direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C23×Dic15, C24.3D15, C30.67C24, C23.41D30, C15⋊11(C23×C4), (C23×C6).3D5, C5⋊3(C23×Dic3), C3⋊2(C23×Dic5), C30⋊11(C22×C4), (C22×C30)⋊13C4, (C23×C30).3C2, (C23×C10).5S3, (C22×C6)⋊5Dic5, C6⋊2(C22×Dic5), C2.2(C23×D15), C6.67(C23×D5), C10.67(S3×C23), C10⋊3(C22×Dic3), (C2×C30).325C23, (C22×C10)⋊11Dic3, (C22×C10).146D6, (C22×C6).128D10, C22.33(C22×D15), (C22×C30).151C22, (C2×C30)⋊41(C2×C4), (C2×C6)⋊9(C2×Dic5), (C2×C10)⋊16(C2×Dic3), (C2×C6).321(C22×D5), (C2×C10).321(C22×S3), SmallGroup(480,1178)
Series: Derived ►Chief ►Lower central ►Upper central
| C15 — C23×Dic15 |
Subgroups: 1492 in 472 conjugacy classes, 319 normal (13 characteristic)
C1, C2, C2 [×14], C3, C4 [×8], C22 [×35], C5, C6, C6 [×14], C2×C4 [×28], C23 [×15], C10, C10 [×14], Dic3 [×8], C2×C6 [×35], C15, C22×C4 [×14], C24, Dic5 [×8], C2×C10 [×35], C2×Dic3 [×28], C22×C6 [×15], C30, C30 [×14], C23×C4, C2×Dic5 [×28], C22×C10 [×15], C22×Dic3 [×14], C23×C6, Dic15 [×8], C2×C30 [×35], C22×Dic5 [×14], C23×C10, C23×Dic3, C2×Dic15 [×28], C22×C30 [×15], C23×Dic5, C22×Dic15 [×14], C23×C30, C23×Dic15
Quotients:
C1, C2 [×15], C4 [×8], C22 [×35], S3, C2×C4 [×28], C23 [×15], D5, Dic3 [×8], D6 [×7], C22×C4 [×14], C24, Dic5 [×8], D10 [×7], C2×Dic3 [×28], C22×S3 [×7], D15, C23×C4, C2×Dic5 [×28], C22×D5 [×7], C22×Dic3 [×14], S3×C23, Dic15 [×8], D30 [×7], C22×Dic5 [×14], C23×D5, C23×Dic3, C2×Dic15 [×28], C22×D15 [×7], C23×Dic5, C22×Dic15 [×14], C23×D15, C23×Dic15
Generators and relations
G = < a,b,c,d,e | a2=b2=c2=d30=1, e2=d15, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >
►Regular action on 480 points
Generators in S480
(1 134)(2 135)(3 136)(4 137)(5 138)(6 139)(7 140)(8 141)(9 142)(10 143)(11 144)(12 145)(13 146)(14 147)(15 148)(16 149)(17 150)(18 121)(19 122)(20 123)(21 124)(22 125)(23 126)(24 127)(25 128)(26 129)(27 130)(28 131)(29 132)(30 133)(31 157)(32 158)(33 159)(34 160)(35 161)(36 162)(37 163)(38 164)(39 165)(40 166)(41 167)(42 168)(43 169)(44 170)(45 171)(46 172)(47 173)(48 174)(49 175)(50 176)(51 177)(52 178)(53 179)(54 180)(55 151)(56 152)(57 153)(58 154)(59 155)(60 156)(61 181)(62 182)(63 183)(64 184)(65 185)(66 186)(67 187)(68 188)(69 189)(70 190)(71 191)(72 192)(73 193)(74 194)(75 195)(76 196)(77 197)(78 198)(79 199)(80 200)(81 201)(82 202)(83 203)(84 204)(85 205)(86 206)(87 207)(88 208)(89 209)(90 210)(91 225)(92 226)(93 227)(94 228)(95 229)(96 230)(97 231)(98 232)(99 233)(100 234)(101 235)(102 236)(103 237)(104 238)(105 239)(106 240)(107 211)(108 212)(109 213)(110 214)(111 215)(112 216)(113 217)(114 218)(115 219)(116 220)(117 221)(118 222)(119 223)(120 224)(241 381)(242 382)(243 383)(244 384)(245 385)(246 386)(247 387)(248 388)(249 389)(250 390)(251 361)(252 362)(253 363)(254 364)(255 365)(256 366)(257 367)(258 368)(259 369)(260 370)(261 371)(262 372)(263 373)(264 374)(265 375)(266 376)(267 377)(268 378)(269 379)(270 380)(271 416)(272 417)(273 418)(274 419)(275 420)(276 391)(277 392)(278 393)(279 394)(280 395)(281 396)(282 397)(283 398)(284 399)(285 400)(286 401)(287 402)(288 403)(289 404)(290 405)(291 406)(292 407)(293 408)(294 409)(295 410)(296 411)(297 412)(298 413)(299 414)(300 415)(301 441)(302 442)(303 443)(304 444)(305 445)(306 446)(307 447)(308 448)(309 449)(310 450)(311 421)(312 422)(313 423)(314 424)(315 425)(316 426)(317 427)(318 428)(319 429)(320 430)(321 431)(322 432)(323 433)(324 434)(325 435)(326 436)(327 437)(328 438)(329 439)(330 440)(331 476)(332 477)(333 478)(334 479)(335 480)(336 451)(337 452)(338 453)(339 454)(340 455)(341 456)(342 457)(343 458)(344 459)(345 460)(346 461)(347 462)(348 463)(349 464)(350 465)(351 466)(352 467)(353 468)(354 469)(355 470)(356 471)(357 472)(358 473)(359 474)(360 475)
(1 120)(2 91)(3 92)(4 93)(5 94)(6 95)(7 96)(8 97)(9 98)(10 99)(11 100)(12 101)(13 102)(14 103)(15 104)(16 105)(17 106)(18 107)(19 108)(20 109)(21 110)(22 111)(23 112)(24 113)(25 114)(26 115)(27 116)(28 117)(29 118)(30 119)(31 61)(32 62)(33 63)(34 64)(35 65)(36 66)(37 67)(38 68)(39 69)(40 70)(41 71)(42 72)(43 73)(44 74)(45 75)(46 76)(47 77)(48 78)(49 79)(50 80)(51 81)(52 82)(53 83)(54 84)(55 85)(56 86)(57 87)(58 88)(59 89)(60 90)(121 211)(122 212)(123 213)(124 214)(125 215)(126 216)(127 217)(128 218)(129 219)(130 220)(131 221)(132 222)(133 223)(134 224)(135 225)(136 226)(137 227)(138 228)(139 229)(140 230)(141 231)(142 232)(143 233)(144 234)(145 235)(146 236)(147 237)(148 238)(149 239)(150 240)(151 205)(152 206)(153 207)(154 208)(155 209)(156 210)(157 181)(158 182)(159 183)(160 184)(161 185)(162 186)(163 187)(164 188)(165 189)(166 190)(167 191)(168 192)(169 193)(170 194)(171 195)(172 196)(173 197)(174 198)(175 199)(176 200)(177 201)(178 202)(179 203)(180 204)(241 341)(242 342)(243 343)(244 344)(245 345)(246 346)(247 347)(248 348)(249 349)(250 350)(251 351)(252 352)(253 353)(254 354)(255 355)(256 356)(257 357)(258 358)(259 359)(260 360)(261 331)(262 332)(263 333)(264 334)(265 335)(266 336)(267 337)(268 338)(269 339)(270 340)(271 311)(272 312)(273 313)(274 314)(275 315)(276 316)(277 317)(278 318)(279 319)(280 320)(281 321)(282 322)(283 323)(284 324)(285 325)(286 326)(287 327)(288 328)(289 329)(290 330)(291 301)(292 302)(293 303)(294 304)(295 305)(296 306)(297 307)(298 308)(299 309)(300 310)(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)(391 426)(392 427)(393 428)(394 429)(395 430)(396 431)(397 432)(398 433)(399 434)(400 435)(401 436)(402 437)(403 438)(404 439)(405 440)(406 441)(407 442)(408 443)(409 444)(410 445)(411 446)(412 447)(413 448)(414 449)(415 450)(416 421)(417 422)(418 423)(419 424)(420 425)
(1 53)(2 54)(3 55)(4 56)(5 57)(6 58)(7 59)(8 60)(9 31)(10 32)(11 33)(12 34)(13 35)(14 36)(15 37)(16 38)(17 39)(18 40)(19 41)(20 42)(21 43)(22 44)(23 45)(24 46)(25 47)(26 48)(27 49)(28 50)(29 51)(30 52)(61 98)(62 99)(63 100)(64 101)(65 102)(66 103)(67 104)(68 105)(69 106)(70 107)(71 108)(72 109)(73 110)(74 111)(75 112)(76 113)(77 114)(78 115)(79 116)(80 117)(81 118)(82 119)(83 120)(84 91)(85 92)(86 93)(87 94)(88 95)(89 96)(90 97)(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)(181 232)(182 233)(183 234)(184 235)(185 236)(186 237)(187 238)(188 239)(189 240)(190 211)(191 212)(192 213)(193 214)(194 215)(195 216)(196 217)(197 218)(198 219)(199 220)(200 221)(201 222)(202 223)(203 224)(204 225)(205 226)(206 227)(207 228)(208 229)(209 230)(210 231)(241 296)(242 297)(243 298)(244 299)(245 300)(246 271)(247 272)(248 273)(249 274)(250 275)(251 276)(252 277)(253 278)(254 279)(255 280)(256 281)(257 282)(258 283)(259 284)(260 285)(261 286)(262 287)(263 288)(264 289)(265 290)(266 291)(267 292)(268 293)(269 294)(270 295)(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)(361 391)(362 392)(363 393)(364 394)(365 395)(366 396)(367 397)(368 398)(369 399)(370 400)(371 401)(372 402)(373 403)(374 404)(375 405)(376 406)(377 407)(378 408)(379 409)(380 410)(381 411)(382 412)(383 413)(384 414)(385 415)(386 416)(387 417)(388 418)(389 419)(390 420)(421 461)(422 462)(423 463)(424 464)(425 465)(426 466)(427 467)(428 468)(429 469)(430 470)(431 471)(432 472)(433 473)(434 474)(435 475)(436 476)(437 477)(438 478)(439 479)(440 480)(441 451)(442 452)(443 453)(444 454)(445 455)(446 456)(447 457)(448 458)(449 459)(450 460)
(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)
(1 436 16 421)(2 435 17 450)(3 434 18 449)(4 433 19 448)(5 432 20 447)(6 431 21 446)(7 430 22 445)(8 429 23 444)(9 428 24 443)(10 427 25 442)(11 426 26 441)(12 425 27 440)(13 424 28 439)(14 423 29 438)(15 422 30 437)(31 468 46 453)(32 467 47 452)(33 466 48 451)(34 465 49 480)(35 464 50 479)(36 463 51 478)(37 462 52 477)(38 461 53 476)(39 460 54 475)(40 459 55 474)(41 458 56 473)(42 457 57 472)(43 456 58 471)(44 455 59 470)(45 454 60 469)(61 363 76 378)(62 362 77 377)(63 361 78 376)(64 390 79 375)(65 389 80 374)(66 388 81 373)(67 387 82 372)(68 386 83 371)(69 385 84 370)(70 384 85 369)(71 383 86 368)(72 382 87 367)(73 381 88 366)(74 380 89 365)(75 379 90 364)(91 400 106 415)(92 399 107 414)(93 398 108 413)(94 397 109 412)(95 396 110 411)(96 395 111 410)(97 394 112 409)(98 393 113 408)(99 392 114 407)(100 391 115 406)(101 420 116 405)(102 419 117 404)(103 418 118 403)(104 417 119 402)(105 416 120 401)(121 309 136 324)(122 308 137 323)(123 307 138 322)(124 306 139 321)(125 305 140 320)(126 304 141 319)(127 303 142 318)(128 302 143 317)(129 301 144 316)(130 330 145 315)(131 329 146 314)(132 328 147 313)(133 327 148 312)(134 326 149 311)(135 325 150 310)(151 359 166 344)(152 358 167 343)(153 357 168 342)(154 356 169 341)(155 355 170 340)(156 354 171 339)(157 353 172 338)(158 352 173 337)(159 351 174 336)(160 350 175 335)(161 349 176 334)(162 348 177 333)(163 347 178 332)(164 346 179 331)(165 345 180 360)(181 253 196 268)(182 252 197 267)(183 251 198 266)(184 250 199 265)(185 249 200 264)(186 248 201 263)(187 247 202 262)(188 246 203 261)(189 245 204 260)(190 244 205 259)(191 243 206 258)(192 242 207 257)(193 241 208 256)(194 270 209 255)(195 269 210 254)(211 299 226 284)(212 298 227 283)(213 297 228 282)(214 296 229 281)(215 295 230 280)(216 294 231 279)(217 293 232 278)(218 292 233 277)(219 291 234 276)(220 290 235 275)(221 289 236 274)(222 288 237 273)(223 287 238 272)(224 286 239 271)(225 285 240 300)
G:=sub<Sym(480)| (1,134)(2,135)(3,136)(4,137)(5,138)(6,139)(7,140)(8,141)(9,142)(10,143)(11,144)(12,145)(13,146)(14,147)(15,148)(16,149)(17,150)(18,121)(19,122)(20,123)(21,124)(22,125)(23,126)(24,127)(25,128)(26,129)(27,130)(28,131)(29,132)(30,133)(31,157)(32,158)(33,159)(34,160)(35,161)(36,162)(37,163)(38,164)(39,165)(40,166)(41,167)(42,168)(43,169)(44,170)(45,171)(46,172)(47,173)(48,174)(49,175)(50,176)(51,177)(52,178)(53,179)(54,180)(55,151)(56,152)(57,153)(58,154)(59,155)(60,156)(61,181)(62,182)(63,183)(64,184)(65,185)(66,186)(67,187)(68,188)(69,189)(70,190)(71,191)(72,192)(73,193)(74,194)(75,195)(76,196)(77,197)(78,198)(79,199)(80,200)(81,201)(82,202)(83,203)(84,204)(85,205)(86,206)(87,207)(88,208)(89,209)(90,210)(91,225)(92,226)(93,227)(94,228)(95,229)(96,230)(97,231)(98,232)(99,233)(100,234)(101,235)(102,236)(103,237)(104,238)(105,239)(106,240)(107,211)(108,212)(109,213)(110,214)(111,215)(112,216)(113,217)(114,218)(115,219)(116,220)(117,221)(118,222)(119,223)(120,224)(241,381)(242,382)(243,383)(244,384)(245,385)(246,386)(247,387)(248,388)(249,389)(250,390)(251,361)(252,362)(253,363)(254,364)(255,365)(256,366)(257,367)(258,368)(259,369)(260,370)(261,371)(262,372)(263,373)(264,374)(265,375)(266,376)(267,377)(268,378)(269,379)(270,380)(271,416)(272,417)(273,418)(274,419)(275,420)(276,391)(277,392)(278,393)(279,394)(280,395)(281,396)(282,397)(283,398)(284,399)(285,400)(286,401)(287,402)(288,403)(289,404)(290,405)(291,406)(292,407)(293,408)(294,409)(295,410)(296,411)(297,412)(298,413)(299,414)(300,415)(301,441)(302,442)(303,443)(304,444)(305,445)(306,446)(307,447)(308,448)(309,449)(310,450)(311,421)(312,422)(313,423)(314,424)(315,425)(316,426)(317,427)(318,428)(319,429)(320,430)(321,431)(322,432)(323,433)(324,434)(325,435)(326,436)(327,437)(328,438)(329,439)(330,440)(331,476)(332,477)(333,478)(334,479)(335,480)(336,451)(337,452)(338,453)(339,454)(340,455)(341,456)(342,457)(343,458)(344,459)(345,460)(346,461)(347,462)(348,463)(349,464)(350,465)(351,466)(352,467)(353,468)(354,469)(355,470)(356,471)(357,472)(358,473)(359,474)(360,475), (1,120)(2,91)(3,92)(4,93)(5,94)(6,95)(7,96)(8,97)(9,98)(10,99)(11,100)(12,101)(13,102)(14,103)(15,104)(16,105)(17,106)(18,107)(19,108)(20,109)(21,110)(22,111)(23,112)(24,113)(25,114)(26,115)(27,116)(28,117)(29,118)(30,119)(31,61)(32,62)(33,63)(34,64)(35,65)(36,66)(37,67)(38,68)(39,69)(40,70)(41,71)(42,72)(43,73)(44,74)(45,75)(46,76)(47,77)(48,78)(49,79)(50,80)(51,81)(52,82)(53,83)(54,84)(55,85)(56,86)(57,87)(58,88)(59,89)(60,90)(121,211)(122,212)(123,213)(124,214)(125,215)(126,216)(127,217)(128,218)(129,219)(130,220)(131,221)(132,222)(133,223)(134,224)(135,225)(136,226)(137,227)(138,228)(139,229)(140,230)(141,231)(142,232)(143,233)(144,234)(145,235)(146,236)(147,237)(148,238)(149,239)(150,240)(151,205)(152,206)(153,207)(154,208)(155,209)(156,210)(157,181)(158,182)(159,183)(160,184)(161,185)(162,186)(163,187)(164,188)(165,189)(166,190)(167,191)(168,192)(169,193)(170,194)(171,195)(172,196)(173,197)(174,198)(175,199)(176,200)(177,201)(178,202)(179,203)(180,204)(241,341)(242,342)(243,343)(244,344)(245,345)(246,346)(247,347)(248,348)(249,349)(250,350)(251,351)(252,352)(253,353)(254,354)(255,355)(256,356)(257,357)(258,358)(259,359)(260,360)(261,331)(262,332)(263,333)(264,334)(265,335)(266,336)(267,337)(268,338)(269,339)(270,340)(271,311)(272,312)(273,313)(274,314)(275,315)(276,316)(277,317)(278,318)(279,319)(280,320)(281,321)(282,322)(283,323)(284,324)(285,325)(286,326)(287,327)(288,328)(289,329)(290,330)(291,301)(292,302)(293,303)(294,304)(295,305)(296,306)(297,307)(298,308)(299,309)(300,310)(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)(391,426)(392,427)(393,428)(394,429)(395,430)(396,431)(397,432)(398,433)(399,434)(400,435)(401,436)(402,437)(403,438)(404,439)(405,440)(406,441)(407,442)(408,443)(409,444)(410,445)(411,446)(412,447)(413,448)(414,449)(415,450)(416,421)(417,422)(418,423)(419,424)(420,425), (1,53)(2,54)(3,55)(4,56)(5,57)(6,58)(7,59)(8,60)(9,31)(10,32)(11,33)(12,34)(13,35)(14,36)(15,37)(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)(22,44)(23,45)(24,46)(25,47)(26,48)(27,49)(28,50)(29,51)(30,52)(61,98)(62,99)(63,100)(64,101)(65,102)(66,103)(67,104)(68,105)(69,106)(70,107)(71,108)(72,109)(73,110)(74,111)(75,112)(76,113)(77,114)(78,115)(79,116)(80,117)(81,118)(82,119)(83,120)(84,91)(85,92)(86,93)(87,94)(88,95)(89,96)(90,97)(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)(181,232)(182,233)(183,234)(184,235)(185,236)(186,237)(187,238)(188,239)(189,240)(190,211)(191,212)(192,213)(193,214)(194,215)(195,216)(196,217)(197,218)(198,219)(199,220)(200,221)(201,222)(202,223)(203,224)(204,225)(205,226)(206,227)(207,228)(208,229)(209,230)(210,231)(241,296)(242,297)(243,298)(244,299)(245,300)(246,271)(247,272)(248,273)(249,274)(250,275)(251,276)(252,277)(253,278)(254,279)(255,280)(256,281)(257,282)(258,283)(259,284)(260,285)(261,286)(262,287)(263,288)(264,289)(265,290)(266,291)(267,292)(268,293)(269,294)(270,295)(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)(361,391)(362,392)(363,393)(364,394)(365,395)(366,396)(367,397)(368,398)(369,399)(370,400)(371,401)(372,402)(373,403)(374,404)(375,405)(376,406)(377,407)(378,408)(379,409)(380,410)(381,411)(382,412)(383,413)(384,414)(385,415)(386,416)(387,417)(388,418)(389,419)(390,420)(421,461)(422,462)(423,463)(424,464)(425,465)(426,466)(427,467)(428,468)(429,469)(430,470)(431,471)(432,472)(433,473)(434,474)(435,475)(436,476)(437,477)(438,478)(439,479)(440,480)(441,451)(442,452)(443,453)(444,454)(445,455)(446,456)(447,457)(448,458)(449,459)(450,460), (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), 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G:=Group( 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(1,436,16,421)(2,435,17,450)(3,434,18,449)(4,433,19,448)(5,432,20,447)(6,431,21,446)(7,430,22,445)(8,429,23,444)(9,428,24,443)(10,427,25,442)(11,426,26,441)(12,425,27,440)(13,424,28,439)(14,423,29,438)(15,422,30,437)(31,468,46,453)(32,467,47,452)(33,466,48,451)(34,465,49,480)(35,464,50,479)(36,463,51,478)(37,462,52,477)(38,461,53,476)(39,460,54,475)(40,459,55,474)(41,458,56,473)(42,457,57,472)(43,456,58,471)(44,455,59,470)(45,454,60,469)(61,363,76,378)(62,362,77,377)(63,361,78,376)(64,390,79,375)(65,389,80,374)(66,388,81,373)(67,387,82,372)(68,386,83,371)(69,385,84,370)(70,384,85,369)(71,383,86,368)(72,382,87,367)(73,381,88,366)(74,380,89,365)(75,379,90,364)(91,400,106,415)(92,399,107,414)(93,398,108,413)(94,397,109,412)(95,396,110,411)(96,395,111,410)(97,394,112,409)(98,393,113,408)(99,392,114,407)(100,391,115,406)(101,420,116,405)(102,419,117,404)(103,418,118,403)(104,417,119,402)(105,416,120,401)(121,309,136,324)(122,308,137,323)(123,307,138,322)(124,306,139,321)(125,305,140,320)(126,304,141,319)(127,303,142,318)(128,302,143,317)(129,301,144,316)(130,330,145,315)(131,329,146,314)(132,328,147,313)(133,327,148,312)(134,326,149,311)(135,325,150,310)(151,359,166,344)(152,358,167,343)(153,357,168,342)(154,356,169,341)(155,355,170,340)(156,354,171,339)(157,353,172,338)(158,352,173,337)(159,351,174,336)(160,350,175,335)(161,349,176,334)(162,348,177,333)(163,347,178,332)(164,346,179,331)(165,345,180,360)(181,253,196,268)(182,252,197,267)(183,251,198,266)(184,250,199,265)(185,249,200,264)(186,248,201,263)(187,247,202,262)(188,246,203,261)(189,245,204,260)(190,244,205,259)(191,243,206,258)(192,242,207,257)(193,241,208,256)(194,270,209,255)(195,269,210,254)(211,299,226,284)(212,298,227,283)(213,297,228,282)(214,296,229,281)(215,295,230,280)(216,294,231,279)(217,293,232,278)(218,292,233,277)(219,291,234,276)(220,290,235,275)(221,289,236,274)(222,288,237,273)(223,287,238,272)(224,286,239,271)(225,285,240,300) );
G=PermutationGroup([(1,134),(2,135),(3,136),(4,137),(5,138),(6,139),(7,140),(8,141),(9,142),(10,143),(11,144),(12,145),(13,146),(14,147),(15,148),(16,149),(17,150),(18,121),(19,122),(20,123),(21,124),(22,125),(23,126),(24,127),(25,128),(26,129),(27,130),(28,131),(29,132),(30,133),(31,157),(32,158),(33,159),(34,160),(35,161),(36,162),(37,163),(38,164),(39,165),(40,166),(41,167),(42,168),(43,169),(44,170),(45,171),(46,172),(47,173),(48,174),(49,175),(50,176),(51,177),(52,178),(53,179),(54,180),(55,151),(56,152),(57,153),(58,154),(59,155),(60,156),(61,181),(62,182),(63,183),(64,184),(65,185),(66,186),(67,187),(68,188),(69,189),(70,190),(71,191),(72,192),(73,193),(74,194),(75,195),(76,196),(77,197),(78,198),(79,199),(80,200),(81,201),(82,202),(83,203),(84,204),(85,205),(86,206),(87,207),(88,208),(89,209),(90,210),(91,225),(92,226),(93,227),(94,228),(95,229),(96,230),(97,231),(98,232),(99,233),(100,234),(101,235),(102,236),(103,237),(104,238),(105,239),(106,240),(107,211),(108,212),(109,213),(110,214),(111,215),(112,216),(113,217),(114,218),(115,219),(116,220),(117,221),(118,222),(119,223),(120,224),(241,381),(242,382),(243,383),(244,384),(245,385),(246,386),(247,387),(248,388),(249,389),(250,390),(251,361),(252,362),(253,363),(254,364),(255,365),(256,366),(257,367),(258,368),(259,369),(260,370),(261,371),(262,372),(263,373),(264,374),(265,375),(266,376),(267,377),(268,378),(269,379),(270,380),(271,416),(272,417),(273,418),(274,419),(275,420),(276,391),(277,392),(278,393),(279,394),(280,395),(281,396),(282,397),(283,398),(284,399),(285,400),(286,401),(287,402),(288,403),(289,404),(290,405),(291,406),(292,407),(293,408),(294,409),(295,410),(296,411),(297,412),(298,413),(299,414),(300,415),(301,441),(302,442),(303,443),(304,444),(305,445),(306,446),(307,447),(308,448),(309,449),(310,450),(311,421),(312,422),(313,423),(314,424),(315,425),(316,426),(317,427),(318,428),(319,429),(320,430),(321,431),(322,432),(323,433),(324,434),(325,435),(326,436),(327,437),(328,438),(329,439),(330,440),(331,476),(332,477),(333,478),(334,479),(335,480),(336,451),(337,452),(338,453),(339,454),(340,455),(341,456),(342,457),(343,458),(344,459),(345,460),(346,461),(347,462),(348,463),(349,464),(350,465),(351,466),(352,467),(353,468),(354,469),(355,470),(356,471),(357,472),(358,473),(359,474),(360,475)], [(1,120),(2,91),(3,92),(4,93),(5,94),(6,95),(7,96),(8,97),(9,98),(10,99),(11,100),(12,101),(13,102),(14,103),(15,104),(16,105),(17,106),(18,107),(19,108),(20,109),(21,110),(22,111),(23,112),(24,113),(25,114),(26,115),(27,116),(28,117),(29,118),(30,119),(31,61),(32,62),(33,63),(34,64),(35,65),(36,66),(37,67),(38,68),(39,69),(40,70),(41,71),(42,72),(43,73),(44,74),(45,75),(46,76),(47,77),(48,78),(49,79),(50,80),(51,81),(52,82),(53,83),(54,84),(55,85),(56,86),(57,87),(58,88),(59,89),(60,90),(121,211),(122,212),(123,213),(124,214),(125,215),(126,216),(127,217),(128,218),(129,219),(130,220),(131,221),(132,222),(133,223),(134,224),(135,225),(136,226),(137,227),(138,228),(139,229),(140,230),(141,231),(142,232),(143,233),(144,234),(145,235),(146,236),(147,237),(148,238),(149,239),(150,240),(151,205),(152,206),(153,207),(154,208),(155,209),(156,210),(157,181),(158,182),(159,183),(160,184),(161,185),(162,186),(163,187),(164,188),(165,189),(166,190),(167,191),(168,192),(169,193),(170,194),(171,195),(172,196),(173,197),(174,198),(175,199),(176,200),(177,201),(178,202),(179,203),(180,204),(241,341),(242,342),(243,343),(244,344),(245,345),(246,346),(247,347),(248,348),(249,349),(250,350),(251,351),(252,352),(253,353),(254,354),(255,355),(256,356),(257,357),(258,358),(259,359),(260,360),(261,331),(262,332),(263,333),(264,334),(265,335),(266,336),(267,337),(268,338),(269,339),(270,340),(271,311),(272,312),(273,313),(274,314),(275,315),(276,316),(277,317),(278,318),(279,319),(280,320),(281,321),(282,322),(283,323),(284,324),(285,325),(286,326),(287,327),(288,328),(289,329),(290,330),(291,301),(292,302),(293,303),(294,304),(295,305),(296,306),(297,307),(298,308),(299,309),(300,310),(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),(391,426),(392,427),(393,428),(394,429),(395,430),(396,431),(397,432),(398,433),(399,434),(400,435),(401,436),(402,437),(403,438),(404,439),(405,440),(406,441),(407,442),(408,443),(409,444),(410,445),(411,446),(412,447),(413,448),(414,449),(415,450),(416,421),(417,422),(418,423),(419,424),(420,425)], [(1,53),(2,54),(3,55),(4,56),(5,57),(6,58),(7,59),(8,60),(9,31),(10,32),(11,33),(12,34),(13,35),(14,36),(15,37),(16,38),(17,39),(18,40),(19,41),(20,42),(21,43),(22,44),(23,45),(24,46),(25,47),(26,48),(27,49),(28,50),(29,51),(30,52),(61,98),(62,99),(63,100),(64,101),(65,102),(66,103),(67,104),(68,105),(69,106),(70,107),(71,108),(72,109),(73,110),(74,111),(75,112),(76,113),(77,114),(78,115),(79,116),(80,117),(81,118),(82,119),(83,120),(84,91),(85,92),(86,93),(87,94),(88,95),(89,96),(90,97),(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),(181,232),(182,233),(183,234),(184,235),(185,236),(186,237),(187,238),(188,239),(189,240),(190,211),(191,212),(192,213),(193,214),(194,215),(195,216),(196,217),(197,218),(198,219),(199,220),(200,221),(201,222),(202,223),(203,224),(204,225),(205,226),(206,227),(207,228),(208,229),(209,230),(210,231),(241,296),(242,297),(243,298),(244,299),(245,300),(246,271),(247,272),(248,273),(249,274),(250,275),(251,276),(252,277),(253,278),(254,279),(255,280),(256,281),(257,282),(258,283),(259,284),(260,285),(261,286),(262,287),(263,288),(264,289),(265,290),(266,291),(267,292),(268,293),(269,294),(270,295),(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),(361,391),(362,392),(363,393),(364,394),(365,395),(366,396),(367,397),(368,398),(369,399),(370,400),(371,401),(372,402),(373,403),(374,404),(375,405),(376,406),(377,407),(378,408),(379,409),(380,410),(381,411),(382,412),(383,413),(384,414),(385,415),(386,416),(387,417),(388,418),(389,419),(390,420),(421,461),(422,462),(423,463),(424,464),(425,465),(426,466),(427,467),(428,468),(429,469),(430,470),(431,471),(432,472),(433,473),(434,474),(435,475),(436,476),(437,477),(438,478),(439,479),(440,480),(441,451),(442,452),(443,453),(444,454),(445,455),(446,456),(447,457),(448,458),(449,459),(450,460)], [(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)], [(1,436,16,421),(2,435,17,450),(3,434,18,449),(4,433,19,448),(5,432,20,447),(6,431,21,446),(7,430,22,445),(8,429,23,444),(9,428,24,443),(10,427,25,442),(11,426,26,441),(12,425,27,440),(13,424,28,439),(14,423,29,438),(15,422,30,437),(31,468,46,453),(32,467,47,452),(33,466,48,451),(34,465,49,480),(35,464,50,479),(36,463,51,478),(37,462,52,477),(38,461,53,476),(39,460,54,475),(40,459,55,474),(41,458,56,473),(42,457,57,472),(43,456,58,471),(44,455,59,470),(45,454,60,469),(61,363,76,378),(62,362,77,377),(63,361,78,376),(64,390,79,375),(65,389,80,374),(66,388,81,373),(67,387,82,372),(68,386,83,371),(69,385,84,370),(70,384,85,369),(71,383,86,368),(72,382,87,367),(73,381,88,366),(74,380,89,365),(75,379,90,364),(91,400,106,415),(92,399,107,414),(93,398,108,413),(94,397,109,412),(95,396,110,411),(96,395,111,410),(97,394,112,409),(98,393,113,408),(99,392,114,407),(100,391,115,406),(101,420,116,405),(102,419,117,404),(103,418,118,403),(104,417,119,402),(105,416,120,401),(121,309,136,324),(122,308,137,323),(123,307,138,322),(124,306,139,321),(125,305,140,320),(126,304,141,319),(127,303,142,318),(128,302,143,317),(129,301,144,316),(130,330,145,315),(131,329,146,314),(132,328,147,313),(133,327,148,312),(134,326,149,311),(135,325,150,310),(151,359,166,344),(152,358,167,343),(153,357,168,342),(154,356,169,341),(155,355,170,340),(156,354,171,339),(157,353,172,338),(158,352,173,337),(159,351,174,336),(160,350,175,335),(161,349,176,334),(162,348,177,333),(163,347,178,332),(164,346,179,331),(165,345,180,360),(181,253,196,268),(182,252,197,267),(183,251,198,266),(184,250,199,265),(185,249,200,264),(186,248,201,263),(187,247,202,262),(188,246,203,261),(189,245,204,260),(190,244,205,259),(191,243,206,258),(192,242,207,257),(193,241,208,256),(194,270,209,255),(195,269,210,254),(211,299,226,284),(212,298,227,283),(213,297,228,282),(214,296,229,281),(215,295,230,280),(216,294,231,279),(217,293,232,278),(218,292,233,277),(219,291,234,276),(220,290,235,275),(221,289,236,274),(222,288,237,273),(223,287,238,272),(224,286,239,271),(225,285,240,300)])
Matrix representation ►G ⊆ GL7(𝔽61)
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 60 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 60 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 60 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 60 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 60 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 60 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 60 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 60 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 60 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 60 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 60 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 60 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 60 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 60 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 60 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 27 | 0 | 0 | 0 |
| 0 | 0 | 0 | 2 | 52 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 5 | 0 |
| 0 | 0 | 0 | 0 | 0 | 50 | 49 |
| 60 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 49 | 55 | 0 | 0 | 0 | 0 |
| 0 | 34 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 55 | 47 | 0 | 0 |
| 0 | 0 | 0 | 7 | 6 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 | 13 |
| 0 | 0 | 0 | 0 | 0 | 17 | 49 |
G:=sub<GL(7,GF(61))| [1,0,0,0,0,0,0,0,60,0,0,0,0,0,0,0,60,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1],[60,0,0,0,0,0,0,0,60,0,0,0,0,0,0,0,60,0,0,0,0,0,0,0,60,0,0,0,0,0,0,0,60,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1],[60,0,0,0,0,0,0,0,60,0,0,0,0,0,0,0,60,0,0,0,0,0,0,0,60,0,0,0,0,0,0,0,60,0,0,0,0,0,0,0,60,0,0,0,0,0,0,0,60],[1,0,0,0,0,0,0,0,0,60,0,0,0,0,0,1,17,0,0,0,0,0,0,0,27,2,0,0,0,0,0,0,52,0,0,0,0,0,0,0,5,50,0,0,0,0,0,0,49],[60,0,0,0,0,0,0,0,49,34,0,0,0,0,0,55,12,0,0,0,0,0,0,0,55,7,0,0,0,0,0,47,6,0,0,0,0,0,0,0,12,17,0,0,0,0,0,13,49] >;
144 conjugacy classes
| class | 1 | 2A | ··· | 2O | 3 | 4A | ··· | 4P | 5A | 5B | 6A | ··· | 6O | 10A | ··· | 10AD | 15A | 15B | 15C | 15D | 30A | ··· | 30BH |
| order | 1 | 2 | ··· | 2 | 3 | 4 | ··· | 4 | 5 | 5 | 6 | ··· | 6 | 10 | ··· | 10 | 15 | 15 | 15 | 15 | 30 | ··· | 30 |
| size | 1 | 1 | ··· | 1 | 2 | 15 | ··· | 15 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 |
144 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | - | + | - | + | + | - | + | |
| image | C1 | C2 | C2 | C4 | S3 | D5 | Dic3 | D6 | Dic5 | D10 | D15 | Dic15 | D30 |
| kernel | C23×Dic15 | C22×Dic15 | C23×C30 | C22×C30 | C23×C10 | C23×C6 | C22×C10 | C22×C10 | C22×C6 | C22×C6 | C24 | C23 | C23 |
| # reps | 1 | 14 | 1 | 16 | 1 | 2 | 8 | 7 | 16 | 14 | 4 | 32 | 28 |
In GAP, Magma, Sage, TeX
C_2^3\times Dic_{15} % in TeX
G:=Group("C2^3xDic15"); // GroupNames label
G:=SmallGroup(480,1178);
// by ID
G=gap.SmallGroup(480,1178);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,112,2693,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^2=d^30=1,e^2=d^15,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,e*d*e^-1=d^-1>;
// generators/relations
×
⋊
ℤ
𝔽
○
≀