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G = C24×C30order 480 = 25·3·5

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

direct product, abelian, monomial, 2-elementary

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

Series: Derived Chief Lower central Upper central

C1 — C24×C30
C1C5C15C30C2×C30C22×C30C23×C30 — C24×C30
C1 — C24×C30
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 [×31], C3, C22 [×155], C5, C6 [×31], C23 [×155], C10 [×31], C2×C6 [×155], C15, C24 [×31], C2×C10 [×155], C22×C6 [×155], C30 [×31], C25, C22×C10 [×155], C23×C6 [×31], C2×C30 [×155], C23×C10 [×31], C24×C6, C22×C30 [×155], C24×C10, C23×C30 [×31], C24×C30
Quotients: C1, C2 [×31], C3, C22 [×155], C5, C6 [×31], C23 [×155], C10 [×31], C2×C6 [×155], C15, C24 [×31], C2×C10 [×155], C22×C6 [×155], C30 [×31], C25, C22×C10 [×155], C23×C6 [×31], C2×C30 [×155], C23×C10 [×31], C24×C6, C22×C30 [×155], C24×C10, C23×C30 [×31], C24×C30

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

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

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

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

480 conjugacy classes

class 1 2A···2AE3A3B5A5B5C5D6A···6BJ10A···10DT15A···15H30A···30IN
order12···23355556···610···1015···1530···30
size11···11111111···11···11···11···1

480 irreducible representations

dim11111111
type++
imageC1C2C3C5C6C10C15C30
kernelC24×C30C23×C30C24×C10C24×C6C23×C10C23×C6C25C24
# reps13124621248248

Matrix representation of C24×C30 in GL5(𝔽31)

10000
01000
00100
000300
000030
,
10000
01000
003000
000300
000030
,
10000
030000
003000
00010
000030
,
300000
030000
003000
000300
000030
,
300000
011000
001100
000110
00005

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