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## G = C22×C15⋊Q8order 480 = 25·3·5

### Direct product of C22 and C15⋊Q8

Series: Derived Chief Lower central Upper central

 Derived series C1 — C30 — C22×C15⋊Q8
 Chief series C1 — C5 — C15 — C30 — C3×Dic5 — C15⋊Q8 — C2×C15⋊Q8 — C22×C15⋊Q8
 Lower central C15 — C30 — C22×C15⋊Q8
 Upper central C1 — C23

Generators and relations for C22×C15⋊Q8
G = < a,b,c,d,e | a2=b2=c15=d4=1, e2=d2, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, dcd-1=c11, ece-1=c4, ede-1=d-1 >

Subgroups: 1244 in 312 conjugacy classes, 148 normal (18 characteristic)
C1, C2, C2, C3, C4, C22, C5, C6, C6, C2×C4, Q8, C23, C10, C10, Dic3, Dic3, C12, C2×C6, C15, C22×C4, C2×Q8, Dic5, Dic5, C20, C2×C10, Dic6, C2×Dic3, C2×Dic3, C2×C12, C22×C6, C30, C30, C22×Q8, Dic10, C2×Dic5, C2×Dic5, C2×C20, C22×C10, C2×Dic6, C22×Dic3, C22×Dic3, C22×C12, C5×Dic3, C3×Dic5, Dic15, C2×C30, C2×Dic10, C22×Dic5, C22×Dic5, C22×C20, C22×Dic6, C15⋊Q8, C6×Dic5, C10×Dic3, C2×Dic15, C22×C30, C22×Dic10, C2×C15⋊Q8, C2×C6×Dic5, Dic3×C2×C10, C22×Dic15, C22×C15⋊Q8
Quotients: C1, C2, C22, S3, Q8, C23, D5, D6, C2×Q8, C24, D10, Dic6, C22×S3, C22×Q8, Dic10, C22×D5, C2×Dic6, S3×C23, S3×D5, C2×Dic10, C23×D5, C22×Dic6, C15⋊Q8, C2×S3×D5, C22×Dic10, C2×C15⋊Q8, C22×S3×D5, C22×C15⋊Q8

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

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

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

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

84 conjugacy classes

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

84 irreducible representations

 dim 1 1 1 1 1 2 2 2 2 2 2 2 2 2 4 4 4 type + + + + + + - + + + + + - - + - + image C1 C2 C2 C2 C2 S3 Q8 D5 D6 D6 D10 D10 Dic6 Dic10 S3×D5 C15⋊Q8 C2×S3×D5 kernel C22×C15⋊Q8 C2×C15⋊Q8 C2×C6×Dic5 Dic3×C2×C10 C22×Dic15 C22×Dic5 C2×C30 C22×Dic3 C2×Dic5 C22×C10 C2×Dic3 C22×C6 C2×C10 C2×C6 C23 C22 C22 # reps 1 12 1 1 1 1 4 2 6 1 12 2 8 16 2 8 6

Matrix representation of C22×C15⋊Q8 in GL5(𝔽61)

 1 0 0 0 0 0 60 0 0 0 0 0 60 0 0 0 0 0 60 0 0 0 0 0 60
,
 60 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1
,
 1 0 0 0 0 0 60 60 0 0 0 1 0 0 0 0 0 0 0 44 0 0 0 18 43
,
 1 0 0 0 0 0 22 13 0 0 0 52 39 0 0 0 0 0 25 7 0 0 0 50 36
,
 60 0 0 0 0 0 60 0 0 0 0 0 60 0 0 0 0 0 31 14 0 0 0 1 30

G:=sub<GL(5,GF(61))| [1,0,0,0,0,0,60,0,0,0,0,0,60,0,0,0,0,0,60,0,0,0,0,0,60],[60,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,60,1,0,0,0,60,0,0,0,0,0,0,0,18,0,0,0,44,43],[1,0,0,0,0,0,22,52,0,0,0,13,39,0,0,0,0,0,25,50,0,0,0,7,36],[60,0,0,0,0,0,60,0,0,0,0,0,60,0,0,0,0,0,31,1,0,0,0,14,30] >;

C22×C15⋊Q8 in GAP, Magma, Sage, TeX

C_2^2\times C_{15}\rtimes Q_8
% in TeX

G:=Group("C2^2xC15:Q8");
// GroupNames label

G:=SmallGroup(480,1121);
// by ID

G=gap.SmallGroup(480,1121);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,112,253,120,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^2=c^15=d^4=1,e^2=d^2,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,d*c*d^-1=c^11,e*c*e^-1=c^4,e*d*e^-1=d^-1>;
// generators/relations

׿
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