direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C3×Q8×Dic5, C5⋊4(Q8×C12), C15⋊22(C4×Q8), (C5×Q8)⋊9C12, C6.54(Q8×D5), (Q8×C15)⋊12C4, (Q8×C10).9C6, (C6×Q8).10D5, C10.16(C6×Q8), C4.4(C6×Dic5), C20.35(C2×C12), C60.169(C2×C4), C4⋊Dic5.12C6, (Q8×C30).10C2, C30.106(C2×Q8), (C4×Dic5).4C6, (C2×C12).367D10, C12.33(C2×Dic5), C30.265(C4○D4), (C2×C30).374C23, C10.39(C22×C12), (C2×C60).299C22, C30.224(C22×C4), C6.53(Q8⋊2D5), (C12×Dic5).14C2, C6.36(C22×Dic5), (C6×Dic5).254C22, C2.3(C3×Q8×D5), C2.7(C2×C6×Dic5), (C2×C4).55(C6×D5), (C2×Q8).7(C3×D5), C22.26(D5×C2×C6), (C2×C20).36(C2×C6), C10.35(C3×C4○D4), C2.3(C3×Q8⋊2D5), (C3×C4⋊Dic5).26C2, (C2×C10).57(C22×C6), (C2×Dic5).64(C2×C6), (C2×C6).370(C22×D5), SmallGroup(480,738)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C3×Q8×Dic5
G = < a,b,c,d,e | a3=b4=d10=1, c2=b2, e2=d5, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=b-1, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >
Subgroups: 304 in 140 conjugacy classes, 102 normal (28 characteristic)
C1, C2, C3, C4, C4, C22, C5, C6, C2×C4, C2×C4, Q8, C10, C12, C12, C2×C6, C15, C42, C4⋊C4, C2×Q8, Dic5, Dic5, C20, C2×C10, C2×C12, C2×C12, C3×Q8, C30, C4×Q8, C2×Dic5, C2×Dic5, C2×C20, C5×Q8, C4×C12, C3×C4⋊C4, C6×Q8, C3×Dic5, C3×Dic5, C60, C2×C30, C4×Dic5, C4⋊Dic5, Q8×C10, Q8×C12, C6×Dic5, C6×Dic5, C2×C60, Q8×C15, Q8×Dic5, C12×Dic5, C3×C4⋊Dic5, Q8×C30, C3×Q8×Dic5
Quotients: C1, C2, C3, C4, C22, C6, C2×C4, Q8, C23, D5, C12, C2×C6, C22×C4, C2×Q8, C4○D4, Dic5, D10, C2×C12, C3×Q8, C22×C6, C3×D5, C4×Q8, C2×Dic5, C22×D5, C22×C12, C6×Q8, C3×C4○D4, C3×Dic5, C6×D5, Q8×D5, Q8⋊2D5, C22×Dic5, Q8×C12, C6×Dic5, D5×C2×C6, Q8×Dic5, C3×Q8×D5, C3×Q8⋊2D5, C2×C6×Dic5, C3×Q8×Dic5
►Regular action on 480 points
Generators in S480
(1 58 38)(2 59 39)(3 60 40)(4 51 31)(5 52 32)(6 53 33)(7 54 34)(8 55 35)(9 56 36)(10 57 37)(11 462 442)(12 463 443)(13 464 444)(14 465 445)(15 466 446)(16 467 447)(17 468 448)(18 469 449)(19 470 450)(20 461 441)(21 61 41)(22 62 42)(23 63 43)(24 64 44)(25 65 45)(26 66 46)(27 67 47)(28 68 48)(29 69 49)(30 70 50)(71 111 91)(72 112 92)(73 113 93)(74 114 94)(75 115 95)(76 116 96)(77 117 97)(78 118 98)(79 119 99)(80 120 100)(81 121 101)(82 122 102)(83 123 103)(84 124 104)(85 125 105)(86 126 106)(87 127 107)(88 128 108)(89 129 109)(90 130 110)(131 171 151)(132 172 152)(133 173 153)(134 174 154)(135 175 155)(136 176 156)(137 177 157)(138 178 158)(139 179 159)(140 180 160)(141 181 161)(142 182 162)(143 183 163)(144 184 164)(145 185 165)(146 186 166)(147 187 167)(148 188 168)(149 189 169)(150 190 170)(191 231 211)(192 232 212)(193 233 213)(194 234 214)(195 235 215)(196 236 216)(197 237 217)(198 238 218)(199 239 219)(200 240 220)(201 248 221)(202 249 222)(203 250 223)(204 241 224)(205 242 225)(206 243 226)(207 244 227)(208 245 228)(209 246 229)(210 247 230)(251 291 271)(252 292 272)(253 293 273)(254 294 274)(255 295 275)(256 296 276)(257 297 277)(258 298 278)(259 299 279)(260 300 280)(261 301 281)(262 302 282)(263 303 283)(264 304 284)(265 305 285)(266 306 286)(267 307 287)(268 308 288)(269 309 289)(270 310 290)(311 351 331)(312 352 332)(313 353 333)(314 354 334)(315 355 335)(316 356 336)(317 357 337)(318 358 338)(319 359 339)(320 360 340)(321 361 341)(322 362 342)(323 363 343)(324 364 344)(325 365 345)(326 366 346)(327 367 347)(328 368 348)(329 369 349)(330 370 350)(371 411 391)(372 412 392)(373 413 393)(374 414 394)(375 415 395)(376 416 396)(377 417 397)(378 418 398)(379 419 399)(380 420 400)(381 421 401)(382 422 402)(383 423 403)(384 424 404)(385 425 405)(386 426 406)(387 427 407)(388 428 408)(389 429 409)(390 430 410)(431 471 451)(432 472 452)(433 473 453)(434 474 454)(435 475 455)(436 476 456)(437 477 457)(438 478 458)(439 479 459)(440 480 460)
(1 88 28 78)(2 89 29 79)(3 90 30 80)(4 81 21 71)(5 82 22 72)(6 83 23 73)(7 84 24 74)(8 85 25 75)(9 86 26 76)(10 87 27 77)(11 411 471 422)(12 412 472 423)(13 413 473 424)(14 414 474 425)(15 415 475 426)(16 416 476 427)(17 417 477 428)(18 418 478 429)(19 419 479 430)(20 420 480 421)(31 101 41 91)(32 102 42 92)(33 103 43 93)(34 104 44 94)(35 105 45 95)(36 106 46 96)(37 107 47 97)(38 108 48 98)(39 109 49 99)(40 110 50 100)(51 121 61 111)(52 122 62 112)(53 123 63 113)(54 124 64 114)(55 125 65 115)(56 126 66 116)(57 127 67 117)(58 128 68 118)(59 129 69 119)(60 130 70 120)(131 191 141 201)(132 192 142 202)(133 193 143 203)(134 194 144 204)(135 195 145 205)(136 196 146 206)(137 197 147 207)(138 198 148 208)(139 199 149 209)(140 200 150 210)(151 211 161 221)(152 212 162 222)(153 213 163 223)(154 214 164 224)(155 215 165 225)(156 216 166 226)(157 217 167 227)(158 218 168 228)(159 219 169 229)(160 220 170 230)(171 231 181 248)(172 232 182 249)(173 233 183 250)(174 234 184 241)(175 235 185 242)(176 236 186 243)(177 237 187 244)(178 238 188 245)(179 239 189 246)(180 240 190 247)(251 322 262 311)(252 323 263 312)(253 324 264 313)(254 325 265 314)(255 326 266 315)(256 327 267 316)(257 328 268 317)(258 329 269 318)(259 330 270 319)(260 321 261 320)(271 342 282 331)(272 343 283 332)(273 344 284 333)(274 345 285 334)(275 346 286 335)(276 347 287 336)(277 348 288 337)(278 349 289 338)(279 350 290 339)(280 341 281 340)(291 362 302 351)(292 363 303 352)(293 364 304 353)(294 365 305 354)(295 366 306 355)(296 367 307 356)(297 368 308 357)(298 369 309 358)(299 370 310 359)(300 361 301 360)(371 431 382 442)(372 432 383 443)(373 433 384 444)(374 434 385 445)(375 435 386 446)(376 436 387 447)(377 437 388 448)(378 438 389 449)(379 439 390 450)(380 440 381 441)(391 451 402 462)(392 452 403 463)(393 453 404 464)(394 454 405 465)(395 455 406 466)(396 456 407 467)(397 457 408 468)(398 458 409 469)(399 459 410 470)(400 460 401 461)
(1 148 28 138)(2 149 29 139)(3 150 30 140)(4 141 21 131)(5 142 22 132)(6 143 23 133)(7 144 24 134)(8 145 25 135)(9 146 26 136)(10 147 27 137)(11 362 471 351)(12 363 472 352)(13 364 473 353)(14 365 474 354)(15 366 475 355)(16 367 476 356)(17 368 477 357)(18 369 478 358)(19 370 479 359)(20 361 480 360)(31 161 41 151)(32 162 42 152)(33 163 43 153)(34 164 44 154)(35 165 45 155)(36 166 46 156)(37 167 47 157)(38 168 48 158)(39 169 49 159)(40 170 50 160)(51 181 61 171)(52 182 62 172)(53 183 63 173)(54 184 64 174)(55 185 65 175)(56 186 66 176)(57 187 67 177)(58 188 68 178)(59 189 69 179)(60 190 70 180)(71 201 81 191)(72 202 82 192)(73 203 83 193)(74 204 84 194)(75 205 85 195)(76 206 86 196)(77 207 87 197)(78 208 88 198)(79 209 89 199)(80 210 90 200)(91 221 101 211)(92 222 102 212)(93 223 103 213)(94 224 104 214)(95 225 105 215)(96 226 106 216)(97 227 107 217)(98 228 108 218)(99 229 109 219)(100 230 110 220)(111 248 121 231)(112 249 122 232)(113 250 123 233)(114 241 124 234)(115 242 125 235)(116 243 126 236)(117 244 127 237)(118 245 128 238)(119 246 129 239)(120 247 130 240)(251 382 262 371)(252 383 263 372)(253 384 264 373)(254 385 265 374)(255 386 266 375)(256 387 267 376)(257 388 268 377)(258 389 269 378)(259 390 270 379)(260 381 261 380)(271 402 282 391)(272 403 283 392)(273 404 284 393)(274 405 285 394)(275 406 286 395)(276 407 287 396)(277 408 288 397)(278 409 289 398)(279 410 290 399)(280 401 281 400)(291 422 302 411)(292 423 303 412)(293 424 304 413)(294 425 305 414)(295 426 306 415)(296 427 307 416)(297 428 308 417)(298 429 309 418)(299 430 310 419)(300 421 301 420)(311 442 322 431)(312 443 323 432)(313 444 324 433)(314 445 325 434)(315 446 326 435)(316 447 327 436)(317 448 328 437)(318 449 329 438)(319 450 330 439)(320 441 321 440)(331 462 342 451)(332 463 343 452)(333 464 344 453)(334 465 345 454)(335 466 346 455)(336 467 347 456)(337 468 348 457)(338 469 349 458)(339 470 350 459)(340 461 341 460)
(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)
(1 251 6 256)(2 260 7 255)(3 259 8 254)(4 258 9 253)(5 257 10 252)(11 250 16 245)(12 249 17 244)(13 248 18 243)(14 247 19 242)(15 246 20 241)(21 269 26 264)(22 268 27 263)(23 267 28 262)(24 266 29 261)(25 265 30 270)(31 278 36 273)(32 277 37 272)(33 276 38 271)(34 275 39 280)(35 274 40 279)(41 289 46 284)(42 288 47 283)(43 287 48 282)(44 286 49 281)(45 285 50 290)(51 298 56 293)(52 297 57 292)(53 296 58 291)(54 295 59 300)(55 294 60 299)(61 309 66 304)(62 308 67 303)(63 307 68 302)(64 306 69 301)(65 305 70 310)(71 318 76 313)(72 317 77 312)(73 316 78 311)(74 315 79 320)(75 314 80 319)(81 329 86 324)(82 328 87 323)(83 327 88 322)(84 326 89 321)(85 325 90 330)(91 338 96 333)(92 337 97 332)(93 336 98 331)(94 335 99 340)(95 334 100 339)(101 349 106 344)(102 348 107 343)(103 347 108 342)(104 346 109 341)(105 345 110 350)(111 358 116 353)(112 357 117 352)(113 356 118 351)(114 355 119 360)(115 354 120 359)(121 369 126 364)(122 368 127 363)(123 367 128 362)(124 366 129 361)(125 365 130 370)(131 378 136 373)(132 377 137 372)(133 376 138 371)(134 375 139 380)(135 374 140 379)(141 389 146 384)(142 388 147 383)(143 387 148 382)(144 386 149 381)(145 385 150 390)(151 398 156 393)(152 397 157 392)(153 396 158 391)(154 395 159 400)(155 394 160 399)(161 409 166 404)(162 408 167 403)(163 407 168 402)(164 406 169 401)(165 405 170 410)(171 418 176 413)(172 417 177 412)(173 416 178 411)(174 415 179 420)(175 414 180 419)(181 429 186 424)(182 428 187 423)(183 427 188 422)(184 426 189 421)(185 425 190 430)(191 438 196 433)(192 437 197 432)(193 436 198 431)(194 435 199 440)(195 434 200 439)(201 449 206 444)(202 448 207 443)(203 447 208 442)(204 446 209 441)(205 445 210 450)(211 458 216 453)(212 457 217 452)(213 456 218 451)(214 455 219 460)(215 454 220 459)(221 469 226 464)(222 468 227 463)(223 467 228 462)(224 466 229 461)(225 465 230 470)(231 478 236 473)(232 477 237 472)(233 476 238 471)(234 475 239 480)(235 474 240 479)
G:=sub<Sym(480)| (1,58,38)(2,59,39)(3,60,40)(4,51,31)(5,52,32)(6,53,33)(7,54,34)(8,55,35)(9,56,36)(10,57,37)(11,462,442)(12,463,443)(13,464,444)(14,465,445)(15,466,446)(16,467,447)(17,468,448)(18,469,449)(19,470,450)(20,461,441)(21,61,41)(22,62,42)(23,63,43)(24,64,44)(25,65,45)(26,66,46)(27,67,47)(28,68,48)(29,69,49)(30,70,50)(71,111,91)(72,112,92)(73,113,93)(74,114,94)(75,115,95)(76,116,96)(77,117,97)(78,118,98)(79,119,99)(80,120,100)(81,121,101)(82,122,102)(83,123,103)(84,124,104)(85,125,105)(86,126,106)(87,127,107)(88,128,108)(89,129,109)(90,130,110)(131,171,151)(132,172,152)(133,173,153)(134,174,154)(135,175,155)(136,176,156)(137,177,157)(138,178,158)(139,179,159)(140,180,160)(141,181,161)(142,182,162)(143,183,163)(144,184,164)(145,185,165)(146,186,166)(147,187,167)(148,188,168)(149,189,169)(150,190,170)(191,231,211)(192,232,212)(193,233,213)(194,234,214)(195,235,215)(196,236,216)(197,237,217)(198,238,218)(199,239,219)(200,240,220)(201,248,221)(202,249,222)(203,250,223)(204,241,224)(205,242,225)(206,243,226)(207,244,227)(208,245,228)(209,246,229)(210,247,230)(251,291,271)(252,292,272)(253,293,273)(254,294,274)(255,295,275)(256,296,276)(257,297,277)(258,298,278)(259,299,279)(260,300,280)(261,301,281)(262,302,282)(263,303,283)(264,304,284)(265,305,285)(266,306,286)(267,307,287)(268,308,288)(269,309,289)(270,310,290)(311,351,331)(312,352,332)(313,353,333)(314,354,334)(315,355,335)(316,356,336)(317,357,337)(318,358,338)(319,359,339)(320,360,340)(321,361,341)(322,362,342)(323,363,343)(324,364,344)(325,365,345)(326,366,346)(327,367,347)(328,368,348)(329,369,349)(330,370,350)(371,411,391)(372,412,392)(373,413,393)(374,414,394)(375,415,395)(376,416,396)(377,417,397)(378,418,398)(379,419,399)(380,420,400)(381,421,401)(382,422,402)(383,423,403)(384,424,404)(385,425,405)(386,426,406)(387,427,407)(388,428,408)(389,429,409)(390,430,410)(431,471,451)(432,472,452)(433,473,453)(434,474,454)(435,475,455)(436,476,456)(437,477,457)(438,478,458)(439,479,459)(440,480,460), (1,88,28,78)(2,89,29,79)(3,90,30,80)(4,81,21,71)(5,82,22,72)(6,83,23,73)(7,84,24,74)(8,85,25,75)(9,86,26,76)(10,87,27,77)(11,411,471,422)(12,412,472,423)(13,413,473,424)(14,414,474,425)(15,415,475,426)(16,416,476,427)(17,417,477,428)(18,418,478,429)(19,419,479,430)(20,420,480,421)(31,101,41,91)(32,102,42,92)(33,103,43,93)(34,104,44,94)(35,105,45,95)(36,106,46,96)(37,107,47,97)(38,108,48,98)(39,109,49,99)(40,110,50,100)(51,121,61,111)(52,122,62,112)(53,123,63,113)(54,124,64,114)(55,125,65,115)(56,126,66,116)(57,127,67,117)(58,128,68,118)(59,129,69,119)(60,130,70,120)(131,191,141,201)(132,192,142,202)(133,193,143,203)(134,194,144,204)(135,195,145,205)(136,196,146,206)(137,197,147,207)(138,198,148,208)(139,199,149,209)(140,200,150,210)(151,211,161,221)(152,212,162,222)(153,213,163,223)(154,214,164,224)(155,215,165,225)(156,216,166,226)(157,217,167,227)(158,218,168,228)(159,219,169,229)(160,220,170,230)(171,231,181,248)(172,232,182,249)(173,233,183,250)(174,234,184,241)(175,235,185,242)(176,236,186,243)(177,237,187,244)(178,238,188,245)(179,239,189,246)(180,240,190,247)(251,322,262,311)(252,323,263,312)(253,324,264,313)(254,325,265,314)(255,326,266,315)(256,327,267,316)(257,328,268,317)(258,329,269,318)(259,330,270,319)(260,321,261,320)(271,342,282,331)(272,343,283,332)(273,344,284,333)(274,345,285,334)(275,346,286,335)(276,347,287,336)(277,348,288,337)(278,349,289,338)(279,350,290,339)(280,341,281,340)(291,362,302,351)(292,363,303,352)(293,364,304,353)(294,365,305,354)(295,366,306,355)(296,367,307,356)(297,368,308,357)(298,369,309,358)(299,370,310,359)(300,361,301,360)(371,431,382,442)(372,432,383,443)(373,433,384,444)(374,434,385,445)(375,435,386,446)(376,436,387,447)(377,437,388,448)(378,438,389,449)(379,439,390,450)(380,440,381,441)(391,451,402,462)(392,452,403,463)(393,453,404,464)(394,454,405,465)(395,455,406,466)(396,456,407,467)(397,457,408,468)(398,458,409,469)(399,459,410,470)(400,460,401,461), (1,148,28,138)(2,149,29,139)(3,150,30,140)(4,141,21,131)(5,142,22,132)(6,143,23,133)(7,144,24,134)(8,145,25,135)(9,146,26,136)(10,147,27,137)(11,362,471,351)(12,363,472,352)(13,364,473,353)(14,365,474,354)(15,366,475,355)(16,367,476,356)(17,368,477,357)(18,369,478,358)(19,370,479,359)(20,361,480,360)(31,161,41,151)(32,162,42,152)(33,163,43,153)(34,164,44,154)(35,165,45,155)(36,166,46,156)(37,167,47,157)(38,168,48,158)(39,169,49,159)(40,170,50,160)(51,181,61,171)(52,182,62,172)(53,183,63,173)(54,184,64,174)(55,185,65,175)(56,186,66,176)(57,187,67,177)(58,188,68,178)(59,189,69,179)(60,190,70,180)(71,201,81,191)(72,202,82,192)(73,203,83,193)(74,204,84,194)(75,205,85,195)(76,206,86,196)(77,207,87,197)(78,208,88,198)(79,209,89,199)(80,210,90,200)(91,221,101,211)(92,222,102,212)(93,223,103,213)(94,224,104,214)(95,225,105,215)(96,226,106,216)(97,227,107,217)(98,228,108,218)(99,229,109,219)(100,230,110,220)(111,248,121,231)(112,249,122,232)(113,250,123,233)(114,241,124,234)(115,242,125,235)(116,243,126,236)(117,244,127,237)(118,245,128,238)(119,246,129,239)(120,247,130,240)(251,382,262,371)(252,383,263,372)(253,384,264,373)(254,385,265,374)(255,386,266,375)(256,387,267,376)(257,388,268,377)(258,389,269,378)(259,390,270,379)(260,381,261,380)(271,402,282,391)(272,403,283,392)(273,404,284,393)(274,405,285,394)(275,406,286,395)(276,407,287,396)(277,408,288,397)(278,409,289,398)(279,410,290,399)(280,401,281,400)(291,422,302,411)(292,423,303,412)(293,424,304,413)(294,425,305,414)(295,426,306,415)(296,427,307,416)(297,428,308,417)(298,429,309,418)(299,430,310,419)(300,421,301,420)(311,442,322,431)(312,443,323,432)(313,444,324,433)(314,445,325,434)(315,446,326,435)(316,447,327,436)(317,448,328,437)(318,449,329,438)(319,450,330,439)(320,441,321,440)(331,462,342,451)(332,463,343,452)(333,464,344,453)(334,465,345,454)(335,466,346,455)(336,467,347,456)(337,468,348,457)(338,469,349,458)(339,470,350,459)(340,461,341,460), (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), (1,251,6,256)(2,260,7,255)(3,259,8,254)(4,258,9,253)(5,257,10,252)(11,250,16,245)(12,249,17,244)(13,248,18,243)(14,247,19,242)(15,246,20,241)(21,269,26,264)(22,268,27,263)(23,267,28,262)(24,266,29,261)(25,265,30,270)(31,278,36,273)(32,277,37,272)(33,276,38,271)(34,275,39,280)(35,274,40,279)(41,289,46,284)(42,288,47,283)(43,287,48,282)(44,286,49,281)(45,285,50,290)(51,298,56,293)(52,297,57,292)(53,296,58,291)(54,295,59,300)(55,294,60,299)(61,309,66,304)(62,308,67,303)(63,307,68,302)(64,306,69,301)(65,305,70,310)(71,318,76,313)(72,317,77,312)(73,316,78,311)(74,315,79,320)(75,314,80,319)(81,329,86,324)(82,328,87,323)(83,327,88,322)(84,326,89,321)(85,325,90,330)(91,338,96,333)(92,337,97,332)(93,336,98,331)(94,335,99,340)(95,334,100,339)(101,349,106,344)(102,348,107,343)(103,347,108,342)(104,346,109,341)(105,345,110,350)(111,358,116,353)(112,357,117,352)(113,356,118,351)(114,355,119,360)(115,354,120,359)(121,369,126,364)(122,368,127,363)(123,367,128,362)(124,366,129,361)(125,365,130,370)(131,378,136,373)(132,377,137,372)(133,376,138,371)(134,375,139,380)(135,374,140,379)(141,389,146,384)(142,388,147,383)(143,387,148,382)(144,386,149,381)(145,385,150,390)(151,398,156,393)(152,397,157,392)(153,396,158,391)(154,395,159,400)(155,394,160,399)(161,409,166,404)(162,408,167,403)(163,407,168,402)(164,406,169,401)(165,405,170,410)(171,418,176,413)(172,417,177,412)(173,416,178,411)(174,415,179,420)(175,414,180,419)(181,429,186,424)(182,428,187,423)(183,427,188,422)(184,426,189,421)(185,425,190,430)(191,438,196,433)(192,437,197,432)(193,436,198,431)(194,435,199,440)(195,434,200,439)(201,449,206,444)(202,448,207,443)(203,447,208,442)(204,446,209,441)(205,445,210,450)(211,458,216,453)(212,457,217,452)(213,456,218,451)(214,455,219,460)(215,454,220,459)(221,469,226,464)(222,468,227,463)(223,467,228,462)(224,466,229,461)(225,465,230,470)(231,478,236,473)(232,477,237,472)(233,476,238,471)(234,475,239,480)(235,474,240,479)>;
G:=Group( (1,58,38)(2,59,39)(3,60,40)(4,51,31)(5,52,32)(6,53,33)(7,54,34)(8,55,35)(9,56,36)(10,57,37)(11,462,442)(12,463,443)(13,464,444)(14,465,445)(15,466,446)(16,467,447)(17,468,448)(18,469,449)(19,470,450)(20,461,441)(21,61,41)(22,62,42)(23,63,43)(24,64,44)(25,65,45)(26,66,46)(27,67,47)(28,68,48)(29,69,49)(30,70,50)(71,111,91)(72,112,92)(73,113,93)(74,114,94)(75,115,95)(76,116,96)(77,117,97)(78,118,98)(79,119,99)(80,120,100)(81,121,101)(82,122,102)(83,123,103)(84,124,104)(85,125,105)(86,126,106)(87,127,107)(88,128,108)(89,129,109)(90,130,110)(131,171,151)(132,172,152)(133,173,153)(134,174,154)(135,175,155)(136,176,156)(137,177,157)(138,178,158)(139,179,159)(140,180,160)(141,181,161)(142,182,162)(143,183,163)(144,184,164)(145,185,165)(146,186,166)(147,187,167)(148,188,168)(149,189,169)(150,190,170)(191,231,211)(192,232,212)(193,233,213)(194,234,214)(195,235,215)(196,236,216)(197,237,217)(198,238,218)(199,239,219)(200,240,220)(201,248,221)(202,249,222)(203,250,223)(204,241,224)(205,242,225)(206,243,226)(207,244,227)(208,245,228)(209,246,229)(210,247,230)(251,291,271)(252,292,272)(253,293,273)(254,294,274)(255,295,275)(256,296,276)(257,297,277)(258,298,278)(259,299,279)(260,300,280)(261,301,281)(262,302,282)(263,303,283)(264,304,284)(265,305,285)(266,306,286)(267,307,287)(268,308,288)(269,309,289)(270,310,290)(311,351,331)(312,352,332)(313,353,333)(314,354,334)(315,355,335)(316,356,336)(317,357,337)(318,358,338)(319,359,339)(320,360,340)(321,361,341)(322,362,342)(323,363,343)(324,364,344)(325,365,345)(326,366,346)(327,367,347)(328,368,348)(329,369,349)(330,370,350)(371,411,391)(372,412,392)(373,413,393)(374,414,394)(375,415,395)(376,416,396)(377,417,397)(378,418,398)(379,419,399)(380,420,400)(381,421,401)(382,422,402)(383,423,403)(384,424,404)(385,425,405)(386,426,406)(387,427,407)(388,428,408)(389,429,409)(390,430,410)(431,471,451)(432,472,452)(433,473,453)(434,474,454)(435,475,455)(436,476,456)(437,477,457)(438,478,458)(439,479,459)(440,480,460), 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(1,251,6,256)(2,260,7,255)(3,259,8,254)(4,258,9,253)(5,257,10,252)(11,250,16,245)(12,249,17,244)(13,248,18,243)(14,247,19,242)(15,246,20,241)(21,269,26,264)(22,268,27,263)(23,267,28,262)(24,266,29,261)(25,265,30,270)(31,278,36,273)(32,277,37,272)(33,276,38,271)(34,275,39,280)(35,274,40,279)(41,289,46,284)(42,288,47,283)(43,287,48,282)(44,286,49,281)(45,285,50,290)(51,298,56,293)(52,297,57,292)(53,296,58,291)(54,295,59,300)(55,294,60,299)(61,309,66,304)(62,308,67,303)(63,307,68,302)(64,306,69,301)(65,305,70,310)(71,318,76,313)(72,317,77,312)(73,316,78,311)(74,315,79,320)(75,314,80,319)(81,329,86,324)(82,328,87,323)(83,327,88,322)(84,326,89,321)(85,325,90,330)(91,338,96,333)(92,337,97,332)(93,336,98,331)(94,335,99,340)(95,334,100,339)(101,349,106,344)(102,348,107,343)(103,347,108,342)(104,346,109,341)(105,345,110,350)(111,358,116,353)(112,357,117,352)(113,356,118,351)(114,355,119,360)(115,354,120,359)(121,369,126,364)(122,368,127,363)(123,367,128,362)(124,366,129,361)(125,365,130,370)(131,378,136,373)(132,377,137,372)(133,376,138,371)(134,375,139,380)(135,374,140,379)(141,389,146,384)(142,388,147,383)(143,387,148,382)(144,386,149,381)(145,385,150,390)(151,398,156,393)(152,397,157,392)(153,396,158,391)(154,395,159,400)(155,394,160,399)(161,409,166,404)(162,408,167,403)(163,407,168,402)(164,406,169,401)(165,405,170,410)(171,418,176,413)(172,417,177,412)(173,416,178,411)(174,415,179,420)(175,414,180,419)(181,429,186,424)(182,428,187,423)(183,427,188,422)(184,426,189,421)(185,425,190,430)(191,438,196,433)(192,437,197,432)(193,436,198,431)(194,435,199,440)(195,434,200,439)(201,449,206,444)(202,448,207,443)(203,447,208,442)(204,446,209,441)(205,445,210,450)(211,458,216,453)(212,457,217,452)(213,456,218,451)(214,455,219,460)(215,454,220,459)(221,469,226,464)(222,468,227,463)(223,467,228,462)(224,466,229,461)(225,465,230,470)(231,478,236,473)(232,477,237,472)(233,476,238,471)(234,475,239,480)(235,474,240,479) );
G=PermutationGroup([[(1,58,38),(2,59,39),(3,60,40),(4,51,31),(5,52,32),(6,53,33),(7,54,34),(8,55,35),(9,56,36),(10,57,37),(11,462,442),(12,463,443),(13,464,444),(14,465,445),(15,466,446),(16,467,447),(17,468,448),(18,469,449),(19,470,450),(20,461,441),(21,61,41),(22,62,42),(23,63,43),(24,64,44),(25,65,45),(26,66,46),(27,67,47),(28,68,48),(29,69,49),(30,70,50),(71,111,91),(72,112,92),(73,113,93),(74,114,94),(75,115,95),(76,116,96),(77,117,97),(78,118,98),(79,119,99),(80,120,100),(81,121,101),(82,122,102),(83,123,103),(84,124,104),(85,125,105),(86,126,106),(87,127,107),(88,128,108),(89,129,109),(90,130,110),(131,171,151),(132,172,152),(133,173,153),(134,174,154),(135,175,155),(136,176,156),(137,177,157),(138,178,158),(139,179,159),(140,180,160),(141,181,161),(142,182,162),(143,183,163),(144,184,164),(145,185,165),(146,186,166),(147,187,167),(148,188,168),(149,189,169),(150,190,170),(191,231,211),(192,232,212),(193,233,213),(194,234,214),(195,235,215),(196,236,216),(197,237,217),(198,238,218),(199,239,219),(200,240,220),(201,248,221),(202,249,222),(203,250,223),(204,241,224),(205,242,225),(206,243,226),(207,244,227),(208,245,228),(209,246,229),(210,247,230),(251,291,271),(252,292,272),(253,293,273),(254,294,274),(255,295,275),(256,296,276),(257,297,277),(258,298,278),(259,299,279),(260,300,280),(261,301,281),(262,302,282),(263,303,283),(264,304,284),(265,305,285),(266,306,286),(267,307,287),(268,308,288),(269,309,289),(270,310,290),(311,351,331),(312,352,332),(313,353,333),(314,354,334),(315,355,335),(316,356,336),(317,357,337),(318,358,338),(319,359,339),(320,360,340),(321,361,341),(322,362,342),(323,363,343),(324,364,344),(325,365,345),(326,366,346),(327,367,347),(328,368,348),(329,369,349),(330,370,350),(371,411,391),(372,412,392),(373,413,393),(374,414,394),(375,415,395),(376,416,396),(377,417,397),(378,418,398),(379,419,399),(380,420,400),(381,421,401),(382,422,402),(383,423,403),(384,424,404),(385,425,405),(386,426,406),(387,427,407),(388,428,408),(389,429,409),(390,430,410),(431,471,451),(432,472,452),(433,473,453),(434,474,454),(435,475,455),(436,476,456),(437,477,457),(438,478,458),(439,479,459),(440,480,460)], [(1,88,28,78),(2,89,29,79),(3,90,30,80),(4,81,21,71),(5,82,22,72),(6,83,23,73),(7,84,24,74),(8,85,25,75),(9,86,26,76),(10,87,27,77),(11,411,471,422),(12,412,472,423),(13,413,473,424),(14,414,474,425),(15,415,475,426),(16,416,476,427),(17,417,477,428),(18,418,478,429),(19,419,479,430),(20,420,480,421),(31,101,41,91),(32,102,42,92),(33,103,43,93),(34,104,44,94),(35,105,45,95),(36,106,46,96),(37,107,47,97),(38,108,48,98),(39,109,49,99),(40,110,50,100),(51,121,61,111),(52,122,62,112),(53,123,63,113),(54,124,64,114),(55,125,65,115),(56,126,66,116),(57,127,67,117),(58,128,68,118),(59,129,69,119),(60,130,70,120),(131,191,141,201),(132,192,142,202),(133,193,143,203),(134,194,144,204),(135,195,145,205),(136,196,146,206),(137,197,147,207),(138,198,148,208),(139,199,149,209),(140,200,150,210),(151,211,161,221),(152,212,162,222),(153,213,163,223),(154,214,164,224),(155,215,165,225),(156,216,166,226),(157,217,167,227),(158,218,168,228),(159,219,169,229),(160,220,170,230),(171,231,181,248),(172,232,182,249),(173,233,183,250),(174,234,184,241),(175,235,185,242),(176,236,186,243),(177,237,187,244),(178,238,188,245),(179,239,189,246),(180,240,190,247),(251,322,262,311),(252,323,263,312),(253,324,264,313),(254,325,265,314),(255,326,266,315),(256,327,267,316),(257,328,268,317),(258,329,269,318),(259,330,270,319),(260,321,261,320),(271,342,282,331),(272,343,283,332),(273,344,284,333),(274,345,285,334),(275,346,286,335),(276,347,287,336),(277,348,288,337),(278,349,289,338),(279,350,290,339),(280,341,281,340),(291,362,302,351),(292,363,303,352),(293,364,304,353),(294,365,305,354),(295,366,306,355),(296,367,307,356),(297,368,308,357),(298,369,309,358),(299,370,310,359),(300,361,301,360),(371,431,382,442),(372,432,383,443),(373,433,384,444),(374,434,385,445),(375,435,386,446),(376,436,387,447),(377,437,388,448),(378,438,389,449),(379,439,390,450),(380,440,381,441),(391,451,402,462),(392,452,403,463),(393,453,404,464),(394,454,405,465),(395,455,406,466),(396,456,407,467),(397,457,408,468),(398,458,409,469),(399,459,410,470),(400,460,401,461)], [(1,148,28,138),(2,149,29,139),(3,150,30,140),(4,141,21,131),(5,142,22,132),(6,143,23,133),(7,144,24,134),(8,145,25,135),(9,146,26,136),(10,147,27,137),(11,362,471,351),(12,363,472,352),(13,364,473,353),(14,365,474,354),(15,366,475,355),(16,367,476,356),(17,368,477,357),(18,369,478,358),(19,370,479,359),(20,361,480,360),(31,161,41,151),(32,162,42,152),(33,163,43,153),(34,164,44,154),(35,165,45,155),(36,166,46,156),(37,167,47,157),(38,168,48,158),(39,169,49,159),(40,170,50,160),(51,181,61,171),(52,182,62,172),(53,183,63,173),(54,184,64,174),(55,185,65,175),(56,186,66,176),(57,187,67,177),(58,188,68,178),(59,189,69,179),(60,190,70,180),(71,201,81,191),(72,202,82,192),(73,203,83,193),(74,204,84,194),(75,205,85,195),(76,206,86,196),(77,207,87,197),(78,208,88,198),(79,209,89,199),(80,210,90,200),(91,221,101,211),(92,222,102,212),(93,223,103,213),(94,224,104,214),(95,225,105,215),(96,226,106,216),(97,227,107,217),(98,228,108,218),(99,229,109,219),(100,230,110,220),(111,248,121,231),(112,249,122,232),(113,250,123,233),(114,241,124,234),(115,242,125,235),(116,243,126,236),(117,244,127,237),(118,245,128,238),(119,246,129,239),(120,247,130,240),(251,382,262,371),(252,383,263,372),(253,384,264,373),(254,385,265,374),(255,386,266,375),(256,387,267,376),(257,388,268,377),(258,389,269,378),(259,390,270,379),(260,381,261,380),(271,402,282,391),(272,403,283,392),(273,404,284,393),(274,405,285,394),(275,406,286,395),(276,407,287,396),(277,408,288,397),(278,409,289,398),(279,410,290,399),(280,401,281,400),(291,422,302,411),(292,423,303,412),(293,424,304,413),(294,425,305,414),(295,426,306,415),(296,427,307,416),(297,428,308,417),(298,429,309,418),(299,430,310,419),(300,421,301,420),(311,442,322,431),(312,443,323,432),(313,444,324,433),(314,445,325,434),(315,446,326,435),(316,447,327,436),(317,448,328,437),(318,449,329,438),(319,450,330,439),(320,441,321,440),(331,462,342,451),(332,463,343,452),(333,464,344,453),(334,465,345,454),(335,466,346,455),(336,467,347,456),(337,468,348,457),(338,469,349,458),(339,470,350,459),(340,461,341,460)], [(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)], [(1,251,6,256),(2,260,7,255),(3,259,8,254),(4,258,9,253),(5,257,10,252),(11,250,16,245),(12,249,17,244),(13,248,18,243),(14,247,19,242),(15,246,20,241),(21,269,26,264),(22,268,27,263),(23,267,28,262),(24,266,29,261),(25,265,30,270),(31,278,36,273),(32,277,37,272),(33,276,38,271),(34,275,39,280),(35,274,40,279),(41,289,46,284),(42,288,47,283),(43,287,48,282),(44,286,49,281),(45,285,50,290),(51,298,56,293),(52,297,57,292),(53,296,58,291),(54,295,59,300),(55,294,60,299),(61,309,66,304),(62,308,67,303),(63,307,68,302),(64,306,69,301),(65,305,70,310),(71,318,76,313),(72,317,77,312),(73,316,78,311),(74,315,79,320),(75,314,80,319),(81,329,86,324),(82,328,87,323),(83,327,88,322),(84,326,89,321),(85,325,90,330),(91,338,96,333),(92,337,97,332),(93,336,98,331),(94,335,99,340),(95,334,100,339),(101,349,106,344),(102,348,107,343),(103,347,108,342),(104,346,109,341),(105,345,110,350),(111,358,116,353),(112,357,117,352),(113,356,118,351),(114,355,119,360),(115,354,120,359),(121,369,126,364),(122,368,127,363),(123,367,128,362),(124,366,129,361),(125,365,130,370),(131,378,136,373),(132,377,137,372),(133,376,138,371),(134,375,139,380),(135,374,140,379),(141,389,146,384),(142,388,147,383),(143,387,148,382),(144,386,149,381),(145,385,150,390),(151,398,156,393),(152,397,157,392),(153,396,158,391),(154,395,159,400),(155,394,160,399),(161,409,166,404),(162,408,167,403),(163,407,168,402),(164,406,169,401),(165,405,170,410),(171,418,176,413),(172,417,177,412),(173,416,178,411),(174,415,179,420),(175,414,180,419),(181,429,186,424),(182,428,187,423),(183,427,188,422),(184,426,189,421),(185,425,190,430),(191,438,196,433),(192,437,197,432),(193,436,198,431),(194,435,199,440),(195,434,200,439),(201,449,206,444),(202,448,207,443),(203,447,208,442),(204,446,209,441),(205,445,210,450),(211,458,216,453),(212,457,217,452),(213,456,218,451),(214,455,219,460),(215,454,220,459),(221,469,226,464),(222,468,227,463),(223,467,228,462),(224,466,229,461),(225,465,230,470),(231,478,236,473),(232,477,237,472),(233,476,238,471),(234,475,239,480),(235,474,240,479)]])
120 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3A | 3B | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 4K | ··· | 4P | 5A | 5B | 6A | ··· | 6F | 10A | ··· | 10F | 12A | ··· | 12L | 12M | ··· | 12T | 12U | ··· | 12AF | 15A | 15B | 15C | 15D | 20A | ··· | 20L | 30A | ··· | 30L | 60A | ··· | 60X |
| order | 1 | 2 | 2 | 2 | 3 | 3 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 5 | 5 | 6 | ··· | 6 | 10 | ··· | 10 | 12 | ··· | 12 | 12 | ··· | 12 | 12 | ··· | 12 | 15 | 15 | 15 | 15 | 20 | ··· | 20 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 5 | 5 | 5 | 5 | 10 | ··· | 10 | 2 | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | ··· | 2 | 5 | ··· | 5 | 10 | ··· | 10 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
120 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | - | + | + | - | - | + | ||||||||||||||
| image | C1 | C2 | C2 | C2 | C3 | C4 | C6 | C6 | C6 | C12 | Q8 | D5 | C4○D4 | D10 | Dic5 | C3×Q8 | C3×D5 | C3×C4○D4 | C6×D5 | C3×Dic5 | Q8×D5 | Q8⋊2D5 | C3×Q8×D5 | C3×Q8⋊2D5 |
| kernel | C3×Q8×Dic5 | C12×Dic5 | C3×C4⋊Dic5 | Q8×C30 | Q8×Dic5 | Q8×C15 | C4×Dic5 | C4⋊Dic5 | Q8×C10 | C5×Q8 | C3×Dic5 | C6×Q8 | C30 | C2×C12 | C3×Q8 | Dic5 | C2×Q8 | C10 | C2×C4 | Q8 | C6 | C6 | C2 | C2 |
| # reps | 1 | 3 | 3 | 1 | 2 | 8 | 6 | 6 | 2 | 16 | 2 | 2 | 2 | 6 | 8 | 4 | 4 | 4 | 12 | 16 | 2 | 2 | 4 | 4 |
Matrix representation of C3×Q8×Dic5 ►in GL4(𝔽61) generated by
| 47 | 0 | 0 | 0 |
| 0 | 47 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 27 | 53 |
| 0 | 0 | 15 | 34 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 24 | 6 |
| 0 | 0 | 36 | 37 |
| 0 | 60 | 0 | 0 |
| 1 | 18 | 0 | 0 |
| 0 | 0 | 60 | 0 |
| 0 | 0 | 0 | 60 |
| 11 | 15 | 0 | 0 |
| 0 | 50 | 0 | 0 |
| 0 | 0 | 50 | 0 |
| 0 | 0 | 0 | 50 |
G:=sub<GL(4,GF(61))| [47,0,0,0,0,47,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,27,15,0,0,53,34],[1,0,0,0,0,1,0,0,0,0,24,36,0,0,6,37],[0,1,0,0,60,18,0,0,0,0,60,0,0,0,0,60],[11,0,0,0,15,50,0,0,0,0,50,0,0,0,0,50] >;
C3×Q8×Dic5 in GAP, Magma, Sage, TeX
C_3\times Q_8\times {\rm Dic}_5 % in TeX
G:=Group("C3xQ8xDic5"); // GroupNames label
G:=SmallGroup(480,738);
// by ID
G=gap.SmallGroup(480,738);
# by ID
G:=PCGroup([7,-2,-2,-2,-3,-2,-2,-5,168,344,555,268,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^3=b^4=d^10=1,c^2=b^2,e^2=d^5,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c^-1=b^-1,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations