102 213 441 467 346)(103 347 468 442 214)(104 215 443 469 348)(113 464 453 255 354)(114 355 256 454 457)(115 458 455 249 356)(116 357 250 456 459)(117 460 449 251 358)(118 359 252 450 461)(119 462 451 253 360)(120 353 254 452 463)(121 237 219 474 337)(122 338 475 220 238)(123 239 221 476 339)(124 340 477 222 240)(125 233 223 478 341)(126 342 479 224 234)(127 235 217 480 343)(128 344 473 218 236)
(1 2 3 4 5 6 7 8)(9 10 11 12 13 14 15 16)(17 18 19 20 21 22 23 24)(25 26 27 28 29 30 31 32)(33 34 35 36 37 38 39 40)(41 42 43 44 45 46 47 48)(49 50 51 52 53 54 55 56)(57 58 59 60 61 62 63 64)(65 66 67 68 69 70 71 72)(73 74 75 76 77 78 79 80)(81 82 83 84 85 86 87 88)(89 90 91 92 93 94 95 96)(97 98 99 100 101 102 103 104)(105 106 107 108 109 110 111 112)(113 114 115 116 117 118 119 120)(121 122 123 124 125 126 127 128)(129 130 131 132 133 134 135 136)(137 138 139 140 141 142 143 144)(145 146 147 148 149 150 151 152)(153 154 155 156 157 158 159 160)(161 162 163 164 165 166 167 168)(169 170 171 172 173 174 175 176)(177 178 179 180 181 182 183 184)(185 186 187 188 189 190 191 192)(193 194 195 196 197 198 199 200)(201 202 203 204 205 206 207 208)(209 210 211 212 213 214 215 216)(217 218 219 220 221 222 223 224)(225 226 227 228 229 230 231 232)(233 234 235 236 237 238 239 240)(241 242 243 244 245 246 247 248)(249 250 251 252 253 254 255 256)(257 258 259 260 261 262 263 264)(265 266 267 268 269 270 271 272)(273 274 275 276 277 278 279 280)(281 282 283 284 285 286 287 288)(289 290 291 292 293 294 295 296)(297 298 299 300 301 302 303 304)(305 306 307 308 309 310 311 312)(313 314 315 316 317 318 319 320)(321 322 323 324 325 326 327 328)(329 330 331 332 333 334 335 336)(337 338 339 340 341 342 343 344)(345 346 347 348 349 350 351 352)(353 354 355 356 357 358 359 360)(361 362 363 364 365 366 367 368)(369 370 371 372 373 374 375 376)(377 378 379 380 381 382 383 384)(385 386 387 388 389 390 391 392)(393 394 395 396 397 398 399 400)(401 402 403 404 405 406 407 408)(409 410 411 412 413 414 415 416)(417 418 419 420 421 422 423 424)(425 426 427 428 429 430 431 432)(433 434 435 436 437 438 439 440)(441 442 443 444 445 446 447 448)(449 450 451 452 453 454 455 456)(457 458 459 460 461 462 463 464)(465 466 467 468 469 470 471 472)(473 474 475 476 477 478 479 480)

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

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

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

156 conjugacy classes

 class 1 2A 2B 2C 3A 3B 4A 4B 4C 4D 4E 4F 4G 4H 5A 5B 6A ··· 6F 8A ··· 8H 10A ··· 10F 12A ··· 12H 12I ··· 12P 15A 15B 15C 15D 20A ··· 20X 24A ··· 24P 30A ··· 30L 60A ··· 60AV order 1 2 2 2 3 3 4 4 4 4 4 4 4 4 5 5 6 ··· 6 8 ··· 8 10 ··· 10 12 ··· 12 12 ··· 12 15 15 15 15 20 ··· 20 24 ··· 24 30 ··· 30 60 ··· 60 size 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 ··· 1 10 ··· 10 2 ··· 2 1 ··· 1 2 ··· 2 2 2 2 2 2 ··· 2 10 ··· 10 2 ··· 2 2 ··· 2

156 irreducible representations

 dim 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 type + + + + - + image C1 C2 C2 C3 C4 C4 C6 C6 C12 C12 D5 M4(2) Dic5 D10 C3×D5 C4×D5 C3×M4(2) C3×Dic5 C6×D5 C4.Dic5 D5×C12 C3×C4.Dic5 kernel C3×C42.D5 C6×C5⋊2C8 C4×C60 C42.D5 C3×C5⋊2C8 C2×C60 C2×C5⋊2C8 C4×C20 C5⋊2C8 C2×C20 C4×C12 C30 C2×C12 C2×C12 C42 C12 C10 C2×C4 C2×C4 C6 C4 C2 # reps 1 2 1 2 8 4 4 2 16 8 2 4 4 2 4 8 8 8 4 16 16 32

Matrix representation of C3×C42.D5 in GL3(𝔽241) generated by

 225 0 0 0 15 0 0 0 15
,
 177 0 0 0 197 238 0 3 44
,
 1 0 0 0 64 0 0 0 64
,
 1 0 0 0 51 240 0 1 0
,
 240 0 0 0 51 21 0 212 190
G:=sub<GL(3,GF(241))| [225,0,0,0,15,0,0,0,15],[177,0,0,0,197,3,0,238,44],[1,0,0,0,64,0,0,0,64],[1,0,0,0,51,1,0,240,0],[240,0,0,0,51,212,0,21,190] >;

C3×C42.D5 in GAP, Magma, Sage, TeX

C_3\times C_4^2.D_5
% in TeX

G:=Group("C3xC4^2.D5");
// GroupNames label

G:=SmallGroup(480,81);
// by ID

G=gap.SmallGroup(480,81);
# by ID

G:=PCGroup([7,-2,-2,-3,-2,-2,-2,-5,84,701,176,136,18822]);
// Polycyclic

G:=Group<a,b,c,d,e|a^3=b^4=c^4=d^5=1,e^2=c,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*c^2,c*d=d*c,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations

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