direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C22×C15⋊Q8, C30.49C24, Dic15.44C23, (C2×C30)⋊5Q8, C30⋊4(C2×Q8), C15⋊5(C22×Q8), C10⋊2(C2×Dic6), (C2×C10)⋊9Dic6, (C2×C6)⋊6Dic10, C6⋊2(C2×Dic10), C5⋊2(C22×Dic6), C6.49(C23×D5), C23.73(S3×D5), C3⋊2(C22×Dic10), C10.49(S3×C23), (C2×C30).252C23, (C2×Dic5).199D6, (C22×C10).121D6, (C22×C6).104D10, (C22×Dic5).9S3, (C22×Dic3).7D5, (C2×Dic3).170D10, (C22×C30).90C22, (C5×Dic3).36C23, Dic3.31(C22×D5), Dic5.47(C22×S3), (C3×Dic5).52C23, (C6×Dic5).230C22, (C22×Dic15).14C2, (C10×Dic3).210C22, (C2×Dic15).235C22, (C2×C6×Dic5).8C2, C2.49(C22×S3×D5), (Dic3×C2×C10).8C2, C22.112(C2×S3×D5), (C2×C6).258(C22×D5), (C2×C10).256(C22×S3), SmallGroup(480,1121)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1244 in 312 conjugacy classes, 148 normal (18 characteristic)
C1, C2, C2 [×6], C3, C4 [×12], C22 [×7], C5, C6, C6 [×6], C2×C4 [×18], Q8 [×16], C23, C10, C10 [×6], Dic3 [×4], Dic3 [×4], C12 [×4], C2×C6 [×7], C15, C22×C4 [×3], C2×Q8 [×12], Dic5 [×4], Dic5 [×4], C20 [×4], C2×C10 [×7], Dic6 [×16], C2×Dic3 [×6], C2×Dic3 [×6], C2×C12 [×6], C22×C6, C30, C30 [×6], C22×Q8, Dic10 [×16], C2×Dic5 [×6], C2×Dic5 [×6], C2×C20 [×6], C22×C10, C2×Dic6 [×12], C22×Dic3, C22×Dic3, C22×C12, C5×Dic3 [×4], C3×Dic5 [×4], Dic15 [×4], C2×C30 [×7], C2×Dic10 [×12], C22×Dic5, C22×Dic5, C22×C20, C22×Dic6, C15⋊Q8 [×16], C6×Dic5 [×6], C10×Dic3 [×6], C2×Dic15 [×6], C22×C30, C22×Dic10, C2×C15⋊Q8 [×12], C2×C6×Dic5, Dic3×C2×C10, C22×Dic15, C22×C15⋊Q8
Quotients:
C1, C2 [×15], C22 [×35], S3, Q8 [×4], C23 [×15], D5, D6 [×7], C2×Q8 [×6], C24, D10 [×7], Dic6 [×4], C22×S3 [×7], C22×Q8, Dic10 [×4], C22×D5 [×7], C2×Dic6 [×6], S3×C23, S3×D5, C2×Dic10 [×6], C23×D5, C22×Dic6, C15⋊Q8 [×4], C2×S3×D5 [×3], C22×Dic10, C2×C15⋊Q8 [×6], C22×S3×D5, C22×C15⋊Q8
Generators and relations
G = < a,b,c,d,e | a2=b2=c15=d4=1, e2=d2, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, dcd-1=c11, ece-1=c4, ede-1=d-1 >
►Regular action on 480 points
Generators in S480
(1 117)(2 118)(3 119)(4 120)(5 106)(6 107)(7 108)(8 109)(9 110)(10 111)(11 112)(12 113)(13 114)(14 115)(15 116)(16 99)(17 100)(18 101)(19 102)(20 103)(21 104)(22 105)(23 91)(24 92)(25 93)(26 94)(27 95)(28 96)(29 97)(30 98)(31 81)(32 82)(33 83)(34 84)(35 85)(36 86)(37 87)(38 88)(39 89)(40 90)(41 76)(42 77)(43 78)(44 79)(45 80)(46 69)(47 70)(48 71)(49 72)(50 73)(51 74)(52 75)(53 61)(54 62)(55 63)(56 64)(57 65)(58 66)(59 67)(60 68)(121 226)(122 227)(123 228)(124 229)(125 230)(126 231)(127 232)(128 233)(129 234)(130 235)(131 236)(132 237)(133 238)(134 239)(135 240)(136 211)(137 212)(138 213)(139 214)(140 215)(141 216)(142 217)(143 218)(144 219)(145 220)(146 221)(147 222)(148 223)(149 224)(150 225)(151 205)(152 206)(153 207)(154 208)(155 209)(156 210)(157 196)(158 197)(159 198)(160 199)(161 200)(162 201)(163 202)(164 203)(165 204)(166 194)(167 195)(168 181)(169 182)(170 183)(171 184)(172 185)(173 186)(174 187)(175 188)(176 189)(177 190)(178 191)(179 192)(180 193)(241 355)(242 356)(243 357)(244 358)(245 359)(246 360)(247 346)(248 347)(249 348)(250 349)(251 350)(252 351)(253 352)(254 353)(255 354)(256 341)(257 342)(258 343)(259 344)(260 345)(261 331)(262 332)(263 333)(264 334)(265 335)(266 336)(267 337)(268 338)(269 339)(270 340)(271 330)(272 316)(273 317)(274 318)(275 319)(276 320)(277 321)(278 322)(279 323)(280 324)(281 325)(282 326)(283 327)(284 328)(285 329)(286 301)(287 302)(288 303)(289 304)(290 305)(291 306)(292 307)(293 308)(294 309)(295 310)(296 311)(297 312)(298 313)(299 314)(300 315)(361 477)(362 478)(363 479)(364 480)(365 466)(366 467)(367 468)(368 469)(369 470)(370 471)(371 472)(372 473)(373 474)(374 475)(375 476)(376 462)(377 463)(378 464)(379 465)(380 451)(381 452)(382 453)(383 454)(384 455)(385 456)(386 457)(387 458)(388 459)(389 460)(390 461)(391 436)(392 437)(393 438)(394 439)(395 440)(396 441)(397 442)(398 443)(399 444)(400 445)(401 446)(402 447)(403 448)(404 449)(405 450)(406 432)(407 433)(408 434)(409 435)(410 421)(411 422)(412 423)(413 424)(414 425)(415 426)(416 427)(417 428)(418 429)(419 430)(420 431)
(1 54)(2 55)(3 56)(4 57)(5 58)(6 59)(7 60)(8 46)(9 47)(10 48)(11 49)(12 50)(13 51)(14 52)(15 53)(16 43)(17 44)(18 45)(19 31)(20 32)(21 33)(22 34)(23 35)(24 36)(25 37)(26 38)(27 39)(28 40)(29 41)(30 42)(61 116)(62 117)(63 118)(64 119)(65 120)(66 106)(67 107)(68 108)(69 109)(70 110)(71 111)(72 112)(73 113)(74 114)(75 115)(76 97)(77 98)(78 99)(79 100)(80 101)(81 102)(82 103)(83 104)(84 105)(85 91)(86 92)(87 93)(88 94)(89 95)(90 96)(121 174)(122 175)(123 176)(124 177)(125 178)(126 179)(127 180)(128 166)(129 167)(130 168)(131 169)(132 170)(133 171)(134 172)(135 173)(136 155)(137 156)(138 157)(139 158)(140 159)(141 160)(142 161)(143 162)(144 163)(145 164)(146 165)(147 151)(148 152)(149 153)(150 154)(181 235)(182 236)(183 237)(184 238)(185 239)(186 240)(187 226)(188 227)(189 228)(190 229)(191 230)(192 231)(193 232)(194 233)(195 234)(196 213)(197 214)(198 215)(199 216)(200 217)(201 218)(202 219)(203 220)(204 221)(205 222)(206 223)(207 224)(208 225)(209 211)(210 212)(241 289)(242 290)(243 291)(244 292)(245 293)(246 294)(247 295)(248 296)(249 297)(250 298)(251 299)(252 300)(253 286)(254 287)(255 288)(256 275)(257 276)(258 277)(259 278)(260 279)(261 280)(262 281)(263 282)(264 283)(265 284)(266 285)(267 271)(268 272)(269 273)(270 274)(301 352)(302 353)(303 354)(304 355)(305 356)(306 357)(307 358)(308 359)(309 360)(310 346)(311 347)(312 348)(313 349)(314 350)(315 351)(316 338)(317 339)(318 340)(319 341)(320 342)(321 343)(322 344)(323 345)(324 331)(325 332)(326 333)(327 334)(328 335)(329 336)(330 337)(361 410)(362 411)(363 412)(364 413)(365 414)(366 415)(367 416)(368 417)(369 418)(370 419)(371 420)(372 406)(373 407)(374 408)(375 409)(376 391)(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)(421 477)(422 478)(423 479)(424 480)(425 466)(426 467)(427 468)(428 469)(429 470)(430 471)(431 472)(432 473)(433 474)(434 475)(435 476)(436 462)(437 463)(438 464)(439 465)(440 451)(441 452)(442 453)(443 454)(444 455)(445 456)(446 457)(447 458)(448 459)(449 460)(450 461)
(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)
(1 233 30 220)(2 229 16 216)(3 240 17 212)(4 236 18 223)(5 232 19 219)(6 228 20 215)(7 239 21 211)(8 235 22 222)(9 231 23 218)(10 227 24 214)(11 238 25 225)(12 234 26 221)(13 230 27 217)(14 226 28 213)(15 237 29 224)(31 202 58 193)(32 198 59 189)(33 209 60 185)(34 205 46 181)(35 201 47 192)(36 197 48 188)(37 208 49 184)(38 204 50 195)(39 200 51 191)(40 196 52 187)(41 207 53 183)(42 203 54 194)(43 199 55 190)(44 210 56 186)(45 206 57 182)(61 170 76 153)(62 166 77 164)(63 177 78 160)(64 173 79 156)(65 169 80 152)(66 180 81 163)(67 176 82 159)(68 172 83 155)(69 168 84 151)(70 179 85 162)(71 175 86 158)(72 171 87 154)(73 167 88 165)(74 178 89 161)(75 174 90 157)(91 143 110 126)(92 139 111 122)(93 150 112 133)(94 146 113 129)(95 142 114 125)(96 138 115 121)(97 149 116 132)(98 145 117 128)(99 141 118 124)(100 137 119 135)(101 148 120 131)(102 144 106 127)(103 140 107 123)(104 136 108 134)(105 147 109 130)(241 460 269 479)(242 456 270 475)(243 452 256 471)(244 463 257 467)(245 459 258 478)(246 455 259 474)(247 451 260 470)(248 462 261 466)(249 458 262 477)(250 454 263 473)(251 465 264 469)(252 461 265 480)(253 457 266 476)(254 453 267 472)(255 464 268 468)(271 431 287 442)(272 427 288 438)(273 423 289 449)(274 434 290 445)(275 430 291 441)(276 426 292 437)(277 422 293 448)(278 433 294 444)(279 429 295 440)(280 425 296 436)(281 421 297 447)(282 432 298 443)(283 428 299 439)(284 424 300 450)(285 435 286 446)(301 401 329 409)(302 397 330 420)(303 393 316 416)(304 404 317 412)(305 400 318 408)(306 396 319 419)(307 392 320 415)(308 403 321 411)(309 399 322 407)(310 395 323 418)(311 391 324 414)(312 402 325 410)(313 398 326 406)(314 394 327 417)(315 405 328 413)(331 365 347 376)(332 361 348 387)(333 372 349 383)(334 368 350 379)(335 364 351 390)(336 375 352 386)(337 371 353 382)(338 367 354 378)(339 363 355 389)(340 374 356 385)(341 370 357 381)(342 366 358 377)(343 362 359 388)(344 373 360 384)(345 369 346 380)
(1 346 30 345)(2 350 16 334)(3 354 17 338)(4 358 18 342)(5 347 19 331)(6 351 20 335)(7 355 21 339)(8 359 22 343)(9 348 23 332)(10 352 24 336)(11 356 25 340)(12 360 26 344)(13 349 27 333)(14 353 28 337)(15 357 29 341)(31 324 58 311)(32 328 59 315)(33 317 60 304)(34 321 46 308)(35 325 47 312)(36 329 48 301)(37 318 49 305)(38 322 50 309)(39 326 51 313)(40 330 52 302)(41 319 53 306)(42 323 54 310)(43 327 55 314)(44 316 56 303)(45 320 57 307)(61 291 76 275)(62 295 77 279)(63 299 78 283)(64 288 79 272)(65 292 80 276)(66 296 81 280)(67 300 82 284)(68 289 83 273)(69 293 84 277)(70 297 85 281)(71 286 86 285)(72 290 87 274)(73 294 88 278)(74 298 89 282)(75 287 90 271)(91 262 110 249)(92 266 111 253)(93 270 112 242)(94 259 113 246)(95 263 114 250)(96 267 115 254)(97 256 116 243)(98 260 117 247)(99 264 118 251)(100 268 119 255)(101 257 120 244)(102 261 106 248)(103 265 107 252)(104 269 108 241)(105 258 109 245)(121 472 138 453)(122 476 139 457)(123 480 140 461)(124 469 141 465)(125 473 142 454)(126 477 143 458)(127 466 144 462)(128 470 145 451)(129 474 146 455)(130 478 147 459)(131 467 148 463)(132 471 149 452)(133 475 150 456)(134 479 136 460)(135 468 137 464)(151 448 168 422)(152 437 169 426)(153 441 170 430)(154 445 171 434)(155 449 172 423)(156 438 173 427)(157 442 174 431)(158 446 175 435)(159 450 176 424)(160 439 177 428)(161 443 178 432)(162 447 179 421)(163 436 180 425)(164 440 166 429)(165 444 167 433)(181 411 205 403)(182 415 206 392)(183 419 207 396)(184 408 208 400)(185 412 209 404)(186 416 210 393)(187 420 196 397)(188 409 197 401)(189 413 198 405)(190 417 199 394)(191 406 200 398)(192 410 201 402)(193 414 202 391)(194 418 203 395)(195 407 204 399)(211 389 239 363)(212 378 240 367)(213 382 226 371)(214 386 227 375)(215 390 228 364)(216 379 229 368)(217 383 230 372)(218 387 231 361)(219 376 232 365)(220 380 233 369)(221 384 234 373)(222 388 235 362)(223 377 236 366)(224 381 237 370)(225 385 238 374)
G:=sub<Sym(480)| (1,117)(2,118)(3,119)(4,120)(5,106)(6,107)(7,108)(8,109)(9,110)(10,111)(11,112)(12,113)(13,114)(14,115)(15,116)(16,99)(17,100)(18,101)(19,102)(20,103)(21,104)(22,105)(23,91)(24,92)(25,93)(26,94)(27,95)(28,96)(29,97)(30,98)(31,81)(32,82)(33,83)(34,84)(35,85)(36,86)(37,87)(38,88)(39,89)(40,90)(41,76)(42,77)(43,78)(44,79)(45,80)(46,69)(47,70)(48,71)(49,72)(50,73)(51,74)(52,75)(53,61)(54,62)(55,63)(56,64)(57,65)(58,66)(59,67)(60,68)(121,226)(122,227)(123,228)(124,229)(125,230)(126,231)(127,232)(128,233)(129,234)(130,235)(131,236)(132,237)(133,238)(134,239)(135,240)(136,211)(137,212)(138,213)(139,214)(140,215)(141,216)(142,217)(143,218)(144,219)(145,220)(146,221)(147,222)(148,223)(149,224)(150,225)(151,205)(152,206)(153,207)(154,208)(155,209)(156,210)(157,196)(158,197)(159,198)(160,199)(161,200)(162,201)(163,202)(164,203)(165,204)(166,194)(167,195)(168,181)(169,182)(170,183)(171,184)(172,185)(173,186)(174,187)(175,188)(176,189)(177,190)(178,191)(179,192)(180,193)(241,355)(242,356)(243,357)(244,358)(245,359)(246,360)(247,346)(248,347)(249,348)(250,349)(251,350)(252,351)(253,352)(254,353)(255,354)(256,341)(257,342)(258,343)(259,344)(260,345)(261,331)(262,332)(263,333)(264,334)(265,335)(266,336)(267,337)(268,338)(269,339)(270,340)(271,330)(272,316)(273,317)(274,318)(275,319)(276,320)(277,321)(278,322)(279,323)(280,324)(281,325)(282,326)(283,327)(284,328)(285,329)(286,301)(287,302)(288,303)(289,304)(290,305)(291,306)(292,307)(293,308)(294,309)(295,310)(296,311)(297,312)(298,313)(299,314)(300,315)(361,477)(362,478)(363,479)(364,480)(365,466)(366,467)(367,468)(368,469)(369,470)(370,471)(371,472)(372,473)(373,474)(374,475)(375,476)(376,462)(377,463)(378,464)(379,465)(380,451)(381,452)(382,453)(383,454)(384,455)(385,456)(386,457)(387,458)(388,459)(389,460)(390,461)(391,436)(392,437)(393,438)(394,439)(395,440)(396,441)(397,442)(398,443)(399,444)(400,445)(401,446)(402,447)(403,448)(404,449)(405,450)(406,432)(407,433)(408,434)(409,435)(410,421)(411,422)(412,423)(413,424)(414,425)(415,426)(416,427)(417,428)(418,429)(419,430)(420,431), (1,54)(2,55)(3,56)(4,57)(5,58)(6,59)(7,60)(8,46)(9,47)(10,48)(11,49)(12,50)(13,51)(14,52)(15,53)(16,43)(17,44)(18,45)(19,31)(20,32)(21,33)(22,34)(23,35)(24,36)(25,37)(26,38)(27,39)(28,40)(29,41)(30,42)(61,116)(62,117)(63,118)(64,119)(65,120)(66,106)(67,107)(68,108)(69,109)(70,110)(71,111)(72,112)(73,113)(74,114)(75,115)(76,97)(77,98)(78,99)(79,100)(80,101)(81,102)(82,103)(83,104)(84,105)(85,91)(86,92)(87,93)(88,94)(89,95)(90,96)(121,174)(122,175)(123,176)(124,177)(125,178)(126,179)(127,180)(128,166)(129,167)(130,168)(131,169)(132,170)(133,171)(134,172)(135,173)(136,155)(137,156)(138,157)(139,158)(140,159)(141,160)(142,161)(143,162)(144,163)(145,164)(146,165)(147,151)(148,152)(149,153)(150,154)(181,235)(182,236)(183,237)(184,238)(185,239)(186,240)(187,226)(188,227)(189,228)(190,229)(191,230)(192,231)(193,232)(194,233)(195,234)(196,213)(197,214)(198,215)(199,216)(200,217)(201,218)(202,219)(203,220)(204,221)(205,222)(206,223)(207,224)(208,225)(209,211)(210,212)(241,289)(242,290)(243,291)(244,292)(245,293)(246,294)(247,295)(248,296)(249,297)(250,298)(251,299)(252,300)(253,286)(254,287)(255,288)(256,275)(257,276)(258,277)(259,278)(260,279)(261,280)(262,281)(263,282)(264,283)(265,284)(266,285)(267,271)(268,272)(269,273)(270,274)(301,352)(302,353)(303,354)(304,355)(305,356)(306,357)(307,358)(308,359)(309,360)(310,346)(311,347)(312,348)(313,349)(314,350)(315,351)(316,338)(317,339)(318,340)(319,341)(320,342)(321,343)(322,344)(323,345)(324,331)(325,332)(326,333)(327,334)(328,335)(329,336)(330,337)(361,410)(362,411)(363,412)(364,413)(365,414)(366,415)(367,416)(368,417)(369,418)(370,419)(371,420)(372,406)(373,407)(374,408)(375,409)(376,391)(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)(421,477)(422,478)(423,479)(424,480)(425,466)(426,467)(427,468)(428,469)(429,470)(430,471)(431,472)(432,473)(433,474)(434,475)(435,476)(436,462)(437,463)(438,464)(439,465)(440,451)(441,452)(442,453)(443,454)(444,455)(445,456)(446,457)(447,458)(448,459)(449,460)(450,461), (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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(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15)(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), (1,233,30,220)(2,229,16,216)(3,240,17,212)(4,236,18,223)(5,232,19,219)(6,228,20,215)(7,239,21,211)(8,235,22,222)(9,231,23,218)(10,227,24,214)(11,238,25,225)(12,234,26,221)(13,230,27,217)(14,226,28,213)(15,237,29,224)(31,202,58,193)(32,198,59,189)(33,209,60,185)(34,205,46,181)(35,201,47,192)(36,197,48,188)(37,208,49,184)(38,204,50,195)(39,200,51,191)(40,196,52,187)(41,207,53,183)(42,203,54,194)(43,199,55,190)(44,210,56,186)(45,206,57,182)(61,170,76,153)(62,166,77,164)(63,177,78,160)(64,173,79,156)(65,169,80,152)(66,180,81,163)(67,176,82,159)(68,172,83,155)(69,168,84,151)(70,179,85,162)(71,175,86,158)(72,171,87,154)(73,167,88,165)(74,178,89,161)(75,174,90,157)(91,143,110,126)(92,139,111,122)(93,150,112,133)(94,146,113,129)(95,142,114,125)(96,138,115,121)(97,149,116,132)(98,145,117,128)(99,141,118,124)(100,137,119,135)(101,148,120,131)(102,144,106,127)(103,140,107,123)(104,136,108,134)(105,147,109,130)(241,460,269,479)(242,456,270,475)(243,452,256,471)(244,463,257,467)(245,459,258,478)(246,455,259,474)(247,451,260,470)(248,462,261,466)(249,458,262,477)(250,454,263,473)(251,465,264,469)(252,461,265,480)(253,457,266,476)(254,453,267,472)(255,464,268,468)(271,431,287,442)(272,427,288,438)(273,423,289,449)(274,434,290,445)(275,430,291,441)(276,426,292,437)(277,422,293,448)(278,433,294,444)(279,429,295,440)(280,425,296,436)(281,421,297,447)(282,432,298,443)(283,428,299,439)(284,424,300,450)(285,435,286,446)(301,401,329,409)(302,397,330,420)(303,393,316,416)(304,404,317,412)(305,400,318,408)(306,396,319,419)(307,392,320,415)(308,403,321,411)(309,399,322,407)(310,395,323,418)(311,391,324,414)(312,402,325,410)(313,398,326,406)(314,394,327,417)(315,405,328,413)(331,365,347,376)(332,361,348,387)(333,372,349,383)(334,368,350,379)(335,364,351,390)(336,375,352,386)(337,371,353,382)(338,367,354,378)(339,363,355,389)(340,374,356,385)(341,370,357,381)(342,366,358,377)(343,362,359,388)(344,373,360,384)(345,369,346,380), (1,346,30,345)(2,350,16,334)(3,354,17,338)(4,358,18,342)(5,347,19,331)(6,351,20,335)(7,355,21,339)(8,359,22,343)(9,348,23,332)(10,352,24,336)(11,356,25,340)(12,360,26,344)(13,349,27,333)(14,353,28,337)(15,357,29,341)(31,324,58,311)(32,328,59,315)(33,317,60,304)(34,321,46,308)(35,325,47,312)(36,329,48,301)(37,318,49,305)(38,322,50,309)(39,326,51,313)(40,330,52,302)(41,319,53,306)(42,323,54,310)(43,327,55,314)(44,316,56,303)(45,320,57,307)(61,291,76,275)(62,295,77,279)(63,299,78,283)(64,288,79,272)(65,292,80,276)(66,296,81,280)(67,300,82,284)(68,289,83,273)(69,293,84,277)(70,297,85,281)(71,286,86,285)(72,290,87,274)(73,294,88,278)(74,298,89,282)(75,287,90,271)(91,262,110,249)(92,266,111,253)(93,270,112,242)(94,259,113,246)(95,263,114,250)(96,267,115,254)(97,256,116,243)(98,260,117,247)(99,264,118,251)(100,268,119,255)(101,257,120,244)(102,261,106,248)(103,265,107,252)(104,269,108,241)(105,258,109,245)(121,472,138,453)(122,476,139,457)(123,480,140,461)(124,469,141,465)(125,473,142,454)(126,477,143,458)(127,466,144,462)(128,470,145,451)(129,474,146,455)(130,478,147,459)(131,467,148,463)(132,471,149,452)(133,475,150,456)(134,479,136,460)(135,468,137,464)(151,448,168,422)(152,437,169,426)(153,441,170,430)(154,445,171,434)(155,449,172,423)(156,438,173,427)(157,442,174,431)(158,446,175,435)(159,450,176,424)(160,439,177,428)(161,443,178,432)(162,447,179,421)(163,436,180,425)(164,440,166,429)(165,444,167,433)(181,411,205,403)(182,415,206,392)(183,419,207,396)(184,408,208,400)(185,412,209,404)(186,416,210,393)(187,420,196,397)(188,409,197,401)(189,413,198,405)(190,417,199,394)(191,406,200,398)(192,410,201,402)(193,414,202,391)(194,418,203,395)(195,407,204,399)(211,389,239,363)(212,378,240,367)(213,382,226,371)(214,386,227,375)(215,390,228,364)(216,379,229,368)(217,383,230,372)(218,387,231,361)(219,376,232,365)(220,380,233,369)(221,384,234,373)(222,388,235,362)(223,377,236,366)(224,381,237,370)(225,385,238,374) );
G=PermutationGroup([(1,117),(2,118),(3,119),(4,120),(5,106),(6,107),(7,108),(8,109),(9,110),(10,111),(11,112),(12,113),(13,114),(14,115),(15,116),(16,99),(17,100),(18,101),(19,102),(20,103),(21,104),(22,105),(23,91),(24,92),(25,93),(26,94),(27,95),(28,96),(29,97),(30,98),(31,81),(32,82),(33,83),(34,84),(35,85),(36,86),(37,87),(38,88),(39,89),(40,90),(41,76),(42,77),(43,78),(44,79),(45,80),(46,69),(47,70),(48,71),(49,72),(50,73),(51,74),(52,75),(53,61),(54,62),(55,63),(56,64),(57,65),(58,66),(59,67),(60,68),(121,226),(122,227),(123,228),(124,229),(125,230),(126,231),(127,232),(128,233),(129,234),(130,235),(131,236),(132,237),(133,238),(134,239),(135,240),(136,211),(137,212),(138,213),(139,214),(140,215),(141,216),(142,217),(143,218),(144,219),(145,220),(146,221),(147,222),(148,223),(149,224),(150,225),(151,205),(152,206),(153,207),(154,208),(155,209),(156,210),(157,196),(158,197),(159,198),(160,199),(161,200),(162,201),(163,202),(164,203),(165,204),(166,194),(167,195),(168,181),(169,182),(170,183),(171,184),(172,185),(173,186),(174,187),(175,188),(176,189),(177,190),(178,191),(179,192),(180,193),(241,355),(242,356),(243,357),(244,358),(245,359),(246,360),(247,346),(248,347),(249,348),(250,349),(251,350),(252,351),(253,352),(254,353),(255,354),(256,341),(257,342),(258,343),(259,344),(260,345),(261,331),(262,332),(263,333),(264,334),(265,335),(266,336),(267,337),(268,338),(269,339),(270,340),(271,330),(272,316),(273,317),(274,318),(275,319),(276,320),(277,321),(278,322),(279,323),(280,324),(281,325),(282,326),(283,327),(284,328),(285,329),(286,301),(287,302),(288,303),(289,304),(290,305),(291,306),(292,307),(293,308),(294,309),(295,310),(296,311),(297,312),(298,313),(299,314),(300,315),(361,477),(362,478),(363,479),(364,480),(365,466),(366,467),(367,468),(368,469),(369,470),(370,471),(371,472),(372,473),(373,474),(374,475),(375,476),(376,462),(377,463),(378,464),(379,465),(380,451),(381,452),(382,453),(383,454),(384,455),(385,456),(386,457),(387,458),(388,459),(389,460),(390,461),(391,436),(392,437),(393,438),(394,439),(395,440),(396,441),(397,442),(398,443),(399,444),(400,445),(401,446),(402,447),(403,448),(404,449),(405,450),(406,432),(407,433),(408,434),(409,435),(410,421),(411,422),(412,423),(413,424),(414,425),(415,426),(416,427),(417,428),(418,429),(419,430),(420,431)], [(1,54),(2,55),(3,56),(4,57),(5,58),(6,59),(7,60),(8,46),(9,47),(10,48),(11,49),(12,50),(13,51),(14,52),(15,53),(16,43),(17,44),(18,45),(19,31),(20,32),(21,33),(22,34),(23,35),(24,36),(25,37),(26,38),(27,39),(28,40),(29,41),(30,42),(61,116),(62,117),(63,118),(64,119),(65,120),(66,106),(67,107),(68,108),(69,109),(70,110),(71,111),(72,112),(73,113),(74,114),(75,115),(76,97),(77,98),(78,99),(79,100),(80,101),(81,102),(82,103),(83,104),(84,105),(85,91),(86,92),(87,93),(88,94),(89,95),(90,96),(121,174),(122,175),(123,176),(124,177),(125,178),(126,179),(127,180),(128,166),(129,167),(130,168),(131,169),(132,170),(133,171),(134,172),(135,173),(136,155),(137,156),(138,157),(139,158),(140,159),(141,160),(142,161),(143,162),(144,163),(145,164),(146,165),(147,151),(148,152),(149,153),(150,154),(181,235),(182,236),(183,237),(184,238),(185,239),(186,240),(187,226),(188,227),(189,228),(190,229),(191,230),(192,231),(193,232),(194,233),(195,234),(196,213),(197,214),(198,215),(199,216),(200,217),(201,218),(202,219),(203,220),(204,221),(205,222),(206,223),(207,224),(208,225),(209,211),(210,212),(241,289),(242,290),(243,291),(244,292),(245,293),(246,294),(247,295),(248,296),(249,297),(250,298),(251,299),(252,300),(253,286),(254,287),(255,288),(256,275),(257,276),(258,277),(259,278),(260,279),(261,280),(262,281),(263,282),(264,283),(265,284),(266,285),(267,271),(268,272),(269,273),(270,274),(301,352),(302,353),(303,354),(304,355),(305,356),(306,357),(307,358),(308,359),(309,360),(310,346),(311,347),(312,348),(313,349),(314,350),(315,351),(316,338),(317,339),(318,340),(319,341),(320,342),(321,343),(322,344),(323,345),(324,331),(325,332),(326,333),(327,334),(328,335),(329,336),(330,337),(361,410),(362,411),(363,412),(364,413),(365,414),(366,415),(367,416),(368,417),(369,418),(370,419),(371,420),(372,406),(373,407),(374,408),(375,409),(376,391),(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),(421,477),(422,478),(423,479),(424,480),(425,466),(426,467),(427,468),(428,469),(429,470),(430,471),(431,472),(432,473),(433,474),(434,475),(435,476),(436,462),(437,463),(438,464),(439,465),(440,451),(441,452),(442,453),(443,454),(444,455),(445,456),(446,457),(447,458),(448,459),(449,460),(450,461)], [(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)], [(1,233,30,220),(2,229,16,216),(3,240,17,212),(4,236,18,223),(5,232,19,219),(6,228,20,215),(7,239,21,211),(8,235,22,222),(9,231,23,218),(10,227,24,214),(11,238,25,225),(12,234,26,221),(13,230,27,217),(14,226,28,213),(15,237,29,224),(31,202,58,193),(32,198,59,189),(33,209,60,185),(34,205,46,181),(35,201,47,192),(36,197,48,188),(37,208,49,184),(38,204,50,195),(39,200,51,191),(40,196,52,187),(41,207,53,183),(42,203,54,194),(43,199,55,190),(44,210,56,186),(45,206,57,182),(61,170,76,153),(62,166,77,164),(63,177,78,160),(64,173,79,156),(65,169,80,152),(66,180,81,163),(67,176,82,159),(68,172,83,155),(69,168,84,151),(70,179,85,162),(71,175,86,158),(72,171,87,154),(73,167,88,165),(74,178,89,161),(75,174,90,157),(91,143,110,126),(92,139,111,122),(93,150,112,133),(94,146,113,129),(95,142,114,125),(96,138,115,121),(97,149,116,132),(98,145,117,128),(99,141,118,124),(100,137,119,135),(101,148,120,131),(102,144,106,127),(103,140,107,123),(104,136,108,134),(105,147,109,130),(241,460,269,479),(242,456,270,475),(243,452,256,471),(244,463,257,467),(245,459,258,478),(246,455,259,474),(247,451,260,470),(248,462,261,466),(249,458,262,477),(250,454,263,473),(251,465,264,469),(252,461,265,480),(253,457,266,476),(254,453,267,472),(255,464,268,468),(271,431,287,442),(272,427,288,438),(273,423,289,449),(274,434,290,445),(275,430,291,441),(276,426,292,437),(277,422,293,448),(278,433,294,444),(279,429,295,440),(280,425,296,436),(281,421,297,447),(282,432,298,443),(283,428,299,439),(284,424,300,450),(285,435,286,446),(301,401,329,409),(302,397,330,420),(303,393,316,416),(304,404,317,412),(305,400,318,408),(306,396,319,419),(307,392,320,415),(308,403,321,411),(309,399,322,407),(310,395,323,418),(311,391,324,414),(312,402,325,410),(313,398,326,406),(314,394,327,417),(315,405,328,413),(331,365,347,376),(332,361,348,387),(333,372,349,383),(334,368,350,379),(335,364,351,390),(336,375,352,386),(337,371,353,382),(338,367,354,378),(339,363,355,389),(340,374,356,385),(341,370,357,381),(342,366,358,377),(343,362,359,388),(344,373,360,384),(345,369,346,380)], [(1,346,30,345),(2,350,16,334),(3,354,17,338),(4,358,18,342),(5,347,19,331),(6,351,20,335),(7,355,21,339),(8,359,22,343),(9,348,23,332),(10,352,24,336),(11,356,25,340),(12,360,26,344),(13,349,27,333),(14,353,28,337),(15,357,29,341),(31,324,58,311),(32,328,59,315),(33,317,60,304),(34,321,46,308),(35,325,47,312),(36,329,48,301),(37,318,49,305),(38,322,50,309),(39,326,51,313),(40,330,52,302),(41,319,53,306),(42,323,54,310),(43,327,55,314),(44,316,56,303),(45,320,57,307),(61,291,76,275),(62,295,77,279),(63,299,78,283),(64,288,79,272),(65,292,80,276),(66,296,81,280),(67,300,82,284),(68,289,83,273),(69,293,84,277),(70,297,85,281),(71,286,86,285),(72,290,87,274),(73,294,88,278),(74,298,89,282),(75,287,90,271),(91,262,110,249),(92,266,111,253),(93,270,112,242),(94,259,113,246),(95,263,114,250),(96,267,115,254),(97,256,116,243),(98,260,117,247),(99,264,118,251),(100,268,119,255),(101,257,120,244),(102,261,106,248),(103,265,107,252),(104,269,108,241),(105,258,109,245),(121,472,138,453),(122,476,139,457),(123,480,140,461),(124,469,141,465),(125,473,142,454),(126,477,143,458),(127,466,144,462),(128,470,145,451),(129,474,146,455),(130,478,147,459),(131,467,148,463),(132,471,149,452),(133,475,150,456),(134,479,136,460),(135,468,137,464),(151,448,168,422),(152,437,169,426),(153,441,170,430),(154,445,171,434),(155,449,172,423),(156,438,173,427),(157,442,174,431),(158,446,175,435),(159,450,176,424),(160,439,177,428),(161,443,178,432),(162,447,179,421),(163,436,180,425),(164,440,166,429),(165,444,167,433),(181,411,205,403),(182,415,206,392),(183,419,207,396),(184,408,208,400),(185,412,209,404),(186,416,210,393),(187,420,196,397),(188,409,197,401),(189,413,198,405),(190,417,199,394),(191,406,200,398),(192,410,201,402),(193,414,202,391),(194,418,203,395),(195,407,204,399),(211,389,239,363),(212,378,240,367),(213,382,226,371),(214,386,227,375),(215,390,228,364),(216,379,229,368),(217,383,230,372),(218,387,231,361),(219,376,232,365),(220,380,233,369),(221,384,234,373),(222,388,235,362),(223,377,236,366),(224,381,237,370),(225,385,238,374)])
Matrix representation ►G ⊆ GL5(𝔽61)
| 1 | 0 | 0 | 0 | 0 |
| 0 | 60 | 0 | 0 | 0 |
| 0 | 0 | 60 | 0 | 0 |
| 0 | 0 | 0 | 60 | 0 |
| 0 | 0 | 0 | 0 | 60 |
| 60 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 60 | 60 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 44 |
| 0 | 0 | 0 | 18 | 43 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 22 | 13 | 0 | 0 |
| 0 | 52 | 39 | 0 | 0 |
| 0 | 0 | 0 | 25 | 7 |
| 0 | 0 | 0 | 50 | 36 |
| 60 | 0 | 0 | 0 | 0 |
| 0 | 60 | 0 | 0 | 0 |
| 0 | 0 | 60 | 0 | 0 |
| 0 | 0 | 0 | 31 | 14 |
| 0 | 0 | 0 | 1 | 30 |
G:=sub<GL(5,GF(61))| [1,0,0,0,0,0,60,0,0,0,0,0,60,0,0,0,0,0,60,0,0,0,0,0,60],[60,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,60,1,0,0,0,60,0,0,0,0,0,0,0,18,0,0,0,44,43],[1,0,0,0,0,0,22,52,0,0,0,13,39,0,0,0,0,0,25,50,0,0,0,7,36],[60,0,0,0,0,0,60,0,0,0,0,0,60,0,0,0,0,0,31,1,0,0,0,14,30] >;
84 conjugacy classes
| class | 1 | 2A | ··· | 2G | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 5A | 5B | 6A | ··· | 6G | 10A | ··· | 10N | 12A | ··· | 12H | 15A | 15B | 20A | ··· | 20P | 30A | ··· | 30N |
| order | 1 | 2 | ··· | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | ··· | 6 | 10 | ··· | 10 | 12 | ··· | 12 | 15 | 15 | 20 | ··· | 20 | 30 | ··· | 30 |
| size | 1 | 1 | ··· | 1 | 2 | 6 | 6 | 6 | 6 | 10 | 10 | 10 | 10 | 30 | 30 | 30 | 30 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 10 | ··· | 10 | 4 | 4 | 6 | ··· | 6 | 4 | ··· | 4 |
84 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | - | + | + | + | + | + | - | - | + | - | + |
| image | C1 | C2 | C2 | C2 | C2 | S3 | Q8 | D5 | D6 | D6 | D10 | D10 | Dic6 | Dic10 | S3×D5 | C15⋊Q8 | C2×S3×D5 |
| kernel | C22×C15⋊Q8 | C2×C15⋊Q8 | C2×C6×Dic5 | Dic3×C2×C10 | C22×Dic15 | C22×Dic5 | C2×C30 | C22×Dic3 | C2×Dic5 | C22×C10 | C2×Dic3 | C22×C6 | C2×C10 | C2×C6 | C23 | C22 | C22 |
| # reps | 1 | 12 | 1 | 1 | 1 | 1 | 4 | 2 | 6 | 1 | 12 | 2 | 8 | 16 | 2 | 8 | 6 |
In GAP, Magma, Sage, TeX
C_2^2\times C_{15}\rtimes Q_8 % in TeX
G:=Group("C2^2xC15:Q8"); // GroupNames label
G:=SmallGroup(480,1121);
// by ID
G=gap.SmallGroup(480,1121);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,112,253,120,1356,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^15=d^4=1,e^2=d^2,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,d*c*d^-1=c^11,e*c*e^-1=c^4,e*d*e^-1=d^-1>;
// generators/relations
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