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## G = C5×Q8⋊2Dic3order 480 = 25·3·5

### Direct product of C5 and Q8⋊2Dic3

Series: Derived Chief Lower central Upper central

 Derived series C1 — C12 — C5×Q8⋊2Dic3
 Chief series C1 — C3 — C6 — C12 — C2×C12 — C2×C60 — C5×C4⋊Dic3 — C5×Q8⋊2Dic3
 Lower central C3 — C6 — C12 — C5×Q8⋊2Dic3
 Upper central C1 — C2×C10 — C2×C20 — Q8×C10

Generators and relations for C5×Q82Dic3
G = < a,b,c,d,e | a5=b4=d6=1, c2=b2, e2=d3, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=ebe-1=b-1, bd=db, cd=dc, ece-1=b-1c, ede-1=d-1 >

Subgroups: 164 in 84 conjugacy classes, 50 normal (42 characteristic)
C1, C2, C3, C4, C4, C22, C5, C6, C8, C2×C4, C2×C4, Q8, Q8, C10, Dic3, C12, C12, C2×C6, C15, C4⋊C4, C2×C8, C2×Q8, C20, C20, C2×C10, C3⋊C8, C2×Dic3, C2×C12, C2×C12, C3×Q8, C3×Q8, C30, Q8⋊C4, C40, C2×C20, C2×C20, C5×Q8, C5×Q8, C2×C3⋊C8, C4⋊Dic3, C6×Q8, C5×Dic3, C60, C60, C2×C30, C5×C4⋊C4, C2×C40, Q8×C10, Q82Dic3, C5×C3⋊C8, C10×Dic3, C2×C60, C2×C60, Q8×C15, Q8×C15, C5×Q8⋊C4, C10×C3⋊C8, C5×C4⋊Dic3, Q8×C30, C5×Q82Dic3
Quotients: C1, C2, C4, C22, C5, S3, C2×C4, D4, C10, Dic3, D6, C22⋊C4, SD16, Q16, C20, C2×C10, C2×Dic3, C3⋊D4, C5×S3, Q8⋊C4, C2×C20, C5×D4, Q82S3, C3⋊Q16, C6.D4, C5×Dic3, S3×C10, C5×C22⋊C4, C5×SD16, C5×Q16, Q82Dic3, C10×Dic3, C5×C3⋊D4, C5×Q8⋊C4, C5×Q82S3, C5×C3⋊Q16, C5×C6.D4, C5×Q82Dic3

Smallest permutation representation of C5×Q82Dic3
Regular action on 480 points
Generators in S480
(1 107 83 59 35)(2 108 84 60 36)(3 103 79 55 31)(4 104 80 56 32)(5 105 81 57 33)(6 106 82 58 34)(7 113 89 65 41)(8 114 90 66 42)(9 109 85 61 37)(10 110 86 62 38)(11 111 87 63 39)(12 112 88 64 40)(13 460 436 412 388)(14 461 437 413 389)(15 462 438 414 390)(16 457 433 409 385)(17 458 434 410 386)(18 459 435 411 387)(19 115 91 67 43)(20 116 92 68 44)(21 117 93 69 45)(22 118 94 70 46)(23 119 95 71 47)(24 120 96 72 48)(25 121 97 73 49)(26 122 98 74 50)(27 123 99 75 51)(28 124 100 76 52)(29 125 101 77 53)(30 126 102 78 54)(127 223 199 175 151)(128 224 200 176 152)(129 225 201 177 153)(130 226 202 178 154)(131 227 203 179 155)(132 228 204 180 156)(133 229 205 181 157)(134 230 206 182 158)(135 231 207 183 159)(136 232 208 184 160)(137 233 209 185 161)(138 234 210 186 162)(139 235 211 187 163)(140 236 212 188 164)(141 237 213 189 165)(142 238 214 190 166)(143 239 215 191 167)(144 240 216 192 168)(145 242 217 193 169)(146 243 218 194 170)(147 244 219 195 171)(148 245 220 196 172)(149 246 221 197 173)(150 241 222 198 174)(247 343 319 295 271)(248 344 320 296 272)(249 345 321 297 273)(250 346 322 298 274)(251 347 323 299 275)(252 348 324 300 276)(253 349 325 301 277)(254 350 326 302 278)(255 351 327 303 279)(256 352 328 304 280)(257 353 329 305 281)(258 354 330 306 282)(259 355 331 307 283)(260 356 332 308 284)(261 357 333 309 285)(262 358 334 310 286)(263 359 335 311 287)(264 360 336 312 288)(265 361 337 313 289)(266 362 338 314 290)(267 363 339 315 291)(268 364 340 316 292)(269 365 341 317 293)(270 366 342 318 294)(367 463 439 415 391)(368 464 440 416 392)(369 465 441 417 393)(370 466 442 418 394)(371 467 443 419 395)(372 468 444 420 396)(373 469 445 421 397)(374 470 446 422 398)(375 471 447 423 399)(376 472 448 424 400)(377 473 449 425 401)(378 474 450 426 402)(379 475 451 427 403)(380 476 452 428 404)(381 477 453 429 405)(382 478 454 430 406)(383 479 455 431 407)(384 480 456 432 408)
(1 29 19 12)(2 30 20 7)(3 25 21 8)(4 26 22 9)(5 27 23 10)(6 28 24 11)(13 479 470 466)(14 480 471 467)(15 475 472 468)(16 476 473 463)(17 477 474 464)(18 478 469 465)(31 49 45 42)(32 50 46 37)(33 51 47 38)(34 52 48 39)(35 53 43 40)(36 54 44 41)(55 73 69 66)(56 74 70 61)(57 75 71 62)(58 76 72 63)(59 77 67 64)(60 78 68 65)(79 97 93 90)(80 98 94 85)(81 99 95 86)(82 100 96 87)(83 101 91 88)(84 102 92 89)(103 121 117 114)(104 122 118 109)(105 123 119 110)(106 124 120 111)(107 125 115 112)(108 126 116 113)(127 138 141 145)(128 133 142 146)(129 134 143 147)(130 135 144 148)(131 136 139 149)(132 137 140 150)(151 162 165 169)(152 157 166 170)(153 158 167 171)(154 159 168 172)(155 160 163 173)(156 161 164 174)(175 186 189 193)(176 181 190 194)(177 182 191 195)(178 183 192 196)(179 184 187 197)(180 185 188 198)(199 210 213 217)(200 205 214 218)(201 206 215 219)(202 207 216 220)(203 208 211 221)(204 209 212 222)(223 234 237 242)(224 229 238 243)(225 230 239 244)(226 231 240 245)(227 232 235 246)(228 233 236 241)(247 257 260 265)(248 258 261 266)(249 253 262 267)(250 254 263 268)(251 255 264 269)(252 256 259 270)(271 281 284 289)(272 282 285 290)(273 277 286 291)(274 278 287 292)(275 279 288 293)(276 280 283 294)(295 305 308 313)(296 306 309 314)(297 301 310 315)(298 302 311 316)(299 303 312 317)(300 304 307 318)(319 329 332 337)(320 330 333 338)(321 325 334 339)(322 326 335 340)(323 327 336 341)(324 328 331 342)(343 353 356 361)(344 354 357 362)(345 349 358 363)(346 350 359 364)(347 351 360 365)(348 352 355 366)(367 385 380 377)(368 386 381 378)(369 387 382 373)(370 388 383 374)(371 389 384 375)(372 390 379 376)(391 409 404 401)(392 410 405 402)(393 411 406 397)(394 412 407 398)(395 413 408 399)(396 414 403 400)(415 433 428 425)(416 434 429 426)(417 435 430 421)(418 436 431 422)(419 437 432 423)(420 438 427 424)(439 457 452 449)(440 458 453 450)(441 459 454 445)(442 460 455 446)(443 461 456 447)(444 462 451 448)
(1 142 19 128)(2 143 20 129)(3 144 21 130)(4 139 22 131)(5 140 23 132)(6 141 24 127)(7 147 30 134)(8 148 25 135)(9 149 26 136)(10 150 27 137)(11 145 28 138)(12 146 29 133)(13 356 470 343)(14 357 471 344)(15 358 472 345)(16 359 473 346)(17 360 474 347)(18 355 469 348)(31 168 45 154)(32 163 46 155)(33 164 47 156)(34 165 48 151)(35 166 43 152)(36 167 44 153)(37 173 50 160)(38 174 51 161)(39 169 52 162)(40 170 53 157)(41 171 54 158)(42 172 49 159)(55 192 69 178)(56 187 70 179)(57 188 71 180)(58 189 72 175)(59 190 67 176)(60 191 68 177)(61 197 74 184)(62 198 75 185)(63 193 76 186)(64 194 77 181)(65 195 78 182)(66 196 73 183)(79 216 93 202)(80 211 94 203)(81 212 95 204)(82 213 96 199)(83 214 91 200)(84 215 92 201)(85 221 98 208)(86 222 99 209)(87 217 100 210)(88 218 101 205)(89 219 102 206)(90 220 97 207)(103 240 117 226)(104 235 118 227)(105 236 119 228)(106 237 120 223)(107 238 115 224)(108 239 116 225)(109 246 122 232)(110 241 123 233)(111 242 124 234)(112 243 125 229)(113 244 126 230)(114 245 121 231)(247 388 260 374)(248 389 261 375)(249 390 262 376)(250 385 263 377)(251 386 264 378)(252 387 259 373)(253 372 267 379)(254 367 268 380)(255 368 269 381)(256 369 270 382)(257 370 265 383)(258 371 266 384)(271 412 284 398)(272 413 285 399)(273 414 286 400)(274 409 287 401)(275 410 288 402)(276 411 283 397)(277 396 291 403)(278 391 292 404)(279 392 293 405)(280 393 294 406)(281 394 289 407)(282 395 290 408)(295 436 308 422)(296 437 309 423)(297 438 310 424)(298 433 311 425)(299 434 312 426)(300 435 307 421)(301 420 315 427)(302 415 316 428)(303 416 317 429)(304 417 318 430)(305 418 313 431)(306 419 314 432)(319 460 332 446)(320 461 333 447)(321 462 334 448)(322 457 335 449)(323 458 336 450)(324 459 331 445)(325 444 339 451)(326 439 340 452)(327 440 341 453)(328 441 342 454)(329 442 337 455)(330 443 338 456)(349 468 363 475)(350 463 364 476)(351 464 365 477)(352 465 366 478)(353 466 361 479)(354 467 362 480)
(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)
(1 247 4 250)(2 252 5 249)(3 251 6 248)(7 256 10 253)(8 255 11 258)(9 254 12 257)(13 246 16 243)(14 245 17 242)(15 244 18 241)(19 260 22 263)(20 259 23 262)(21 264 24 261)(25 269 28 266)(26 268 29 265)(27 267 30 270)(31 275 34 272)(32 274 35 271)(33 273 36 276)(37 278 40 281)(38 277 41 280)(39 282 42 279)(43 284 46 287)(44 283 47 286)(45 288 48 285)(49 293 52 290)(50 292 53 289)(51 291 54 294)(55 299 58 296)(56 298 59 295)(57 297 60 300)(61 302 64 305)(62 301 65 304)(63 306 66 303)(67 308 70 311)(68 307 71 310)(69 312 72 309)(73 317 76 314)(74 316 77 313)(75 315 78 318)(79 323 82 320)(80 322 83 319)(81 321 84 324)(85 326 88 329)(86 325 89 328)(87 330 90 327)(91 332 94 335)(92 331 95 334)(93 336 96 333)(97 341 100 338)(98 340 101 337)(99 339 102 342)(103 347 106 344)(104 346 107 343)(105 345 108 348)(109 350 112 353)(110 349 113 352)(111 354 114 351)(115 356 118 359)(116 355 119 358)(117 360 120 357)(121 365 124 362)(122 364 125 361)(123 363 126 366)(127 371 130 368)(128 370 131 367)(129 369 132 372)(133 374 136 377)(134 373 137 376)(135 378 138 375)(139 380 142 383)(140 379 143 382)(141 384 144 381)(145 389 148 386)(146 388 149 385)(147 387 150 390)(151 395 154 392)(152 394 155 391)(153 393 156 396)(157 398 160 401)(158 397 161 400)(159 402 162 399)(163 404 166 407)(164 403 167 406)(165 408 168 405)(169 413 172 410)(170 412 173 409)(171 411 174 414)(175 419 178 416)(176 418 179 415)(177 417 180 420)(181 422 184 425)(182 421 185 424)(183 426 186 423)(187 428 190 431)(188 427 191 430)(189 432 192 429)(193 437 196 434)(194 436 197 433)(195 435 198 438)(199 443 202 440)(200 442 203 439)(201 441 204 444)(205 446 208 449)(206 445 209 448)(207 450 210 447)(211 452 214 455)(212 451 215 454)(213 456 216 453)(217 461 220 458)(218 460 221 457)(219 459 222 462)(223 467 226 464)(224 466 227 463)(225 465 228 468)(229 470 232 473)(230 469 233 472)(231 474 234 471)(235 476 238 479)(236 475 239 478)(237 480 240 477)

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

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

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

120 conjugacy classes

 class 1 2A 2B 2C 3 4A 4B 4C 4D 4E 4F 5A 5B 5C 5D 6A 6B 6C 8A 8B 8C 8D 10A ··· 10L 12A ··· 12F 15A 15B 15C 15D 20A ··· 20H 20I ··· 20P 20Q ··· 20X 30A ··· 30L 40A ··· 40P 60A ··· 60X order 1 2 2 2 3 4 4 4 4 4 4 5 5 5 5 6 6 6 8 8 8 8 10 ··· 10 12 ··· 12 15 15 15 15 20 ··· 20 20 ··· 20 20 ··· 20 30 ··· 30 40 ··· 40 60 ··· 60 size 1 1 1 1 2 2 2 4 4 12 12 1 1 1 1 2 2 2 6 6 6 6 1 ··· 1 4 ··· 4 2 2 2 2 2 ··· 2 4 ··· 4 12 ··· 12 2 ··· 2 6 ··· 6 4 ··· 4

120 irreducible representations

 dim 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 4 type + + + + + + + + - - + - image C1 C2 C2 C2 C4 C5 C10 C10 C10 C20 S3 D4 D4 D6 Dic3 SD16 Q16 C3⋊D4 C3⋊D4 C5×S3 C5×D4 C5×D4 S3×C10 C5×Dic3 C5×SD16 C5×Q16 C5×C3⋊D4 C5×C3⋊D4 Q8⋊2S3 C3⋊Q16 C5×Q8⋊2S3 C5×C3⋊Q16 kernel C5×Q8⋊2Dic3 C10×C3⋊C8 C5×C4⋊Dic3 Q8×C30 Q8×C15 Q8⋊2Dic3 C2×C3⋊C8 C4⋊Dic3 C6×Q8 C3×Q8 Q8×C10 C60 C2×C30 C2×C20 C5×Q8 C30 C30 C20 C2×C10 C2×Q8 C12 C2×C6 C2×C4 Q8 C6 C6 C4 C22 C10 C10 C2 C2 # reps 1 1 1 1 4 4 4 4 4 16 1 1 1 1 2 2 2 2 2 4 4 4 4 8 8 8 8 8 1 1 4 4

Matrix representation of C5×Q82Dic3 in GL6(𝔽241)

 87 0 0 0 0 0 0 87 0 0 0 0 0 0 98 0 0 0 0 0 0 98 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
 0 1 0 0 0 0 240 0 0 0 0 0 0 0 0 1 0 0 0 0 240 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
 121 78 0 0 0 0 78 120 0 0 0 0 0 0 21 194 0 0 0 0 194 220 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 0 240 0 0 0 0 0 0 240 0 0 0 0 0 0 0 240 0 0 0 0 1 240
,
 166 147 0 0 0 0 147 75 0 0 0 0 0 0 45 25 0 0 0 0 25 196 0 0 0 0 0 0 71 81 0 0 0 0 152 170

G:=sub<GL(6,GF(241))| [87,0,0,0,0,0,0,87,0,0,0,0,0,0,98,0,0,0,0,0,0,98,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,240,0,0,0,0,1,0,0,0,0,0,0,0,0,240,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[121,78,0,0,0,0,78,120,0,0,0,0,0,0,21,194,0,0,0,0,194,220,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,240,0,0,0,0,0,0,240,0,0,0,0,0,0,0,1,0,0,0,0,240,240],[166,147,0,0,0,0,147,75,0,0,0,0,0,0,45,25,0,0,0,0,25,196,0,0,0,0,0,0,71,152,0,0,0,0,81,170] >;

C5×Q82Dic3 in GAP, Magma, Sage, TeX

C_5\times Q_8\rtimes_2{\rm Dic}_3
% in TeX

G:=Group("C5xQ8:2Dic3");
// GroupNames label

G:=SmallGroup(480,154);
// by ID

G=gap.SmallGroup(480,154);
# by ID

G:=PCGroup([7,-2,-2,-5,-2,-2,-2,-3,140,589,568,4204,2111,102,15686]);
// Polycyclic

G:=Group<a,b,c,d,e|a^5=b^4=d^6=1,c^2=b^2,e^2=d^3,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c^-1=e*b*e^-1=b^-1,b*d=d*b,c*d=d*c,e*c*e^-1=b^-1*c,e*d*e^-1=d^-1>;
// generators/relations

׿
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𝔽