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G = C2×Dic3×Dic5order 480 = 25·3·5

Direct product of C2, Dic3 and Dic5

direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary

Aliases: C2×Dic3×Dic5, C304C42, C158(C2×C42), C61(C4×Dic5), (C6×Dic5)⋊6C4, C103(C4×Dic3), (C10×Dic3)⋊9C4, C23.60(S3×D5), (C2×Dic15)⋊12C4, Dic1523(C2×C4), (C22×C10).97D6, (C22×C6).80D10, C30.133(C22×C4), (C2×C30).169C23, (C2×Dic5).217D6, (C22×Dic3).8D5, C22.15(S3×Dic5), C22.15(D5×Dic3), C6.14(C22×Dic5), (C2×Dic3).185D10, (C22×C30).31C22, (C22×Dic5).13S3, (C22×Dic15).8C2, C10.27(C22×Dic3), C22.15(D30.C2), (C6×Dic5).215C22, (C10×Dic3).195C22, (C2×Dic15).220C22, C54(C2×C4×Dic3), C32(C2×C4×Dic5), C6.90(C2×C4×D5), C2.3(C2×D5×Dic3), C2.3(C2×S3×Dic5), C10.121(S3×C2×C4), (C2×C6).53(C4×D5), (C2×C6×Dic5).2C2, C22.73(C2×S3×D5), (C2×C10).47(C4×S3), C2.3(C2×D30.C2), (Dic3×C2×C10).2C2, (C2×C30).108(C2×C4), (C3×Dic5)⋊21(C2×C4), (C5×Dic3)⋊21(C2×C4), (C2×C6).17(C2×Dic5), (C2×C10).37(C2×Dic3), (C2×C6).181(C22×D5), (C2×C10).181(C22×S3), SmallGroup(480,603)

Series: Derived Chief Lower central Upper central

C1C15 — C2×Dic3×Dic5
C1C5C15C30C2×C30C6×Dic5Dic3×Dic5 — C2×Dic3×Dic5
C15 — C2×Dic3×Dic5
C1C23

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 [×3], C2 [×4], C3, C4 [×12], C22, C22 [×6], C5, C6 [×3], C6 [×4], C2×C4 [×18], C23, C10 [×3], C10 [×4], Dic3 [×4], Dic3 [×4], C12 [×4], C2×C6, C2×C6 [×6], C15, C42 [×4], C22×C4 [×3], Dic5 [×4], Dic5 [×4], C20 [×4], C2×C10, C2×C10 [×6], C2×Dic3 [×6], C2×Dic3 [×6], C2×C12 [×6], C22×C6, C30 [×3], C30 [×4], C2×C42, C2×Dic5 [×6], C2×Dic5 [×6], C2×C20 [×6], C22×C10, C4×Dic3 [×4], C22×Dic3, C22×Dic3, C22×C12, C5×Dic3 [×4], C3×Dic5 [×4], Dic15 [×4], C2×C30, C2×C30 [×6], C4×Dic5 [×4], C22×Dic5, C22×Dic5, C22×C20, C2×C4×Dic3, C6×Dic5 [×6], C10×Dic3 [×6], C2×Dic15 [×6], C22×C30, C2×C4×Dic5, Dic3×Dic5 [×4], C2×C6×Dic5, Dic3×C2×C10, C22×Dic15, C2×Dic3×Dic5
Quotients: C1, C2 [×7], C4 [×12], C22 [×7], S3, C2×C4 [×18], C23, D5, Dic3 [×4], D6 [×3], C42 [×4], C22×C4 [×3], Dic5 [×4], D10 [×3], C4×S3 [×4], C2×Dic3 [×6], C22×S3, C2×C42, C4×D5 [×4], C2×Dic5 [×6], C22×D5, C4×Dic3 [×4], S3×C2×C4 [×2], C22×Dic3, S3×D5, C4×Dic5 [×4], C2×C4×D5 [×2], C22×Dic5, C2×C4×Dic3, D5×Dic3 [×2], S3×Dic5 [×2], D30.C2 [×2], C2×S3×D5, C2×C4×Dic5, Dic3×Dic5 [×4], C2×D5×Dic3, C2×S3×Dic5, C2×D30.C2, C2×Dic3×Dic5

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

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

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

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

96 conjugacy classes

class 1 2A···2G 3 4A···4H4I···4P4Q···4X5A5B6A···6G10A···10N12A···12H15A15B20A···20P30A···30N
order12···234···44···44···4556···610···1012···12151520···2030···30
size11···123···35···515···15222···22···210···10446···64···4

96 irreducible representations

dim11111111222222222244444
type+++++++-++-+++--++
imageC1C2C2C2C2C4C4C4S3D5Dic3D6D6Dic5D10D10C4×S3C4×D5S3×D5D5×Dic3S3×Dic5D30.C2C2×S3×D5
kernelC2×Dic3×Dic5Dic3×Dic5C2×C6×Dic5Dic3×C2×C10C22×Dic15C6×Dic5C10×Dic3C2×Dic15C22×Dic5C22×Dic3C2×Dic5C2×Dic5C22×C10C2×Dic3C2×Dic3C22×C6C2×C10C2×C6C23C22C22C22C22
# reps141118881242184281624442

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

6000000
0600000
001000
000100
000010
000001
,
100000
010000
0060000
0006000
0000060
000011
,
100000
0600000
0011000
0001100
00003034
0000431
,
6000000
010000
003000
00224100
0000600
0000060
,
1100000
0600000
00405800
0052100
0000110
0000011

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

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