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## G = Dic3×C22×C10order 480 = 25·3·5

### Direct product of C22×C10 and Dic3

Series: Derived Chief Lower central Upper central

 Derived series C1 — C3 — Dic3×C22×C10
 Chief series C1 — C3 — C6 — C30 — C5×Dic3 — C10×Dic3 — Dic3×C2×C10 — Dic3×C22×C10
 Lower central C3 — Dic3×C22×C10
 Upper central C1 — C23×C10

Generators and relations for Dic3×C22×C10
G = < a,b,c,d,e | a2=b2=c10=d6=1, e2=d3, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >

Subgroups: 676 in 472 conjugacy classes, 370 normal (14 characteristic)
C1, C2, C2, C3, C4, C22, C5, C6, C6, C2×C4, C23, C10, C10, Dic3, C2×C6, C15, C22×C4, C24, C20, C2×C10, C2×Dic3, C22×C6, C30, C30, C23×C4, C2×C20, C22×C10, C22×Dic3, C23×C6, C5×Dic3, C2×C30, C22×C20, C23×C10, C23×Dic3, C10×Dic3, C22×C30, C23×C20, Dic3×C2×C10, C23×C30, Dic3×C22×C10
Quotients: C1, C2, C4, C22, C5, S3, C2×C4, C23, C10, Dic3, D6, C22×C4, C24, C20, C2×C10, C2×Dic3, C22×S3, C5×S3, C23×C4, C2×C20, C22×C10, C22×Dic3, S3×C23, C5×Dic3, S3×C10, C22×C20, C23×C10, C23×Dic3, C10×Dic3, S3×C2×C10, C23×C20, Dic3×C2×C10, S3×C22×C10, Dic3×C22×C10

Smallest permutation representation of Dic3×C22×C10
Regular action on 480 points
Generators in S480
(1 278)(2 279)(3 280)(4 271)(5 272)(6 273)(7 274)(8 275)(9 276)(10 277)(11 307)(12 308)(13 309)(14 310)(15 301)(16 302)(17 303)(18 304)(19 305)(20 306)(21 292)(22 293)(23 294)(24 295)(25 296)(26 297)(27 298)(28 299)(29 300)(30 291)(31 311)(32 312)(33 313)(34 314)(35 315)(36 316)(37 317)(38 318)(39 319)(40 320)(41 329)(42 330)(43 321)(44 322)(45 323)(46 324)(47 325)(48 326)(49 327)(50 328)(51 345)(52 346)(53 347)(54 348)(55 349)(56 350)(57 341)(58 342)(59 343)(60 344)(61 284)(62 285)(63 286)(64 287)(65 288)(66 289)(67 290)(68 281)(69 282)(70 283)(71 270)(72 261)(73 262)(74 263)(75 264)(76 265)(77 266)(78 267)(79 268)(80 269)(81 252)(82 253)(83 254)(84 255)(85 256)(86 257)(87 258)(88 259)(89 260)(90 251)(91 231)(92 232)(93 233)(94 234)(95 235)(96 236)(97 237)(98 238)(99 239)(100 240)(101 248)(102 249)(103 250)(104 241)(105 242)(106 243)(107 244)(108 245)(109 246)(110 247)(111 211)(112 212)(113 213)(114 214)(115 215)(116 216)(117 217)(118 218)(119 219)(120 220)(121 224)(122 225)(123 226)(124 227)(125 228)(126 229)(127 230)(128 221)(129 222)(130 223)(131 210)(132 201)(133 202)(134 203)(135 204)(136 205)(137 206)(138 207)(139 208)(140 209)(141 192)(142 193)(143 194)(144 195)(145 196)(146 197)(147 198)(148 199)(149 200)(150 191)(151 171)(152 172)(153 173)(154 174)(155 175)(156 176)(157 177)(158 178)(159 179)(160 180)(161 188)(162 189)(163 190)(164 181)(165 182)(166 183)(167 184)(168 185)(169 186)(170 187)(331 471)(332 472)(333 473)(334 474)(335 475)(336 476)(337 477)(338 478)(339 479)(340 480)(351 451)(352 452)(353 453)(354 454)(355 455)(356 456)(357 457)(358 458)(359 459)(360 460)(361 464)(362 465)(363 466)(364 467)(365 468)(366 469)(367 470)(368 461)(369 462)(370 463)(371 450)(372 441)(373 442)(374 443)(375 444)(376 445)(377 446)(378 447)(379 448)(380 449)(381 432)(382 433)(383 434)(384 435)(385 436)(386 437)(387 438)(388 439)(389 440)(390 431)(391 411)(392 412)(393 413)(394 414)(395 415)(396 416)(397 417)(398 418)(399 419)(400 420)(401 428)(402 429)(403 430)(404 421)(405 422)(406 423)(407 424)(408 425)(409 426)(410 427)
(1 158)(2 159)(3 160)(4 151)(5 152)(6 153)(7 154)(8 155)(9 156)(10 157)(11 427)(12 428)(13 429)(14 430)(15 421)(16 422)(17 423)(18 424)(19 425)(20 426)(21 412)(22 413)(23 414)(24 415)(25 416)(26 417)(27 418)(28 419)(29 420)(30 411)(31 431)(32 432)(33 433)(34 434)(35 435)(36 436)(37 437)(38 438)(39 439)(40 440)(41 449)(42 450)(43 441)(44 442)(45 443)(46 444)(47 445)(48 446)(49 447)(50 448)(51 465)(52 466)(53 467)(54 468)(55 469)(56 470)(57 461)(58 462)(59 463)(60 464)(61 164)(62 165)(63 166)(64 167)(65 168)(66 169)(67 170)(68 161)(69 162)(70 163)(71 150)(72 141)(73 142)(74 143)(75 144)(76 145)(77 146)(78 147)(79 148)(80 149)(81 132)(82 133)(83 134)(84 135)(85 136)(86 137)(87 138)(88 139)(89 140)(90 131)(91 111)(92 112)(93 113)(94 114)(95 115)(96 116)(97 117)(98 118)(99 119)(100 120)(101 128)(102 129)(103 130)(104 121)(105 122)(106 123)(107 124)(108 125)(109 126)(110 127)(171 271)(172 272)(173 273)(174 274)(175 275)(176 276)(177 277)(178 278)(179 279)(180 280)(181 284)(182 285)(183 286)(184 287)(185 288)(186 289)(187 290)(188 281)(189 282)(190 283)(191 270)(192 261)(193 262)(194 263)(195 264)(196 265)(197 266)(198 267)(199 268)(200 269)(201 252)(202 253)(203 254)(204 255)(205 256)(206 257)(207 258)(208 259)(209 260)(210 251)(211 231)(212 232)(213 233)(214 234)(215 235)(216 236)(217 237)(218 238)(219 239)(220 240)(221 248)(222 249)(223 250)(224 241)(225 242)(226 243)(227 244)(228 245)(229 246)(230 247)(291 391)(292 392)(293 393)(294 394)(295 395)(296 396)(297 397)(298 398)(299 399)(300 400)(301 404)(302 405)(303 406)(304 407)(305 408)(306 409)(307 410)(308 401)(309 402)(310 403)(311 390)(312 381)(313 382)(314 383)(315 384)(316 385)(317 386)(318 387)(319 388)(320 389)(321 372)(322 373)(323 374)(324 375)(325 376)(326 377)(327 378)(328 379)(329 380)(330 371)(331 351)(332 352)(333 353)(334 354)(335 355)(336 356)(337 357)(338 358)(339 359)(340 360)(341 368)(342 369)(343 370)(344 361)(345 362)(346 363)(347 364)(348 365)(349 366)(350 367)(451 471)(452 472)(453 473)(454 474)(455 475)(456 476)(457 477)(458 478)(459 479)(460 480)
(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)
(1 75 109 93 89 61)(2 76 110 94 90 62)(3 77 101 95 81 63)(4 78 102 96 82 64)(5 79 103 97 83 65)(6 80 104 98 84 66)(7 71 105 99 85 67)(8 72 106 100 86 68)(9 73 107 91 87 69)(10 74 108 92 88 70)(11 47 479 51 31 23)(12 48 480 52 32 24)(13 49 471 53 33 25)(14 50 472 54 34 26)(15 41 473 55 35 27)(16 42 474 56 36 28)(17 43 475 57 37 29)(18 44 476 58 38 30)(19 45 477 59 39 21)(20 46 478 60 40 22)(111 138 162 156 142 124)(112 139 163 157 143 125)(113 140 164 158 144 126)(114 131 165 159 145 127)(115 132 166 160 146 128)(116 133 167 151 147 129)(117 134 168 152 148 130)(118 135 169 153 149 121)(119 136 170 154 150 122)(120 137 161 155 141 123)(171 198 222 216 202 184)(172 199 223 217 203 185)(173 200 224 218 204 186)(174 191 225 219 205 187)(175 192 226 220 206 188)(176 193 227 211 207 189)(177 194 228 212 208 190)(178 195 229 213 209 181)(179 196 230 214 210 182)(180 197 221 215 201 183)(231 258 282 276 262 244)(232 259 283 277 263 245)(233 260 284 278 264 246)(234 251 285 279 265 247)(235 252 286 280 266 248)(236 253 287 271 267 249)(237 254 288 272 268 250)(238 255 289 273 269 241)(239 256 290 274 270 242)(240 257 281 275 261 243)(291 304 322 336 342 318)(292 305 323 337 343 319)(293 306 324 338 344 320)(294 307 325 339 345 311)(295 308 326 340 346 312)(296 309 327 331 347 313)(297 310 328 332 348 314)(298 301 329 333 349 315)(299 302 330 334 350 316)(300 303 321 335 341 317)(351 364 382 396 402 378)(352 365 383 397 403 379)(353 366 384 398 404 380)(354 367 385 399 405 371)(355 368 386 400 406 372)(356 369 387 391 407 373)(357 370 388 392 408 374)(358 361 389 393 409 375)(359 362 390 394 410 376)(360 363 381 395 401 377)(411 424 442 456 462 438)(412 425 443 457 463 439)(413 426 444 458 464 440)(414 427 445 459 465 431)(415 428 446 460 466 432)(416 429 447 451 467 433)(417 430 448 452 468 434)(418 421 449 453 469 435)(419 422 450 454 470 436)(420 423 441 455 461 437)
(1 393 93 358)(2 394 94 359)(3 395 95 360)(4 396 96 351)(5 397 97 352)(6 398 98 353)(7 399 99 354)(8 400 100 355)(9 391 91 356)(10 392 92 357)(11 230 51 182)(12 221 52 183)(13 222 53 184)(14 223 54 185)(15 224 55 186)(16 225 56 187)(17 226 57 188)(18 227 58 189)(19 228 59 190)(20 229 60 181)(21 212 477 177)(22 213 478 178)(23 214 479 179)(24 215 480 180)(25 216 471 171)(26 217 472 172)(27 218 473 173)(28 219 474 174)(29 220 475 175)(30 211 476 176)(31 210 47 196)(32 201 48 197)(33 202 49 198)(34 203 50 199)(35 204 41 200)(36 205 42 191)(37 206 43 192)(38 207 44 193)(39 208 45 194)(40 209 46 195)(61 409 109 361)(62 410 110 362)(63 401 101 363)(64 402 102 364)(65 403 103 365)(66 404 104 366)(67 405 105 367)(68 406 106 368)(69 407 107 369)(70 408 108 370)(71 385 85 371)(72 386 86 372)(73 387 87 373)(74 388 88 374)(75 389 89 375)(76 390 90 376)(77 381 81 377)(78 382 82 378)(79 383 83 379)(80 384 84 380)(111 336 156 291)(112 337 157 292)(113 338 158 293)(114 339 159 294)(115 340 160 295)(116 331 151 296)(117 332 152 297)(118 333 153 298)(119 334 154 299)(120 335 155 300)(121 349 169 301)(122 350 170 302)(123 341 161 303)(124 342 162 304)(125 343 163 305)(126 344 164 306)(127 345 165 307)(128 346 166 308)(129 347 167 309)(130 348 168 310)(131 325 145 311)(132 326 146 312)(133 327 147 313)(134 328 148 314)(135 329 149 315)(136 330 150 316)(137 321 141 317)(138 322 142 318)(139 323 143 319)(140 324 144 320)(231 456 276 411)(232 457 277 412)(233 458 278 413)(234 459 279 414)(235 460 280 415)(236 451 271 416)(237 452 272 417)(238 453 273 418)(239 454 274 419)(240 455 275 420)(241 469 289 421)(242 470 290 422)(243 461 281 423)(244 462 282 424)(245 463 283 425)(246 464 284 426)(247 465 285 427)(248 466 286 428)(249 467 287 429)(250 468 288 430)(251 445 265 431)(252 446 266 432)(253 447 267 433)(254 448 268 434)(255 449 269 435)(256 450 270 436)(257 441 261 437)(258 442 262 438)(259 443 263 439)(260 444 264 440)

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

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

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

240 conjugacy classes

 class 1 2A ··· 2O 3 4A ··· 4P 5A 5B 5C 5D 6A ··· 6O 10A ··· 10BH 15A 15B 15C 15D 20A ··· 20BL 30A ··· 30BH order 1 2 ··· 2 3 4 ··· 4 5 5 5 5 6 ··· 6 10 ··· 10 15 15 15 15 20 ··· 20 30 ··· 30 size 1 1 ··· 1 2 3 ··· 3 1 1 1 1 2 ··· 2 1 ··· 1 2 2 2 2 3 ··· 3 2 ··· 2

240 irreducible representations

 dim 1 1 1 1 1 1 1 1 2 2 2 2 2 2 type + + + + - + image C1 C2 C2 C4 C5 C10 C10 C20 S3 Dic3 D6 C5×S3 C5×Dic3 S3×C10 kernel Dic3×C22×C10 Dic3×C2×C10 C23×C30 C22×C30 C23×Dic3 C22×Dic3 C23×C6 C22×C6 C23×C10 C22×C10 C22×C10 C24 C23 C23 # reps 1 14 1 16 4 56 4 64 1 8 7 4 32 28

Matrix representation of Dic3×C22×C10 in GL5(𝔽61)

 1 0 0 0 0 0 1 0 0 0 0 0 60 0 0 0 0 0 60 0 0 0 0 0 60
,
 1 0 0 0 0 0 1 0 0 0 0 0 60 0 0 0 0 0 1 0 0 0 0 0 1
,
 60 0 0 0 0 0 1 0 0 0 0 0 60 0 0 0 0 0 58 0 0 0 0 0 58
,
 1 0 0 0 0 0 60 0 0 0 0 0 1 0 0 0 0 0 60 1 0 0 0 60 0
,
 60 0 0 0 0 0 11 0 0 0 0 0 60 0 0 0 0 0 25 53 0 0 0 17 36

G:=sub<GL(5,GF(61))| [1,0,0,0,0,0,1,0,0,0,0,0,60,0,0,0,0,0,60,0,0,0,0,0,60],[1,0,0,0,0,0,1,0,0,0,0,0,60,0,0,0,0,0,1,0,0,0,0,0,1],[60,0,0,0,0,0,1,0,0,0,0,0,60,0,0,0,0,0,58,0,0,0,0,0,58],[1,0,0,0,0,0,60,0,0,0,0,0,1,0,0,0,0,0,60,60,0,0,0,1,0],[60,0,0,0,0,0,11,0,0,0,0,0,60,0,0,0,0,0,25,17,0,0,0,53,36] >;

Dic3×C22×C10 in GAP, Magma, Sage, TeX

{\rm Dic}_3\times C_2^2\times C_{10}
% in TeX

G:=Group("Dic3xC2^2xC10");
// GroupNames label

G:=SmallGroup(480,1163);
// by ID

G=gap.SmallGroup(480,1163);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-5,-2,-3,560,15686]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^2=c^10=d^6=1,e^2=d^3,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations

׿
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𝔽