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G = C2×Dic3×Dic5order 480 = 25·3·5

Direct product of C2, Dic3 and Dic5

Series: Derived Chief Lower central Upper central

 Derived series C1 — C15 — C2×Dic3×Dic5
 Chief series C1 — C5 — C15 — C30 — C2×C30 — C6×Dic5 — Dic3×Dic5 — C2×Dic3×Dic5
 Lower central C15 — C2×Dic3×Dic5
 Upper central C1 — C23

Generators and relations for C2×Dic3×Dic5
G = < a,b,c,d,e | a2=b6=d10=1, c2=b3, e2=d5, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=b-1, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >

Subgroups: 668 in 216 conjugacy classes, 124 normal (30 characteristic)
C1, C2, C2, C3, C4, C22, C22, C5, C6, C6, C2×C4, C23, C10, C10, Dic3, Dic3, C12, C2×C6, C2×C6, C15, C42, C22×C4, Dic5, Dic5, C20, C2×C10, C2×C10, C2×Dic3, C2×Dic3, C2×C12, C22×C6, C30, C30, C2×C42, C2×Dic5, C2×Dic5, C2×C20, C22×C10, C4×Dic3, C22×Dic3, C22×Dic3, C22×C12, C5×Dic3, C3×Dic5, Dic15, C2×C30, C2×C30, C4×Dic5, C22×Dic5, C22×Dic5, C22×C20, C2×C4×Dic3, C6×Dic5, C10×Dic3, C2×Dic15, C22×C30, C2×C4×Dic5, Dic3×Dic5, C2×C6×Dic5, Dic3×C2×C10, C22×Dic15, C2×Dic3×Dic5
Quotients:

Smallest permutation representation of C2×Dic3×Dic5
Regular action on 480 points
Generators in S480
(1 114)(2 115)(3 116)(4 117)(5 118)(6 119)(7 120)(8 111)(9 112)(10 113)(11 90)(12 81)(13 82)(14 83)(15 84)(16 85)(17 86)(18 87)(19 88)(20 89)(21 98)(22 99)(23 100)(24 91)(25 92)(26 93)(27 94)(28 95)(29 96)(30 97)(31 405)(32 406)(33 407)(34 408)(35 409)(36 410)(37 401)(38 402)(39 403)(40 404)(41 129)(42 130)(43 121)(44 122)(45 123)(46 124)(47 125)(48 126)(49 127)(50 128)(51 71)(52 72)(53 73)(54 74)(55 75)(56 76)(57 77)(58 78)(59 79)(60 80)(61 103)(62 104)(63 105)(64 106)(65 107)(66 108)(67 109)(68 110)(69 101)(70 102)(131 231)(132 232)(133 233)(134 234)(135 235)(136 236)(137 237)(138 238)(139 239)(140 240)(141 218)(142 219)(143 220)(144 211)(145 212)(146 213)(147 214)(148 215)(149 216)(150 217)(151 204)(152 205)(153 206)(154 207)(155 208)(156 209)(157 210)(158 201)(159 202)(160 203)(161 246)(162 247)(163 248)(164 249)(165 250)(166 241)(167 242)(168 243)(169 244)(170 245)(171 191)(172 192)(173 193)(174 194)(175 195)(176 196)(177 197)(178 198)(179 199)(180 200)(181 223)(182 224)(183 225)(184 226)(185 227)(186 228)(187 229)(188 230)(189 221)(190 222)(251 356)(252 357)(253 358)(254 359)(255 360)(256 351)(257 352)(258 353)(259 354)(260 355)(261 339)(262 340)(263 331)(264 332)(265 333)(266 334)(267 335)(268 336)(269 337)(270 338)(271 323)(272 324)(273 325)(274 326)(275 327)(276 328)(277 329)(278 330)(279 321)(280 322)(281 368)(282 369)(283 370)(284 361)(285 362)(286 363)(287 364)(288 365)(289 366)(290 367)(291 316)(292 317)(293 318)(294 319)(295 320)(296 311)(297 312)(298 313)(299 314)(300 315)(301 344)(302 345)(303 346)(304 347)(305 348)(306 349)(307 350)(308 341)(309 342)(310 343)(371 476)(372 477)(373 478)(374 479)(375 480)(376 471)(377 472)(378 473)(379 474)(380 475)(381 459)(382 460)(383 451)(384 452)(385 453)(386 454)(387 455)(388 456)(389 457)(390 458)(391 443)(392 444)(393 445)(394 446)(395 447)(396 448)(397 449)(398 450)(399 441)(400 442)(411 436)(412 437)(413 438)(414 439)(415 440)(416 431)(417 432)(418 433)(419 434)(420 435)(421 464)(422 465)(423 466)(424 467)(425 468)(426 469)(427 470)(428 461)(429 462)(430 463)
(1 68 28 59 45 14)(2 69 29 60 46 15)(3 70 30 51 47 16)(4 61 21 52 48 17)(5 62 22 53 49 18)(6 63 23 54 50 19)(7 64 24 55 41 20)(8 65 25 56 42 11)(9 66 26 57 43 12)(10 67 27 58 44 13)(31 436 455 470 476 442)(32 437 456 461 477 443)(33 438 457 462 478 444)(34 439 458 463 479 445)(35 440 459 464 480 446)(36 431 460 465 471 447)(37 432 451 466 472 448)(38 433 452 467 473 449)(39 434 453 468 474 450)(40 435 454 469 475 441)(71 125 85 116 102 97)(72 126 86 117 103 98)(73 127 87 118 104 99)(74 128 88 119 105 100)(75 129 89 120 106 91)(76 130 90 111 107 92)(77 121 81 112 108 93)(78 122 82 113 109 94)(79 123 83 114 110 95)(80 124 84 115 101 96)(131 157 162 176 145 185)(132 158 163 177 146 186)(133 159 164 178 147 187)(134 160 165 179 148 188)(135 151 166 180 149 189)(136 152 167 171 150 190)(137 153 168 172 141 181)(138 154 169 173 142 182)(139 155 170 174 143 183)(140 156 161 175 144 184)(191 217 222 236 205 242)(192 218 223 237 206 243)(193 219 224 238 207 244)(194 220 225 239 208 245)(195 211 226 240 209 246)(196 212 227 231 210 247)(197 213 228 232 201 248)(198 214 229 233 202 249)(199 215 230 234 203 250)(200 216 221 235 204 241)(251 307 267 291 285 280)(252 308 268 292 286 271)(253 309 269 293 287 272)(254 310 270 294 288 273)(255 301 261 295 289 274)(256 302 262 296 290 275)(257 303 263 297 281 276)(258 304 264 298 282 277)(259 305 265 299 283 278)(260 306 266 300 284 279)(311 367 327 351 345 340)(312 368 328 352 346 331)(313 369 329 353 347 332)(314 370 330 354 348 333)(315 361 321 355 349 334)(316 362 322 356 350 335)(317 363 323 357 341 336)(318 364 324 358 342 337)(319 365 325 359 343 338)(320 366 326 360 344 339)(371 400 405 411 387 427)(372 391 406 412 388 428)(373 392 407 413 389 429)(374 393 408 414 390 430)(375 394 409 415 381 421)(376 395 410 416 382 422)(377 396 401 417 383 423)(378 397 402 418 384 424)(379 398 403 419 385 425)(380 399 404 420 386 426)
(1 174 59 139)(2 175 60 140)(3 176 51 131)(4 177 52 132)(5 178 53 133)(6 179 54 134)(7 180 55 135)(8 171 56 136)(9 172 57 137)(10 173 58 138)(11 150 25 152)(12 141 26 153)(13 142 27 154)(14 143 28 155)(15 144 29 156)(16 145 30 157)(17 146 21 158)(18 147 22 159)(19 148 23 160)(20 149 24 151)(31 367 470 345)(32 368 461 346)(33 369 462 347)(34 370 463 348)(35 361 464 349)(36 362 465 350)(37 363 466 341)(38 364 467 342)(39 365 468 343)(40 366 469 344)(41 189 64 166)(42 190 65 167)(43 181 66 168)(44 182 67 169)(45 183 68 170)(46 184 69 161)(47 185 70 162)(48 186 61 163)(49 187 62 164)(50 188 63 165)(71 231 116 196)(72 232 117 197)(73 233 118 198)(74 234 119 199)(75 235 120 200)(76 236 111 191)(77 237 112 192)(78 238 113 193)(79 239 114 194)(80 240 115 195)(81 218 93 206)(82 219 94 207)(83 220 95 208)(84 211 96 209)(85 212 97 210)(86 213 98 201)(87 214 99 202)(88 215 100 203)(89 216 91 204)(90 217 92 205)(101 246 124 226)(102 247 125 227)(103 248 126 228)(104 249 127 229)(105 250 128 230)(106 241 129 221)(107 242 130 222)(108 243 121 223)(109 244 122 224)(110 245 123 225)(251 416 291 376)(252 417 292 377)(253 418 293 378)(254 419 294 379)(255 420 295 380)(256 411 296 371)(257 412 297 372)(258 413 298 373)(259 414 299 374)(260 415 300 375)(261 399 274 386)(262 400 275 387)(263 391 276 388)(264 392 277 389)(265 393 278 390)(266 394 279 381)(267 395 280 382)(268 396 271 383)(269 397 272 384)(270 398 273 385)(281 428 303 406)(282 429 304 407)(283 430 305 408)(284 421 306 409)(285 422 307 410)(286 423 308 401)(287 424 309 402)(288 425 310 403)(289 426 301 404)(290 427 302 405)(311 476 351 436)(312 477 352 437)(313 478 353 438)(314 479 354 439)(315 480 355 440)(316 471 356 431)(317 472 357 432)(318 473 358 433)(319 474 359 434)(320 475 360 435)(321 459 334 446)(322 460 335 447)(323 451 336 448)(324 452 337 449)(325 453 338 450)(326 454 339 441)(327 455 340 442)(328 456 331 443)(329 457 332 444)(330 458 333 445)
(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)
(1 296 6 291)(2 295 7 300)(3 294 8 299)(4 293 9 298)(5 292 10 297)(11 265 16 270)(12 264 17 269)(13 263 18 268)(14 262 19 267)(15 261 20 266)(21 272 26 277)(22 271 27 276)(23 280 28 275)(24 279 29 274)(25 278 30 273)(31 230 36 225)(32 229 37 224)(33 228 38 223)(34 227 39 222)(35 226 40 221)(41 306 46 301)(42 305 47 310)(43 304 48 309)(44 303 49 308)(45 302 50 307)(51 254 56 259)(52 253 57 258)(53 252 58 257)(54 251 59 256)(55 260 60 255)(61 287 66 282)(62 286 67 281)(63 285 68 290)(64 284 69 289)(65 283 70 288)(71 359 76 354)(72 358 77 353)(73 357 78 352)(74 356 79 351)(75 355 80 360)(81 332 86 337)(82 331 87 336)(83 340 88 335)(84 339 89 334)(85 338 90 333)(91 321 96 326)(92 330 97 325)(93 329 98 324)(94 328 99 323)(95 327 100 322)(101 366 106 361)(102 365 107 370)(103 364 108 369)(104 363 109 368)(105 362 110 367)(111 314 116 319)(112 313 117 318)(113 312 118 317)(114 311 119 316)(115 320 120 315)(121 347 126 342)(122 346 127 341)(123 345 128 350)(124 344 129 349)(125 343 130 348)(131 419 136 414)(132 418 137 413)(133 417 138 412)(134 416 139 411)(135 415 140 420)(141 392 146 397)(142 391 147 396)(143 400 148 395)(144 399 149 394)(145 398 150 393)(151 381 156 386)(152 390 157 385)(153 389 158 384)(154 388 159 383)(155 387 160 382)(161 426 166 421)(162 425 167 430)(163 424 168 429)(164 423 169 428)(165 422 170 427)(171 374 176 379)(172 373 177 378)(173 372 178 377)(174 371 179 376)(175 380 180 375)(181 407 186 402)(182 406 187 401)(183 405 188 410)(184 404 189 409)(185 403 190 408)(191 479 196 474)(192 478 197 473)(193 477 198 472)(194 476 199 471)(195 475 200 480)(201 452 206 457)(202 451 207 456)(203 460 208 455)(204 459 209 454)(205 458 210 453)(211 441 216 446)(212 450 217 445)(213 449 218 444)(214 448 219 443)(215 447 220 442)(231 434 236 439)(232 433 237 438)(233 432 238 437)(234 431 239 436)(235 440 240 435)(241 464 246 469)(242 463 247 468)(243 462 248 467)(244 461 249 466)(245 470 250 465)

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

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

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

96 conjugacy classes

 class 1 2A ··· 2G 3 4A ··· 4H 4I ··· 4P 4Q ··· 4X 5A 5B 6A ··· 6G 10A ··· 10N 12A ··· 12H 15A 15B 20A ··· 20P 30A ··· 30N order 1 2 ··· 2 3 4 ··· 4 4 ··· 4 4 ··· 4 5 5 6 ··· 6 10 ··· 10 12 ··· 12 15 15 20 ··· 20 30 ··· 30 size 1 1 ··· 1 2 3 ··· 3 5 ··· 5 15 ··· 15 2 2 2 ··· 2 2 ··· 2 10 ··· 10 4 4 6 ··· 6 4 ··· 4

96 irreducible representations

 dim 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 type + + + + + + + - + + - + + + - - + + image C1 C2 C2 C2 C2 C4 C4 C4 S3 D5 Dic3 D6 D6 Dic5 D10 D10 C4×S3 C4×D5 S3×D5 D5×Dic3 S3×Dic5 D30.C2 C2×S3×D5 kernel C2×Dic3×Dic5 Dic3×Dic5 C2×C6×Dic5 Dic3×C2×C10 C22×Dic15 C6×Dic5 C10×Dic3 C2×Dic15 C22×Dic5 C22×Dic3 C2×Dic5 C2×Dic5 C22×C10 C2×Dic3 C2×Dic3 C22×C6 C2×C10 C2×C6 C23 C22 C22 C22 C22 # reps 1 4 1 1 1 8 8 8 1 2 4 2 1 8 4 2 8 16 2 4 4 4 2

Matrix representation of C2×Dic3×Dic5 in GL6(𝔽61)

 60 0 0 0 0 0 0 60 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
,
 1 0 0 0 0 0 0 1 0 0 0 0 0 0 60 0 0 0 0 0 0 60 0 0 0 0 0 0 0 60 0 0 0 0 1 1
,
 1 0 0 0 0 0 0 60 0 0 0 0 0 0 11 0 0 0 0 0 0 11 0 0 0 0 0 0 30 34 0 0 0 0 4 31
,
 60 0 0 0 0 0 0 1 0 0 0 0 0 0 3 0 0 0 0 0 22 41 0 0 0 0 0 0 60 0 0 0 0 0 0 60
,
 11 0 0 0 0 0 0 60 0 0 0 0 0 0 40 58 0 0 0 0 5 21 0 0 0 0 0 0 11 0 0 0 0 0 0 11

G:=sub<GL(6,GF(61))| [60,0,0,0,0,0,0,60,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,60,0,0,0,0,0,0,60,0,0,0,0,0,0,0,1,0,0,0,0,60,1],[1,0,0,0,0,0,0,60,0,0,0,0,0,0,11,0,0,0,0,0,0,11,0,0,0,0,0,0,30,4,0,0,0,0,34,31],[60,0,0,0,0,0,0,1,0,0,0,0,0,0,3,22,0,0,0,0,0,41,0,0,0,0,0,0,60,0,0,0,0,0,0,60],[11,0,0,0,0,0,0,60,0,0,0,0,0,0,40,5,0,0,0,0,58,21,0,0,0,0,0,0,11,0,0,0,0,0,0,11] >;

C2×Dic3×Dic5 in GAP, Magma, Sage, TeX

C_2\times {\rm Dic}_3\times {\rm Dic}_5
% in TeX

G:=Group("C2xDic3xDic5");
// GroupNames label

G:=SmallGroup(480,603);
// by ID

G=gap.SmallGroup(480,603);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,56,120,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^6=d^10=1,c^2=b^3,e^2=d^5,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c^-1=b^-1,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations

׿
×
𝔽