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## G = C3×Q8⋊Dic5order 480 = 25·3·5

### Direct product of C3 and Q8⋊Dic5

Series: Derived Chief Lower central Upper central

 Derived series C1 — C20 — C3×Q8⋊Dic5
 Chief series C1 — C5 — C10 — C20 — C2×C20 — C2×C60 — C3×C4⋊Dic5 — C3×Q8⋊Dic5
 Lower central C5 — C10 — C20 — C3×Q8⋊Dic5
 Upper central C1 — C2×C6 — C2×C12 — C6×Q8

Generators and relations for C3×Q8⋊Dic5
G = < a,b,c,d,e | a3=b4=d10=1, c2=b2, e2=d5, 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: 208 in 84 conjugacy classes, 50 normal (42 characteristic)
C1, C2 [×3], C3, C4 [×2], C4 [×3], C22, C5, C6 [×3], C8, C2×C4, C2×C4 [×2], Q8 [×2], Q8, C10 [×3], C12 [×2], C12 [×3], C2×C6, C15, C4⋊C4, C2×C8, C2×Q8, Dic5, C20 [×2], C20 [×2], C2×C10, C24, C2×C12, C2×C12 [×2], C3×Q8 [×2], C3×Q8, C30 [×3], Q8⋊C4, C52C8, C2×Dic5, C2×C20, C2×C20, C5×Q8 [×2], C5×Q8, C3×C4⋊C4, C2×C24, C6×Q8, C3×Dic5, C60 [×2], C60 [×2], C2×C30, C2×C52C8, C4⋊Dic5, Q8×C10, C3×Q8⋊C4, C3×C52C8, C6×Dic5, C2×C60, C2×C60, Q8×C15 [×2], Q8×C15, Q8⋊Dic5, C6×C52C8, C3×C4⋊Dic5, Q8×C30, C3×Q8⋊Dic5
Quotients: C1, C2 [×3], C3, C4 [×2], C22, C6 [×3], C2×C4, D4 [×2], D5, C12 [×2], C2×C6, C22⋊C4, SD16, Q16, Dic5 [×2], D10, C2×C12, C3×D4 [×2], C3×D5, Q8⋊C4, C2×Dic5, C5⋊D4 [×2], C3×C22⋊C4, C3×SD16, C3×Q16, C3×Dic5 [×2], C6×D5, Q8⋊D5, C5⋊Q16, C23.D5, C3×Q8⋊C4, C6×Dic5, C3×C5⋊D4 [×2], Q8⋊Dic5, C3×Q8⋊D5, C3×C5⋊Q16, C3×C23.D5, C3×Q8⋊Dic5

Smallest permutation representation of C3×Q8⋊Dic5
Regular action on 480 points
Generators in S480
(1 99 59)(2 100 60)(3 91 51)(4 92 52)(5 93 53)(6 94 54)(7 95 55)(8 96 56)(9 97 57)(10 98 58)(11 110 70)(12 101 61)(13 102 62)(14 103 63)(15 104 64)(16 105 65)(17 106 66)(18 107 67)(19 108 68)(20 109 69)(21 448 408)(22 449 409)(23 450 410)(24 441 401)(25 442 402)(26 443 403)(27 444 404)(28 445 405)(29 446 406)(30 447 407)(31 111 71)(32 112 72)(33 113 73)(34 114 74)(35 115 75)(36 116 76)(37 117 77)(38 118 78)(39 119 79)(40 120 80)(41 121 81)(42 122 82)(43 123 83)(44 124 84)(45 125 85)(46 126 86)(47 127 87)(48 128 88)(49 129 89)(50 130 90)(131 211 171)(132 212 172)(133 213 173)(134 214 174)(135 215 175)(136 216 176)(137 217 177)(138 218 178)(139 219 179)(140 220 180)(141 221 181)(142 222 182)(143 223 183)(144 224 184)(145 225 185)(146 226 186)(147 227 187)(148 228 188)(149 229 189)(150 230 190)(151 231 191)(152 232 192)(153 233 193)(154 234 194)(155 235 195)(156 236 196)(157 237 197)(158 238 198)(159 239 199)(160 240 200)(161 244 201)(162 245 202)(163 246 203)(164 247 204)(165 248 205)(166 249 206)(167 250 207)(168 241 208)(169 242 209)(170 243 210)(251 331 291)(252 332 292)(253 333 293)(254 334 294)(255 335 295)(256 336 296)(257 337 297)(258 338 298)(259 339 299)(260 340 300)(261 341 301)(262 342 302)(263 343 303)(264 344 304)(265 345 305)(266 346 306)(267 347 307)(268 348 308)(269 349 309)(270 350 310)(271 351 311)(272 352 312)(273 353 313)(274 354 314)(275 355 315)(276 356 316)(277 357 317)(278 358 318)(279 359 319)(280 360 320)(281 361 321)(282 362 322)(283 363 323)(284 364 324)(285 365 325)(286 366 326)(287 367 327)(288 368 328)(289 369 329)(290 370 330)(371 451 411)(372 452 412)(373 453 413)(374 454 414)(375 455 415)(376 456 416)(377 457 417)(378 458 418)(379 459 419)(380 460 420)(381 461 421)(382 462 422)(383 463 423)(384 464 424)(385 465 425)(386 466 426)(387 467 427)(388 468 428)(389 469 429)(390 470 430)(391 471 431)(392 472 432)(393 473 433)(394 474 434)(395 475 435)(396 476 436)(397 477 437)(398 478 438)(399 479 439)(400 480 440)
(1 47 31 19)(2 48 32 20)(3 49 33 11)(4 50 34 12)(5 41 35 13)(6 42 36 14)(7 43 37 15)(8 44 38 16)(9 45 39 17)(10 46 40 18)(21 479 462 456)(22 480 463 457)(23 471 464 458)(24 472 465 459)(25 473 466 460)(26 474 467 451)(27 475 468 452)(28 476 469 453)(29 477 470 454)(30 478 461 455)(51 89 73 70)(52 90 74 61)(53 81 75 62)(54 82 76 63)(55 83 77 64)(56 84 78 65)(57 85 79 66)(58 86 80 67)(59 87 71 68)(60 88 72 69)(91 129 113 110)(92 130 114 101)(93 121 115 102)(94 122 116 103)(95 123 117 104)(96 124 118 105)(97 125 119 106)(98 126 120 107)(99 127 111 108)(100 128 112 109)(131 150 153 169)(132 141 154 170)(133 142 155 161)(134 143 156 162)(135 144 157 163)(136 145 158 164)(137 146 159 165)(138 147 160 166)(139 148 151 167)(140 149 152 168)(171 190 193 209)(172 181 194 210)(173 182 195 201)(174 183 196 202)(175 184 197 203)(176 185 198 204)(177 186 199 205)(178 187 200 206)(179 188 191 207)(180 189 192 208)(211 230 233 242)(212 221 234 243)(213 222 235 244)(214 223 236 245)(215 224 237 246)(216 225 238 247)(217 226 239 248)(218 227 240 249)(219 228 231 250)(220 229 232 241)(251 267 274 283)(252 268 275 284)(253 269 276 285)(254 270 277 286)(255 261 278 287)(256 262 279 288)(257 263 280 289)(258 264 271 290)(259 265 272 281)(260 266 273 282)(291 307 314 323)(292 308 315 324)(293 309 316 325)(294 310 317 326)(295 301 318 327)(296 302 319 328)(297 303 320 329)(298 304 311 330)(299 305 312 321)(300 306 313 322)(331 347 354 363)(332 348 355 364)(333 349 356 365)(334 350 357 366)(335 341 358 367)(336 342 359 368)(337 343 360 369)(338 344 351 370)(339 345 352 361)(340 346 353 362)(371 403 394 387)(372 404 395 388)(373 405 396 389)(374 406 397 390)(375 407 398 381)(376 408 399 382)(377 409 400 383)(378 410 391 384)(379 401 392 385)(380 402 393 386)(411 443 434 427)(412 444 435 428)(413 445 436 429)(414 446 437 430)(415 447 438 421)(416 448 439 422)(417 449 440 423)(418 450 431 424)(419 441 432 425)(420 442 433 426)
(1 156 31 134)(2 157 32 135)(3 158 33 136)(4 159 34 137)(5 160 35 138)(6 151 36 139)(7 152 37 140)(8 153 38 131)(9 154 39 132)(10 155 40 133)(11 164 49 145)(12 165 50 146)(13 166 41 147)(14 167 42 148)(15 168 43 149)(16 169 44 150)(17 170 45 141)(18 161 46 142)(19 162 47 143)(20 163 48 144)(21 354 462 331)(22 355 463 332)(23 356 464 333)(24 357 465 334)(25 358 466 335)(26 359 467 336)(27 360 468 337)(28 351 469 338)(29 352 470 339)(30 353 461 340)(51 198 73 176)(52 199 74 177)(53 200 75 178)(54 191 76 179)(55 192 77 180)(56 193 78 171)(57 194 79 172)(58 195 80 173)(59 196 71 174)(60 197 72 175)(61 205 90 186)(62 206 81 187)(63 207 82 188)(64 208 83 189)(65 209 84 190)(66 210 85 181)(67 201 86 182)(68 202 87 183)(69 203 88 184)(70 204 89 185)(91 238 113 216)(92 239 114 217)(93 240 115 218)(94 231 116 219)(95 232 117 220)(96 233 118 211)(97 234 119 212)(98 235 120 213)(99 236 111 214)(100 237 112 215)(101 248 130 226)(102 249 121 227)(103 250 122 228)(104 241 123 229)(105 242 124 230)(106 243 125 221)(107 244 126 222)(108 245 127 223)(109 246 128 224)(110 247 129 225)(251 408 274 382)(252 409 275 383)(253 410 276 384)(254 401 277 385)(255 402 278 386)(256 403 279 387)(257 404 280 388)(258 405 271 389)(259 406 272 390)(260 407 273 381)(261 380 287 393)(262 371 288 394)(263 372 289 395)(264 373 290 396)(265 374 281 397)(266 375 282 398)(267 376 283 399)(268 377 284 400)(269 378 285 391)(270 379 286 392)(291 448 314 422)(292 449 315 423)(293 450 316 424)(294 441 317 425)(295 442 318 426)(296 443 319 427)(297 444 320 428)(298 445 311 429)(299 446 312 430)(300 447 313 421)(301 420 327 433)(302 411 328 434)(303 412 329 435)(304 413 330 436)(305 414 321 437)(306 415 322 438)(307 416 323 439)(308 417 324 440)(309 418 325 431)(310 419 326 432)(341 460 367 473)(342 451 368 474)(343 452 369 475)(344 453 370 476)(345 454 361 477)(346 455 362 478)(347 456 363 479)(348 457 364 480)(349 458 365 471)(350 459 366 472)
(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)
(1 251 6 256)(2 260 7 255)(3 259 8 254)(4 258 9 253)(5 257 10 252)(11 265 16 270)(12 264 17 269)(13 263 18 268)(14 262 19 267)(15 261 20 266)(21 250 26 245)(22 249 27 244)(23 248 28 243)(24 247 29 242)(25 246 30 241)(31 274 36 279)(32 273 37 278)(33 272 38 277)(34 271 39 276)(35 280 40 275)(41 289 46 284)(42 288 47 283)(43 287 48 282)(44 286 49 281)(45 285 50 290)(51 299 56 294)(52 298 57 293)(53 297 58 292)(54 296 59 291)(55 295 60 300)(61 304 66 309)(62 303 67 308)(63 302 68 307)(64 301 69 306)(65 310 70 305)(71 314 76 319)(72 313 77 318)(73 312 78 317)(74 311 79 316)(75 320 80 315)(81 329 86 324)(82 328 87 323)(83 327 88 322)(84 326 89 321)(85 325 90 330)(91 339 96 334)(92 338 97 333)(93 337 98 332)(94 336 99 331)(95 335 100 340)(101 344 106 349)(102 343 107 348)(103 342 108 347)(104 341 109 346)(105 350 110 345)(111 354 116 359)(112 353 117 358)(113 352 118 357)(114 351 119 356)(115 360 120 355)(121 369 126 364)(122 368 127 363)(123 367 128 362)(124 366 129 361)(125 365 130 370)(131 379 136 374)(132 378 137 373)(133 377 138 372)(134 376 139 371)(135 375 140 380)(141 384 146 389)(142 383 147 388)(143 382 148 387)(144 381 149 386)(145 390 150 385)(151 394 156 399)(152 393 157 398)(153 392 158 397)(154 391 159 396)(155 400 160 395)(161 409 166 404)(162 408 167 403)(163 407 168 402)(164 406 169 401)(165 405 170 410)(171 419 176 414)(172 418 177 413)(173 417 178 412)(174 416 179 411)(175 415 180 420)(181 424 186 429)(182 423 187 428)(183 422 188 427)(184 421 189 426)(185 430 190 425)(191 434 196 439)(192 433 197 438)(193 432 198 437)(194 431 199 436)(195 440 200 435)(201 449 206 444)(202 448 207 443)(203 447 208 442)(204 446 209 441)(205 445 210 450)(211 459 216 454)(212 458 217 453)(213 457 218 452)(214 456 219 451)(215 455 220 460)(221 464 226 469)(222 463 227 468)(223 462 228 467)(224 461 229 466)(225 470 230 465)(231 474 236 479)(232 473 237 478)(233 472 238 477)(234 471 239 476)(235 480 240 475)

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

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

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

102 conjugacy classes

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

102 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 C3 C4 C6 C6 C6 C12 D4 D4 D5 SD16 Q16 D10 Dic5 C3×D4 C3×D4 C3×D5 C5⋊D4 C5⋊D4 C3×SD16 C3×Q16 C6×D5 C3×Dic5 C3×C5⋊D4 C3×C5⋊D4 Q8⋊D5 C5⋊Q16 C3×Q8⋊D5 C3×C5⋊Q16 kernel C3×Q8⋊Dic5 C6×C5⋊2C8 C3×C4⋊Dic5 Q8×C30 Q8⋊Dic5 Q8×C15 C2×C5⋊2C8 C4⋊Dic5 Q8×C10 C5×Q8 C60 C2×C30 C6×Q8 C30 C30 C2×C12 C3×Q8 C20 C2×C10 C2×Q8 C12 C2×C6 C10 C10 C2×C4 Q8 C4 C22 C6 C6 C2 C2 # reps 1 1 1 1 2 4 2 2 2 8 1 1 2 2 2 2 4 2 2 4 4 4 4 4 4 8 8 8 2 2 4 4

Matrix representation of C3×Q8⋊Dic5 in GL4(𝔽241) generated by

 15 0 0 0 0 15 0 0 0 0 225 0 0 0 0 225
,
 1 0 0 0 0 1 0 0 0 0 1 123 0 0 192 240
,
 240 0 0 0 0 240 0 0 0 0 177 81 0 0 0 64
,
 190 1 0 0 240 0 0 0 0 0 1 0 0 0 0 1
,
 156 1 0 0 4 85 0 0 0 0 219 93 0 0 57 22
G:=sub<GL(4,GF(241))| [15,0,0,0,0,15,0,0,0,0,225,0,0,0,0,225],[1,0,0,0,0,1,0,0,0,0,1,192,0,0,123,240],[240,0,0,0,0,240,0,0,0,0,177,0,0,0,81,64],[190,240,0,0,1,0,0,0,0,0,1,0,0,0,0,1],[156,4,0,0,1,85,0,0,0,0,219,57,0,0,93,22] >;

C3×Q8⋊Dic5 in GAP, Magma, Sage, TeX

C_3\times Q_8\rtimes {\rm Dic}_5
% in TeX

G:=Group("C3xQ8:Dic5");
// GroupNames label

G:=SmallGroup(480,113);
// by ID

G=gap.SmallGroup(480,113);
# by ID

G:=PCGroup([7,-2,-2,-3,-2,-2,-2,-5,84,365,344,2524,1271,102,18822]);
// Polycyclic

G:=Group<a,b,c,d,e|a^3=b^4=d^10=1,c^2=b^2,e^2=d^5,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

׿
×
𝔽