direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C3×Q8⋊Dic5, C60.119D4, C30.21Q16, C30.36SD16, (C5×Q8)⋊7C12, C20.9(C3×D4), (C6×Q8).6D5, (Q8×C15)⋊10C4, Q8⋊2(C3×Dic5), (C3×Q8)⋊4Dic5, (Q8×C10).5C6, (Q8×C30).6C2, C10.5(C3×Q16), C4.2(C6×Dic5), C60.163(C2×C4), C20.29(C2×C12), (C2×C30).160D4, C6.12(Q8⋊D5), C4⋊Dic5.10C6, C10.8(C3×SD16), C15⋊18(Q8⋊C4), (C2×C12).355D10, C12.93(C5⋊D4), C12.31(C2×Dic5), C6.12(C5⋊Q16), (C2×C60).281C22, C6.25(C23.D5), C30.113(C22⋊C4), C5⋊4(C3×Q8⋊C4), C2.3(C3×Q8⋊D5), (C2×C5⋊2C8).5C6, (C2×C4).34(C6×D5), C4.14(C3×C5⋊D4), (C2×Q8).3(C3×D5), C2.3(C3×C5⋊Q16), (C6×C5⋊2C8).17C2, (C2×C20).17(C2×C6), (C2×C10).35(C3×D4), C2.6(C3×C23.D5), (C2×C6).90(C5⋊D4), C10.27(C3×C22⋊C4), (C3×C4⋊Dic5).24C2, C22.18(C3×C5⋊D4), SmallGroup(480,113)
Series: Derived ►Chief ►Lower central ►Upper central
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, C3, C4, C4, C22, C5, C6, C8, C2×C4, C2×C4, Q8, Q8, C10, C12, C12, C2×C6, C15, C4⋊C4, C2×C8, C2×Q8, Dic5, C20, C20, C2×C10, C24, C2×C12, C2×C12, C3×Q8, C3×Q8, C30, Q8⋊C4, C5⋊2C8, C2×Dic5, C2×C20, C2×C20, C5×Q8, C5×Q8, C3×C4⋊C4, C2×C24, C6×Q8, C3×Dic5, C60, C60, C2×C30, C2×C5⋊2C8, C4⋊Dic5, Q8×C10, C3×Q8⋊C4, C3×C5⋊2C8, C6×Dic5, C2×C60, C2×C60, Q8×C15, Q8×C15, Q8⋊Dic5, C6×C5⋊2C8, C3×C4⋊Dic5, Q8×C30, C3×Q8⋊Dic5
Quotients: C1, C2, C3, C4, C22, C6, C2×C4, D4, D5, C12, C2×C6, C22⋊C4, SD16, Q16, Dic5, D10, C2×C12, C3×D4, C3×D5, Q8⋊C4, C2×Dic5, C5⋊D4, C3×C22⋊C4, C3×SD16, C3×Q16, C3×Dic5, C6×D5, Q8⋊D5, C5⋊Q16, C23.D5, C3×Q8⋊C4, C6×Dic5, C3×C5⋊D4, Q8⋊Dic5, C3×Q8⋊D5, C3×C5⋊Q16, C3×C23.D5, C3×Q8⋊Dic5
►Regular action on 480 points
Generators in S480
(1 95 55)(2 96 56)(3 97 57)(4 98 58)(5 99 59)(6 100 60)(7 91 51)(8 92 52)(9 93 53)(10 94 54)(11 106 66)(12 107 67)(13 108 68)(14 109 69)(15 110 70)(16 101 61)(17 102 62)(18 103 63)(19 104 64)(20 105 65)(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)(21 479 466 460)(22 480 467 451)(23 471 468 452)(24 472 469 453)(25 473 470 454)(26 474 461 455)(27 475 462 456)(28 476 463 457)(29 477 464 458)(30 478 465 459)(51 83 77 70)(52 84 78 61)(53 85 79 62)(54 86 80 63)(55 87 71 64)(56 88 72 65)(57 89 73 66)(58 90 74 67)(59 81 75 68)(60 82 76 69)(91 123 117 110)(92 124 118 101)(93 125 119 102)(94 126 120 103)(95 127 111 104)(96 128 112 105)(97 129 113 106)(98 130 114 107)(99 121 115 108)(100 122 116 109)(131 150 157 163)(132 141 158 164)(133 142 159 165)(134 143 160 166)(135 144 151 167)(136 145 152 168)(137 146 153 169)(138 147 154 170)(139 148 155 161)(140 149 156 162)(171 190 197 203)(172 181 198 204)(173 182 199 205)(174 183 200 206)(175 184 191 207)(176 185 192 208)(177 186 193 209)(178 187 194 210)(179 188 195 201)(180 189 196 202)(211 230 237 246)(212 221 238 247)(213 222 239 248)(214 223 240 249)(215 224 231 250)(216 225 232 241)(217 226 233 242)(218 227 234 243)(219 228 235 244)(220 229 236 245)(251 267 280 289)(252 268 271 290)(253 269 272 281)(254 270 273 282)(255 261 274 283)(256 262 275 284)(257 263 276 285)(258 264 277 286)(259 265 278 287)(260 266 279 288)(291 307 320 329)(292 308 311 330)(293 309 312 321)(294 310 313 322)(295 301 314 323)(296 302 315 324)(297 303 316 325)(298 304 317 326)(299 305 318 327)(300 306 319 328)(331 347 360 369)(332 348 351 370)(333 349 352 361)(334 350 353 362)(335 341 354 363)(336 342 355 364)(337 343 356 365)(338 344 357 366)(339 345 358 367)(340 346 359 368)(371 409 400 387)(372 410 391 388)(373 401 392 389)(374 402 393 390)(375 403 394 381)(376 404 395 382)(377 405 396 383)(378 406 397 384)(379 407 398 385)(380 408 399 386)(411 449 440 427)(412 450 431 428)(413 441 432 429)(414 442 433 430)(415 443 434 421)(416 444 435 422)(417 445 436 423)(418 446 437 424)(419 447 438 425)(420 448 439 426)
(1 156 31 140)(2 157 32 131)(3 158 33 132)(4 159 34 133)(5 160 35 134)(6 151 36 135)(7 152 37 136)(8 153 38 137)(9 154 39 138)(10 155 40 139)(11 164 49 141)(12 165 50 142)(13 166 41 143)(14 167 42 144)(15 168 43 145)(16 169 44 146)(17 170 45 147)(18 161 46 148)(19 162 47 149)(20 163 48 150)(21 354 466 335)(22 355 467 336)(23 356 468 337)(24 357 469 338)(25 358 470 339)(26 359 461 340)(27 360 462 331)(28 351 463 332)(29 352 464 333)(30 353 465 334)(51 192 77 176)(52 193 78 177)(53 194 79 178)(54 195 80 179)(55 196 71 180)(56 197 72 171)(57 198 73 172)(58 199 74 173)(59 200 75 174)(60 191 76 175)(61 209 84 186)(62 210 85 187)(63 201 86 188)(64 202 87 189)(65 203 88 190)(66 204 89 181)(67 205 90 182)(68 206 81 183)(69 207 82 184)(70 208 83 185)(91 232 117 216)(92 233 118 217)(93 234 119 218)(94 235 120 219)(95 236 111 220)(96 237 112 211)(97 238 113 212)(98 239 114 213)(99 240 115 214)(100 231 116 215)(101 242 124 226)(102 243 125 227)(103 244 126 228)(104 245 127 229)(105 246 128 230)(106 247 129 221)(107 248 130 222)(108 249 121 223)(109 250 122 224)(110 241 123 225)(251 404 280 382)(252 405 271 383)(253 406 272 384)(254 407 273 385)(255 408 274 386)(256 409 275 387)(257 410 276 388)(258 401 277 389)(259 402 278 390)(260 403 279 381)(261 380 283 399)(262 371 284 400)(263 372 285 391)(264 373 286 392)(265 374 287 393)(266 375 288 394)(267 376 289 395)(268 377 290 396)(269 378 281 397)(270 379 282 398)(291 444 320 422)(292 445 311 423)(293 446 312 424)(294 447 313 425)(295 448 314 426)(296 449 315 427)(297 450 316 428)(298 441 317 429)(299 442 318 430)(300 443 319 421)(301 420 323 439)(302 411 324 440)(303 412 325 431)(304 413 326 432)(305 414 327 433)(306 415 328 434)(307 416 329 435)(308 417 330 436)(309 418 321 437)(310 419 322 438)(341 460 363 479)(342 451 364 480)(343 452 365 471)(344 453 366 472)(345 454 367 473)(346 455 368 474)(347 456 369 475)(348 457 370 476)(349 458 361 477)(350 459 362 478)
(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)
(1 255 6 260)(2 254 7 259)(3 253 8 258)(4 252 9 257)(5 251 10 256)(11 269 16 264)(12 268 17 263)(13 267 18 262)(14 266 19 261)(15 265 20 270)(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)| (1,95,55)(2,96,56)(3,97,57)(4,98,58)(5,99,59)(6,100,60)(7,91,51)(8,92,52)(9,93,53)(10,94,54)(11,106,66)(12,107,67)(13,108,68)(14,109,69)(15,110,70)(16,101,61)(17,102,62)(18,103,63)(19,104,64)(20,105,65)(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)(21,479,466,460)(22,480,467,451)(23,471,468,452)(24,472,469,453)(25,473,470,454)(26,474,461,455)(27,475,462,456)(28,476,463,457)(29,477,464,458)(30,478,465,459)(51,83,77,70)(52,84,78,61)(53,85,79,62)(54,86,80,63)(55,87,71,64)(56,88,72,65)(57,89,73,66)(58,90,74,67)(59,81,75,68)(60,82,76,69)(91,123,117,110)(92,124,118,101)(93,125,119,102)(94,126,120,103)(95,127,111,104)(96,128,112,105)(97,129,113,106)(98,130,114,107)(99,121,115,108)(100,122,116,109)(131,150,157,163)(132,141,158,164)(133,142,159,165)(134,143,160,166)(135,144,151,167)(136,145,152,168)(137,146,153,169)(138,147,154,170)(139,148,155,161)(140,149,156,162)(171,190,197,203)(172,181,198,204)(173,182,199,205)(174,183,200,206)(175,184,191,207)(176,185,192,208)(177,186,193,209)(178,187,194,210)(179,188,195,201)(180,189,196,202)(211,230,237,246)(212,221,238,247)(213,222,239,248)(214,223,240,249)(215,224,231,250)(216,225,232,241)(217,226,233,242)(218,227,234,243)(219,228,235,244)(220,229,236,245)(251,267,280,289)(252,268,271,290)(253,269,272,281)(254,270,273,282)(255,261,274,283)(256,262,275,284)(257,263,276,285)(258,264,277,286)(259,265,278,287)(260,266,279,288)(291,307,320,329)(292,308,311,330)(293,309,312,321)(294,310,313,322)(295,301,314,323)(296,302,315,324)(297,303,316,325)(298,304,317,326)(299,305,318,327)(300,306,319,328)(331,347,360,369)(332,348,351,370)(333,349,352,361)(334,350,353,362)(335,341,354,363)(336,342,355,364)(337,343,356,365)(338,344,357,366)(339,345,358,367)(340,346,359,368)(371,409,400,387)(372,410,391,388)(373,401,392,389)(374,402,393,390)(375,403,394,381)(376,404,395,382)(377,405,396,383)(378,406,397,384)(379,407,398,385)(380,408,399,386)(411,449,440,427)(412,450,431,428)(413,441,432,429)(414,442,433,430)(415,443,434,421)(416,444,435,422)(417,445,436,423)(418,446,437,424)(419,447,438,425)(420,448,439,426), (1,156,31,140)(2,157,32,131)(3,158,33,132)(4,159,34,133)(5,160,35,134)(6,151,36,135)(7,152,37,136)(8,153,38,137)(9,154,39,138)(10,155,40,139)(11,164,49,141)(12,165,50,142)(13,166,41,143)(14,167,42,144)(15,168,43,145)(16,169,44,146)(17,170,45,147)(18,161,46,148)(19,162,47,149)(20,163,48,150)(21,354,466,335)(22,355,467,336)(23,356,468,337)(24,357,469,338)(25,358,470,339)(26,359,461,340)(27,360,462,331)(28,351,463,332)(29,352,464,333)(30,353,465,334)(51,192,77,176)(52,193,78,177)(53,194,79,178)(54,195,80,179)(55,196,71,180)(56,197,72,171)(57,198,73,172)(58,199,74,173)(59,200,75,174)(60,191,76,175)(61,209,84,186)(62,210,85,187)(63,201,86,188)(64,202,87,189)(65,203,88,190)(66,204,89,181)(67,205,90,182)(68,206,81,183)(69,207,82,184)(70,208,83,185)(91,232,117,216)(92,233,118,217)(93,234,119,218)(94,235,120,219)(95,236,111,220)(96,237,112,211)(97,238,113,212)(98,239,114,213)(99,240,115,214)(100,231,116,215)(101,242,124,226)(102,243,125,227)(103,244,126,228)(104,245,127,229)(105,246,128,230)(106,247,129,221)(107,248,130,222)(108,249,121,223)(109,250,122,224)(110,241,123,225)(251,404,280,382)(252,405,271,383)(253,406,272,384)(254,407,273,385)(255,408,274,386)(256,409,275,387)(257,410,276,388)(258,401,277,389)(259,402,278,390)(260,403,279,381)(261,380,283,399)(262,371,284,400)(263,372,285,391)(264,373,286,392)(265,374,287,393)(266,375,288,394)(267,376,289,395)(268,377,290,396)(269,378,281,397)(270,379,282,398)(291,444,320,422)(292,445,311,423)(293,446,312,424)(294,447,313,425)(295,448,314,426)(296,449,315,427)(297,450,316,428)(298,441,317,429)(299,442,318,430)(300,443,319,421)(301,420,323,439)(302,411,324,440)(303,412,325,431)(304,413,326,432)(305,414,327,433)(306,415,328,434)(307,416,329,435)(308,417,330,436)(309,418,321,437)(310,419,322,438)(341,460,363,479)(342,451,364,480)(343,452,365,471)(344,453,366,472)(345,454,367,473)(346,455,368,474)(347,456,369,475)(348,457,370,476)(349,458,361,477)(350,459,362,478), (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), (1,255,6,260)(2,254,7,259)(3,253,8,258)(4,252,9,257)(5,251,10,256)(11,269,16,264)(12,268,17,263)(13,267,18,262)(14,266,19,261)(15,265,20,270)(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( (1,95,55)(2,96,56)(3,97,57)(4,98,58)(5,99,59)(6,100,60)(7,91,51)(8,92,52)(9,93,53)(10,94,54)(11,106,66)(12,107,67)(13,108,68)(14,109,69)(15,110,70)(16,101,61)(17,102,62)(18,103,63)(19,104,64)(20,105,65)(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)(21,479,466,460)(22,480,467,451)(23,471,468,452)(24,472,469,453)(25,473,470,454)(26,474,461,455)(27,475,462,456)(28,476,463,457)(29,477,464,458)(30,478,465,459)(51,83,77,70)(52,84,78,61)(53,85,79,62)(54,86,80,63)(55,87,71,64)(56,88,72,65)(57,89,73,66)(58,90,74,67)(59,81,75,68)(60,82,76,69)(91,123,117,110)(92,124,118,101)(93,125,119,102)(94,126,120,103)(95,127,111,104)(96,128,112,105)(97,129,113,106)(98,130,114,107)(99,121,115,108)(100,122,116,109)(131,150,157,163)(132,141,158,164)(133,142,159,165)(134,143,160,166)(135,144,151,167)(136,145,152,168)(137,146,153,169)(138,147,154,170)(139,148,155,161)(140,149,156,162)(171,190,197,203)(172,181,198,204)(173,182,199,205)(174,183,200,206)(175,184,191,207)(176,185,192,208)(177,186,193,209)(178,187,194,210)(179,188,195,201)(180,189,196,202)(211,230,237,246)(212,221,238,247)(213,222,239,248)(214,223,240,249)(215,224,231,250)(216,225,232,241)(217,226,233,242)(218,227,234,243)(219,228,235,244)(220,229,236,245)(251,267,280,289)(252,268,271,290)(253,269,272,281)(254,270,273,282)(255,261,274,283)(256,262,275,284)(257,263,276,285)(258,264,277,286)(259,265,278,287)(260,266,279,288)(291,307,320,329)(292,308,311,330)(293,309,312,321)(294,310,313,322)(295,301,314,323)(296,302,315,324)(297,303,316,325)(298,304,317,326)(299,305,318,327)(300,306,319,328)(331,347,360,369)(332,348,351,370)(333,349,352,361)(334,350,353,362)(335,341,354,363)(336,342,355,364)(337,343,356,365)(338,344,357,366)(339,345,358,367)(340,346,359,368)(371,409,400,387)(372,410,391,388)(373,401,392,389)(374,402,393,390)(375,403,394,381)(376,404,395,382)(377,405,396,383)(378,406,397,384)(379,407,398,385)(380,408,399,386)(411,449,440,427)(412,450,431,428)(413,441,432,429)(414,442,433,430)(415,443,434,421)(416,444,435,422)(417,445,436,423)(418,446,437,424)(419,447,438,425)(420,448,439,426), (1,156,31,140)(2,157,32,131)(3,158,33,132)(4,159,34,133)(5,160,35,134)(6,151,36,135)(7,152,37,136)(8,153,38,137)(9,154,39,138)(10,155,40,139)(11,164,49,141)(12,165,50,142)(13,166,41,143)(14,167,42,144)(15,168,43,145)(16,169,44,146)(17,170,45,147)(18,161,46,148)(19,162,47,149)(20,163,48,150)(21,354,466,335)(22,355,467,336)(23,356,468,337)(24,357,469,338)(25,358,470,339)(26,359,461,340)(27,360,462,331)(28,351,463,332)(29,352,464,333)(30,353,465,334)(51,192,77,176)(52,193,78,177)(53,194,79,178)(54,195,80,179)(55,196,71,180)(56,197,72,171)(57,198,73,172)(58,199,74,173)(59,200,75,174)(60,191,76,175)(61,209,84,186)(62,210,85,187)(63,201,86,188)(64,202,87,189)(65,203,88,190)(66,204,89,181)(67,205,90,182)(68,206,81,183)(69,207,82,184)(70,208,83,185)(91,232,117,216)(92,233,118,217)(93,234,119,218)(94,235,120,219)(95,236,111,220)(96,237,112,211)(97,238,113,212)(98,239,114,213)(99,240,115,214)(100,231,116,215)(101,242,124,226)(102,243,125,227)(103,244,126,228)(104,245,127,229)(105,246,128,230)(106,247,129,221)(107,248,130,222)(108,249,121,223)(109,250,122,224)(110,241,123,225)(251,404,280,382)(252,405,271,383)(253,406,272,384)(254,407,273,385)(255,408,274,386)(256,409,275,387)(257,410,276,388)(258,401,277,389)(259,402,278,390)(260,403,279,381)(261,380,283,399)(262,371,284,400)(263,372,285,391)(264,373,286,392)(265,374,287,393)(266,375,288,394)(267,376,289,395)(268,377,290,396)(269,378,281,397)(270,379,282,398)(291,444,320,422)(292,445,311,423)(293,446,312,424)(294,447,313,425)(295,448,314,426)(296,449,315,427)(297,450,316,428)(298,441,317,429)(299,442,318,430)(300,443,319,421)(301,420,323,439)(302,411,324,440)(303,412,325,431)(304,413,326,432)(305,414,327,433)(306,415,328,434)(307,416,329,435)(308,417,330,436)(309,418,321,437)(310,419,322,438)(341,460,363,479)(342,451,364,480)(343,452,365,471)(344,453,366,472)(345,454,367,473)(346,455,368,474)(347,456,369,475)(348,457,370,476)(349,458,361,477)(350,459,362,478), (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), (1,255,6,260)(2,254,7,259)(3,253,8,258)(4,252,9,257)(5,251,10,256)(11,269,16,264)(12,268,17,263)(13,267,18,262)(14,266,19,261)(15,265,20,270)(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([[(1,95,55),(2,96,56),(3,97,57),(4,98,58),(5,99,59),(6,100,60),(7,91,51),(8,92,52),(9,93,53),(10,94,54),(11,106,66),(12,107,67),(13,108,68),(14,109,69),(15,110,70),(16,101,61),(17,102,62),(18,103,63),(19,104,64),(20,105,65),(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),(21,479,466,460),(22,480,467,451),(23,471,468,452),(24,472,469,453),(25,473,470,454),(26,474,461,455),(27,475,462,456),(28,476,463,457),(29,477,464,458),(30,478,465,459),(51,83,77,70),(52,84,78,61),(53,85,79,62),(54,86,80,63),(55,87,71,64),(56,88,72,65),(57,89,73,66),(58,90,74,67),(59,81,75,68),(60,82,76,69),(91,123,117,110),(92,124,118,101),(93,125,119,102),(94,126,120,103),(95,127,111,104),(96,128,112,105),(97,129,113,106),(98,130,114,107),(99,121,115,108),(100,122,116,109),(131,150,157,163),(132,141,158,164),(133,142,159,165),(134,143,160,166),(135,144,151,167),(136,145,152,168),(137,146,153,169),(138,147,154,170),(139,148,155,161),(140,149,156,162),(171,190,197,203),(172,181,198,204),(173,182,199,205),(174,183,200,206),(175,184,191,207),(176,185,192,208),(177,186,193,209),(178,187,194,210),(179,188,195,201),(180,189,196,202),(211,230,237,246),(212,221,238,247),(213,222,239,248),(214,223,240,249),(215,224,231,250),(216,225,232,241),(217,226,233,242),(218,227,234,243),(219,228,235,244),(220,229,236,245),(251,267,280,289),(252,268,271,290),(253,269,272,281),(254,270,273,282),(255,261,274,283),(256,262,275,284),(257,263,276,285),(258,264,277,286),(259,265,278,287),(260,266,279,288),(291,307,320,329),(292,308,311,330),(293,309,312,321),(294,310,313,322),(295,301,314,323),(296,302,315,324),(297,303,316,325),(298,304,317,326),(299,305,318,327),(300,306,319,328),(331,347,360,369),(332,348,351,370),(333,349,352,361),(334,350,353,362),(335,341,354,363),(336,342,355,364),(337,343,356,365),(338,344,357,366),(339,345,358,367),(340,346,359,368),(371,409,400,387),(372,410,391,388),(373,401,392,389),(374,402,393,390),(375,403,394,381),(376,404,395,382),(377,405,396,383),(378,406,397,384),(379,407,398,385),(380,408,399,386),(411,449,440,427),(412,450,431,428),(413,441,432,429),(414,442,433,430),(415,443,434,421),(416,444,435,422),(417,445,436,423),(418,446,437,424),(419,447,438,425),(420,448,439,426)], [(1,156,31,140),(2,157,32,131),(3,158,33,132),(4,159,34,133),(5,160,35,134),(6,151,36,135),(7,152,37,136),(8,153,38,137),(9,154,39,138),(10,155,40,139),(11,164,49,141),(12,165,50,142),(13,166,41,143),(14,167,42,144),(15,168,43,145),(16,169,44,146),(17,170,45,147),(18,161,46,148),(19,162,47,149),(20,163,48,150),(21,354,466,335),(22,355,467,336),(23,356,468,337),(24,357,469,338),(25,358,470,339),(26,359,461,340),(27,360,462,331),(28,351,463,332),(29,352,464,333),(30,353,465,334),(51,192,77,176),(52,193,78,177),(53,194,79,178),(54,195,80,179),(55,196,71,180),(56,197,72,171),(57,198,73,172),(58,199,74,173),(59,200,75,174),(60,191,76,175),(61,209,84,186),(62,210,85,187),(63,201,86,188),(64,202,87,189),(65,203,88,190),(66,204,89,181),(67,205,90,182),(68,206,81,183),(69,207,82,184),(70,208,83,185),(91,232,117,216),(92,233,118,217),(93,234,119,218),(94,235,120,219),(95,236,111,220),(96,237,112,211),(97,238,113,212),(98,239,114,213),(99,240,115,214),(100,231,116,215),(101,242,124,226),(102,243,125,227),(103,244,126,228),(104,245,127,229),(105,246,128,230),(106,247,129,221),(107,248,130,222),(108,249,121,223),(109,250,122,224),(110,241,123,225),(251,404,280,382),(252,405,271,383),(253,406,272,384),(254,407,273,385),(255,408,274,386),(256,409,275,387),(257,410,276,388),(258,401,277,389),(259,402,278,390),(260,403,279,381),(261,380,283,399),(262,371,284,400),(263,372,285,391),(264,373,286,392),(265,374,287,393),(266,375,288,394),(267,376,289,395),(268,377,290,396),(269,378,281,397),(270,379,282,398),(291,444,320,422),(292,445,311,423),(293,446,312,424),(294,447,313,425),(295,448,314,426),(296,449,315,427),(297,450,316,428),(298,441,317,429),(299,442,318,430),(300,443,319,421),(301,420,323,439),(302,411,324,440),(303,412,325,431),(304,413,326,432),(305,414,327,433),(306,415,328,434),(307,416,329,435),(308,417,330,436),(309,418,321,437),(310,419,322,438),(341,460,363,479),(342,451,364,480),(343,452,365,471),(344,453,366,472),(345,454,367,473),(346,455,368,474),(347,456,369,475),(348,457,370,476),(349,458,361,477),(350,459,362,478)], [(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)], [(1,255,6,260),(2,254,7,259),(3,253,8,258),(4,252,9,257),(5,251,10,256),(11,269,16,264),(12,268,17,263),(13,267,18,262),(14,266,19,261),(15,265,20,270),(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