Copied to
clipboard

## G = C24×C30order 480 = 25·3·5

### Abelian group of type [2,2,2,2,30]

Aliases: C24×C30, SmallGroup(480,1213)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C24×C30
 Chief series C1 — C5 — C15 — C30 — C2×C30 — C22×C30 — C23×C30 — C24×C30
 Lower central C1 — C24×C30
 Upper central C1 — C24×C30

Generators and relations for C24×C30
G = < a,b,c,d,e | a2=b2=c2=d2=e30=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, de=ed >

Subgroups: 1496, all normal (8 characteristic)
C1, C2, C3, C22, C5, C6, C23, C10, C2×C6, C15, C24, C2×C10, C22×C6, C30, C25, C22×C10, C23×C6, C2×C30, C23×C10, C24×C6, C22×C30, C24×C10, C23×C30, C24×C30
Quotients: C1, C2, C3, C22, C5, C6, C23, C10, C2×C6, C15, C24, C2×C10, C22×C6, C30, C25, C22×C10, C23×C6, C2×C30, C23×C10, C24×C6, C22×C30, C24×C10, C23×C30, C24×C30

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

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

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

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

480 conjugacy classes

 class 1 2A ··· 2AE 3A 3B 5A 5B 5C 5D 6A ··· 6BJ 10A ··· 10DT 15A ··· 15H 30A ··· 30IN order 1 2 ··· 2 3 3 5 5 5 5 6 ··· 6 10 ··· 10 15 ··· 15 30 ··· 30 size 1 1 ··· 1 1 1 1 1 1 1 1 ··· 1 1 ··· 1 1 ··· 1 1 ··· 1

480 irreducible representations

 dim 1 1 1 1 1 1 1 1 type + + image C1 C2 C3 C5 C6 C10 C15 C30 kernel C24×C30 C23×C30 C24×C10 C24×C6 C23×C10 C23×C6 C25 C24 # reps 1 31 2 4 62 124 8 248

Matrix representation of C24×C30 in GL5(𝔽31)

 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 30 0 0 0 0 0 30
,
 1 0 0 0 0 0 1 0 0 0 0 0 30 0 0 0 0 0 30 0 0 0 0 0 30
,
 1 0 0 0 0 0 30 0 0 0 0 0 30 0 0 0 0 0 1 0 0 0 0 0 30
,
 30 0 0 0 0 0 30 0 0 0 0 0 30 0 0 0 0 0 30 0 0 0 0 0 30
,
 30 0 0 0 0 0 11 0 0 0 0 0 11 0 0 0 0 0 11 0 0 0 0 0 5

G:=sub<GL(5,GF(31))| [1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,30,0,0,0,0,0,30],[1,0,0,0,0,0,1,0,0,0,0,0,30,0,0,0,0,0,30,0,0,0,0,0,30],[1,0,0,0,0,0,30,0,0,0,0,0,30,0,0,0,0,0,1,0,0,0,0,0,30],[30,0,0,0,0,0,30,0,0,0,0,0,30,0,0,0,0,0,30,0,0,0,0,0,30],[30,0,0,0,0,0,11,0,0,0,0,0,11,0,0,0,0,0,11,0,0,0,0,0,5] >;

C24×C30 in GAP, Magma, Sage, TeX

C_2^4\times C_{30}
% in TeX

G:=Group("C2^4xC30");
// GroupNames label

G:=SmallGroup(480,1213);
// by ID

G=gap.SmallGroup(480,1213);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^2=c^2=d^2=e^30=1,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,c*d=d*c,c*e=e*c,d*e=e*d>;
// generators/relations

׿
×
𝔽