direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C4×C15⋊Q8, C60⋊5Q8, C20⋊5Dic6, C12⋊5Dic10, C15⋊12(C4×Q8), C5⋊2(C4×Dic6), C3⋊1(C4×Dic10), C30.55(C2×Q8), (C2×C20).342D6, Dic3.8(C4×D5), C30.97(C4○D4), C6.43(C4○D20), (C2×C12).346D10, C30.66(C22×C4), (C4×Dic5).12S3, Dic5.16(C4×S3), (C12×Dic5).9C2, (C4×Dic3).10D5, (Dic3×C20).9C2, C10.23(C2×Dic6), C6.22(C2×Dic10), C10.46(C4○D12), (C2×C60).244C22, (C2×C30).157C23, (C4×Dic15).20C2, (C2×Dic5).186D6, Dic15.40(C2×C4), C30.Q8.17C2, C6.Dic10.17C2, Dic15⋊5C4.17C2, (C2×Dic3).159D10, C2.7(D6.D10), (C6×Dic5).213C22, (C10×Dic3).193C22, (C2×Dic15).218C22, C2.36(C4×S3×D5), C6.34(C2×C4×D5), C2.1(C2×C15⋊Q8), C10.67(S3×C2×C4), (C2×C15⋊Q8).11C2, C22.69(C2×S3×D5), (C2×C4).247(S3×D5), (C5×Dic3).36(C2×C4), (C3×Dic5).42(C2×C4), (C2×C6).169(C22×D5), (C2×C10).169(C22×S3), SmallGroup(480,543)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4×C15⋊Q8
G = < a,b,c,d | a4=b15=c4=1, d2=c2, ab=ba, ac=ca, ad=da, cbc-1=b11, dbd-1=b4, dcd-1=c-1 >
Subgroups: 556 in 140 conjugacy classes, 66 normal (44 characteristic)
C1, C2, C3, C4, C4, C22, C5, C6, C2×C4, C2×C4, Q8, C10, Dic3, Dic3, C12, C12, C2×C6, C15, C42, C4⋊C4, C2×Q8, Dic5, Dic5, C20, C20, C2×C10, Dic6, C2×Dic3, C2×Dic3, C2×C12, C2×C12, C30, C4×Q8, Dic10, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C4×Dic3, C4×Dic3, Dic3⋊C4, C4⋊Dic3, C4×C12, C2×Dic6, C5×Dic3, C5×Dic3, C3×Dic5, C3×Dic5, Dic15, Dic15, C60, C2×C30, C4×Dic5, C4×Dic5, C10.D4, C4⋊Dic5, C4×C20, C2×Dic10, C4×Dic6, C15⋊Q8, C6×Dic5, C10×Dic3, C2×Dic15, C2×C60, C4×Dic10, C30.Q8, Dic15⋊5C4, C6.Dic10, C12×Dic5, Dic3×C20, C4×Dic15, C2×C15⋊Q8, C4×C15⋊Q8
Quotients: C1, C2, C4, C22, S3, C2×C4, Q8, C23, D5, D6, C22×C4, C2×Q8, C4○D4, D10, Dic6, C4×S3, C22×S3, C4×Q8, Dic10, C4×D5, C22×D5, C2×Dic6, S3×C2×C4, C4○D12, S3×D5, C2×Dic10, C2×C4×D5, C4○D20, C4×Dic6, C15⋊Q8, C2×S3×D5, C4×Dic10, D6.D10, C4×S3×D5, C2×C15⋊Q8, C4×C15⋊Q8
►Regular action on 480 points
Generators in S480
(1 100 40 67)(2 101 41 68)(3 102 42 69)(4 103 43 70)(5 104 44 71)(6 105 45 72)(7 91 31 73)(8 92 32 74)(9 93 33 75)(10 94 34 61)(11 95 35 62)(12 96 36 63)(13 97 37 64)(14 98 38 65)(15 99 39 66)(16 120 55 78)(17 106 56 79)(18 107 57 80)(19 108 58 81)(20 109 59 82)(21 110 60 83)(22 111 46 84)(23 112 47 85)(24 113 48 86)(25 114 49 87)(26 115 50 88)(27 116 51 89)(28 117 52 90)(29 118 53 76)(30 119 54 77)(121 213 164 181)(122 214 165 182)(123 215 151 183)(124 216 152 184)(125 217 153 185)(126 218 154 186)(127 219 155 187)(128 220 156 188)(129 221 157 189)(130 222 158 190)(131 223 159 191)(132 224 160 192)(133 225 161 193)(134 211 162 194)(135 212 163 195)(136 235 173 205)(137 236 174 206)(138 237 175 207)(139 238 176 208)(140 239 177 209)(141 240 178 210)(142 226 179 196)(143 227 180 197)(144 228 166 198)(145 229 167 199)(146 230 168 200)(147 231 169 201)(148 232 170 202)(149 233 171 203)(150 234 172 204)(241 337 276 306)(242 338 277 307)(243 339 278 308)(244 340 279 309)(245 341 280 310)(246 342 281 311)(247 343 282 312)(248 344 283 313)(249 345 284 314)(250 331 285 315)(251 332 271 301)(252 333 272 302)(253 334 273 303)(254 335 274 304)(255 336 275 305)(256 358 288 317)(257 359 289 318)(258 360 290 319)(259 346 291 320)(260 347 292 321)(261 348 293 322)(262 349 294 323)(263 350 295 324)(264 351 296 325)(265 352 297 326)(266 353 298 327)(267 354 299 328)(268 355 300 329)(269 356 286 330)(270 357 287 316)(361 454 405 435)(362 455 391 421)(363 456 392 422)(364 457 393 423)(365 458 394 424)(366 459 395 425)(367 460 396 426)(368 461 397 427)(369 462 398 428)(370 463 399 429)(371 464 400 430)(372 465 401 431)(373 451 402 432)(374 452 403 433)(375 453 404 434)(376 473 406 440)(377 474 407 441)(378 475 408 442)(379 476 409 443)(380 477 410 444)(381 478 411 445)(382 479 412 446)(383 480 413 447)(384 466 414 448)(385 467 415 449)(386 468 416 450)(387 469 417 436)(388 470 418 437)(389 471 419 438)(390 472 420 439)
(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)
(1 136 29 132)(2 147 30 128)(3 143 16 124)(4 139 17 135)(5 150 18 131)(6 146 19 127)(7 142 20 123)(8 138 21 134)(9 149 22 130)(10 145 23 126)(11 141 24 122)(12 137 25 133)(13 148 26 129)(14 144 27 125)(15 140 28 121)(31 179 59 151)(32 175 60 162)(33 171 46 158)(34 167 47 154)(35 178 48 165)(36 174 49 161)(37 170 50 157)(38 166 51 153)(39 177 52 164)(40 173 53 160)(41 169 54 156)(42 180 55 152)(43 176 56 163)(44 172 57 159)(45 168 58 155)(61 199 85 186)(62 210 86 182)(63 206 87 193)(64 202 88 189)(65 198 89 185)(66 209 90 181)(67 205 76 192)(68 201 77 188)(69 197 78 184)(70 208 79 195)(71 204 80 191)(72 200 81 187)(73 196 82 183)(74 207 83 194)(75 203 84 190)(91 226 109 215)(92 237 110 211)(93 233 111 222)(94 229 112 218)(95 240 113 214)(96 236 114 225)(97 232 115 221)(98 228 116 217)(99 239 117 213)(100 235 118 224)(101 231 119 220)(102 227 120 216)(103 238 106 212)(104 234 107 223)(105 230 108 219)(241 368 262 390)(242 364 263 386)(243 375 264 382)(244 371 265 378)(245 367 266 389)(246 363 267 385)(247 374 268 381)(248 370 269 377)(249 366 270 388)(250 362 256 384)(251 373 257 380)(252 369 258 376)(253 365 259 387)(254 361 260 383)(255 372 261 379)(271 402 289 410)(272 398 290 406)(273 394 291 417)(274 405 292 413)(275 401 293 409)(276 397 294 420)(277 393 295 416)(278 404 296 412)(279 400 297 408)(280 396 298 419)(281 392 299 415)(282 403 300 411)(283 399 286 407)(284 395 287 418)(285 391 288 414)(301 432 318 444)(302 428 319 440)(303 424 320 436)(304 435 321 447)(305 431 322 443)(306 427 323 439)(307 423 324 450)(308 434 325 446)(309 430 326 442)(310 426 327 438)(311 422 328 449)(312 433 329 445)(313 429 330 441)(314 425 316 437)(315 421 317 448)(331 455 358 466)(332 451 359 477)(333 462 360 473)(334 458 346 469)(335 454 347 480)(336 465 348 476)(337 461 349 472)(338 457 350 468)(339 453 351 479)(340 464 352 475)(341 460 353 471)(342 456 354 467)(343 452 355 478)(344 463 356 474)(345 459 357 470)
(1 256 29 250)(2 260 30 254)(3 264 16 243)(4 268 17 247)(5 257 18 251)(6 261 19 255)(7 265 20 244)(8 269 21 248)(9 258 22 252)(10 262 23 241)(11 266 24 245)(12 270 25 249)(13 259 26 253)(14 263 27 242)(15 267 28 246)(31 297 59 279)(32 286 60 283)(33 290 46 272)(34 294 47 276)(35 298 48 280)(36 287 49 284)(37 291 50 273)(38 295 51 277)(39 299 52 281)(40 288 53 285)(41 292 54 274)(42 296 55 278)(43 300 56 282)(44 289 57 271)(45 293 58 275)(61 323 85 306)(62 327 86 310)(63 316 87 314)(64 320 88 303)(65 324 89 307)(66 328 90 311)(67 317 76 315)(68 321 77 304)(69 325 78 308)(70 329 79 312)(71 318 80 301)(72 322 81 305)(73 326 82 309)(74 330 83 313)(75 319 84 302)(91 352 109 340)(92 356 110 344)(93 360 111 333)(94 349 112 337)(95 353 113 341)(96 357 114 345)(97 346 115 334)(98 350 116 338)(99 354 117 342)(100 358 118 331)(101 347 119 335)(102 351 120 339)(103 355 106 343)(104 359 107 332)(105 348 108 336)(121 385 140 363)(122 389 141 367)(123 378 142 371)(124 382 143 375)(125 386 144 364)(126 390 145 368)(127 379 146 372)(128 383 147 361)(129 387 148 365)(130 376 149 369)(131 380 150 373)(132 384 136 362)(133 388 137 366)(134 377 138 370)(135 381 139 374)(151 408 179 400)(152 412 180 404)(153 416 166 393)(154 420 167 397)(155 409 168 401)(156 413 169 405)(157 417 170 394)(158 406 171 398)(159 410 172 402)(160 414 173 391)(161 418 174 395)(162 407 175 399)(163 411 176 403)(164 415 177 392)(165 419 178 396)(181 449 209 422)(182 438 210 426)(183 442 196 430)(184 446 197 434)(185 450 198 423)(186 439 199 427)(187 443 200 431)(188 447 201 435)(189 436 202 424)(190 440 203 428)(191 444 204 432)(192 448 205 421)(193 437 206 425)(194 441 207 429)(195 445 208 433)(211 474 237 463)(212 478 238 452)(213 467 239 456)(214 471 240 460)(215 475 226 464)(216 479 227 453)(217 468 228 457)(218 472 229 461)(219 476 230 465)(220 480 231 454)(221 469 232 458)(222 473 233 462)(223 477 234 451)(224 466 235 455)(225 470 236 459)
G:=sub<Sym(480)| (1,100,40,67)(2,101,41,68)(3,102,42,69)(4,103,43,70)(5,104,44,71)(6,105,45,72)(7,91,31,73)(8,92,32,74)(9,93,33,75)(10,94,34,61)(11,95,35,62)(12,96,36,63)(13,97,37,64)(14,98,38,65)(15,99,39,66)(16,120,55,78)(17,106,56,79)(18,107,57,80)(19,108,58,81)(20,109,59,82)(21,110,60,83)(22,111,46,84)(23,112,47,85)(24,113,48,86)(25,114,49,87)(26,115,50,88)(27,116,51,89)(28,117,52,90)(29,118,53,76)(30,119,54,77)(121,213,164,181)(122,214,165,182)(123,215,151,183)(124,216,152,184)(125,217,153,185)(126,218,154,186)(127,219,155,187)(128,220,156,188)(129,221,157,189)(130,222,158,190)(131,223,159,191)(132,224,160,192)(133,225,161,193)(134,211,162,194)(135,212,163,195)(136,235,173,205)(137,236,174,206)(138,237,175,207)(139,238,176,208)(140,239,177,209)(141,240,178,210)(142,226,179,196)(143,227,180,197)(144,228,166,198)(145,229,167,199)(146,230,168,200)(147,231,169,201)(148,232,170,202)(149,233,171,203)(150,234,172,204)(241,337,276,306)(242,338,277,307)(243,339,278,308)(244,340,279,309)(245,341,280,310)(246,342,281,311)(247,343,282,312)(248,344,283,313)(249,345,284,314)(250,331,285,315)(251,332,271,301)(252,333,272,302)(253,334,273,303)(254,335,274,304)(255,336,275,305)(256,358,288,317)(257,359,289,318)(258,360,290,319)(259,346,291,320)(260,347,292,321)(261,348,293,322)(262,349,294,323)(263,350,295,324)(264,351,296,325)(265,352,297,326)(266,353,298,327)(267,354,299,328)(268,355,300,329)(269,356,286,330)(270,357,287,316)(361,454,405,435)(362,455,391,421)(363,456,392,422)(364,457,393,423)(365,458,394,424)(366,459,395,425)(367,460,396,426)(368,461,397,427)(369,462,398,428)(370,463,399,429)(371,464,400,430)(372,465,401,431)(373,451,402,432)(374,452,403,433)(375,453,404,434)(376,473,406,440)(377,474,407,441)(378,475,408,442)(379,476,409,443)(380,477,410,444)(381,478,411,445)(382,479,412,446)(383,480,413,447)(384,466,414,448)(385,467,415,449)(386,468,416,450)(387,469,417,436)(388,470,418,437)(389,471,419,438)(390,472,420,439), (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), (1,136,29,132)(2,147,30,128)(3,143,16,124)(4,139,17,135)(5,150,18,131)(6,146,19,127)(7,142,20,123)(8,138,21,134)(9,149,22,130)(10,145,23,126)(11,141,24,122)(12,137,25,133)(13,148,26,129)(14,144,27,125)(15,140,28,121)(31,179,59,151)(32,175,60,162)(33,171,46,158)(34,167,47,154)(35,178,48,165)(36,174,49,161)(37,170,50,157)(38,166,51,153)(39,177,52,164)(40,173,53,160)(41,169,54,156)(42,180,55,152)(43,176,56,163)(44,172,57,159)(45,168,58,155)(61,199,85,186)(62,210,86,182)(63,206,87,193)(64,202,88,189)(65,198,89,185)(66,209,90,181)(67,205,76,192)(68,201,77,188)(69,197,78,184)(70,208,79,195)(71,204,80,191)(72,200,81,187)(73,196,82,183)(74,207,83,194)(75,203,84,190)(91,226,109,215)(92,237,110,211)(93,233,111,222)(94,229,112,218)(95,240,113,214)(96,236,114,225)(97,232,115,221)(98,228,116,217)(99,239,117,213)(100,235,118,224)(101,231,119,220)(102,227,120,216)(103,238,106,212)(104,234,107,223)(105,230,108,219)(241,368,262,390)(242,364,263,386)(243,375,264,382)(244,371,265,378)(245,367,266,389)(246,363,267,385)(247,374,268,381)(248,370,269,377)(249,366,270,388)(250,362,256,384)(251,373,257,380)(252,369,258,376)(253,365,259,387)(254,361,260,383)(255,372,261,379)(271,402,289,410)(272,398,290,406)(273,394,291,417)(274,405,292,413)(275,401,293,409)(276,397,294,420)(277,393,295,416)(278,404,296,412)(279,400,297,408)(280,396,298,419)(281,392,299,415)(282,403,300,411)(283,399,286,407)(284,395,287,418)(285,391,288,414)(301,432,318,444)(302,428,319,440)(303,424,320,436)(304,435,321,447)(305,431,322,443)(306,427,323,439)(307,423,324,450)(308,434,325,446)(309,430,326,442)(310,426,327,438)(311,422,328,449)(312,433,329,445)(313,429,330,441)(314,425,316,437)(315,421,317,448)(331,455,358,466)(332,451,359,477)(333,462,360,473)(334,458,346,469)(335,454,347,480)(336,465,348,476)(337,461,349,472)(338,457,350,468)(339,453,351,479)(340,464,352,475)(341,460,353,471)(342,456,354,467)(343,452,355,478)(344,463,356,474)(345,459,357,470), (1,256,29,250)(2,260,30,254)(3,264,16,243)(4,268,17,247)(5,257,18,251)(6,261,19,255)(7,265,20,244)(8,269,21,248)(9,258,22,252)(10,262,23,241)(11,266,24,245)(12,270,25,249)(13,259,26,253)(14,263,27,242)(15,267,28,246)(31,297,59,279)(32,286,60,283)(33,290,46,272)(34,294,47,276)(35,298,48,280)(36,287,49,284)(37,291,50,273)(38,295,51,277)(39,299,52,281)(40,288,53,285)(41,292,54,274)(42,296,55,278)(43,300,56,282)(44,289,57,271)(45,293,58,275)(61,323,85,306)(62,327,86,310)(63,316,87,314)(64,320,88,303)(65,324,89,307)(66,328,90,311)(67,317,76,315)(68,321,77,304)(69,325,78,308)(70,329,79,312)(71,318,80,301)(72,322,81,305)(73,326,82,309)(74,330,83,313)(75,319,84,302)(91,352,109,340)(92,356,110,344)(93,360,111,333)(94,349,112,337)(95,353,113,341)(96,357,114,345)(97,346,115,334)(98,350,116,338)(99,354,117,342)(100,358,118,331)(101,347,119,335)(102,351,120,339)(103,355,106,343)(104,359,107,332)(105,348,108,336)(121,385,140,363)(122,389,141,367)(123,378,142,371)(124,382,143,375)(125,386,144,364)(126,390,145,368)(127,379,146,372)(128,383,147,361)(129,387,148,365)(130,376,149,369)(131,380,150,373)(132,384,136,362)(133,388,137,366)(134,377,138,370)(135,381,139,374)(151,408,179,400)(152,412,180,404)(153,416,166,393)(154,420,167,397)(155,409,168,401)(156,413,169,405)(157,417,170,394)(158,406,171,398)(159,410,172,402)(160,414,173,391)(161,418,174,395)(162,407,175,399)(163,411,176,403)(164,415,177,392)(165,419,178,396)(181,449,209,422)(182,438,210,426)(183,442,196,430)(184,446,197,434)(185,450,198,423)(186,439,199,427)(187,443,200,431)(188,447,201,435)(189,436,202,424)(190,440,203,428)(191,444,204,432)(192,448,205,421)(193,437,206,425)(194,441,207,429)(195,445,208,433)(211,474,237,463)(212,478,238,452)(213,467,239,456)(214,471,240,460)(215,475,226,464)(216,479,227,453)(217,468,228,457)(218,472,229,461)(219,476,230,465)(220,480,231,454)(221,469,232,458)(222,473,233,462)(223,477,234,451)(224,466,235,455)(225,470,236,459)>;
G:=Group( (1,100,40,67)(2,101,41,68)(3,102,42,69)(4,103,43,70)(5,104,44,71)(6,105,45,72)(7,91,31,73)(8,92,32,74)(9,93,33,75)(10,94,34,61)(11,95,35,62)(12,96,36,63)(13,97,37,64)(14,98,38,65)(15,99,39,66)(16,120,55,78)(17,106,56,79)(18,107,57,80)(19,108,58,81)(20,109,59,82)(21,110,60,83)(22,111,46,84)(23,112,47,85)(24,113,48,86)(25,114,49,87)(26,115,50,88)(27,116,51,89)(28,117,52,90)(29,118,53,76)(30,119,54,77)(121,213,164,181)(122,214,165,182)(123,215,151,183)(124,216,152,184)(125,217,153,185)(126,218,154,186)(127,219,155,187)(128,220,156,188)(129,221,157,189)(130,222,158,190)(131,223,159,191)(132,224,160,192)(133,225,161,193)(134,211,162,194)(135,212,163,195)(136,235,173,205)(137,236,174,206)(138,237,175,207)(139,238,176,208)(140,239,177,209)(141,240,178,210)(142,226,179,196)(143,227,180,197)(144,228,166,198)(145,229,167,199)(146,230,168,200)(147,231,169,201)(148,232,170,202)(149,233,171,203)(150,234,172,204)(241,337,276,306)(242,338,277,307)(243,339,278,308)(244,340,279,309)(245,341,280,310)(246,342,281,311)(247,343,282,312)(248,344,283,313)(249,345,284,314)(250,331,285,315)(251,332,271,301)(252,333,272,302)(253,334,273,303)(254,335,274,304)(255,336,275,305)(256,358,288,317)(257,359,289,318)(258,360,290,319)(259,346,291,320)(260,347,292,321)(261,348,293,322)(262,349,294,323)(263,350,295,324)(264,351,296,325)(265,352,297,326)(266,353,298,327)(267,354,299,328)(268,355,300,329)(269,356,286,330)(270,357,287,316)(361,454,405,435)(362,455,391,421)(363,456,392,422)(364,457,393,423)(365,458,394,424)(366,459,395,425)(367,460,396,426)(368,461,397,427)(369,462,398,428)(370,463,399,429)(371,464,400,430)(372,465,401,431)(373,451,402,432)(374,452,403,433)(375,453,404,434)(376,473,406,440)(377,474,407,441)(378,475,408,442)(379,476,409,443)(380,477,410,444)(381,478,411,445)(382,479,412,446)(383,480,413,447)(384,466,414,448)(385,467,415,449)(386,468,416,450)(387,469,417,436)(388,470,418,437)(389,471,419,438)(390,472,420,439), (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), (1,136,29,132)(2,147,30,128)(3,143,16,124)(4,139,17,135)(5,150,18,131)(6,146,19,127)(7,142,20,123)(8,138,21,134)(9,149,22,130)(10,145,23,126)(11,141,24,122)(12,137,25,133)(13,148,26,129)(14,144,27,125)(15,140,28,121)(31,179,59,151)(32,175,60,162)(33,171,46,158)(34,167,47,154)(35,178,48,165)(36,174,49,161)(37,170,50,157)(38,166,51,153)(39,177,52,164)(40,173,53,160)(41,169,54,156)(42,180,55,152)(43,176,56,163)(44,172,57,159)(45,168,58,155)(61,199,85,186)(62,210,86,182)(63,206,87,193)(64,202,88,189)(65,198,89,185)(66,209,90,181)(67,205,76,192)(68,201,77,188)(69,197,78,184)(70,208,79,195)(71,204,80,191)(72,200,81,187)(73,196,82,183)(74,207,83,194)(75,203,84,190)(91,226,109,215)(92,237,110,211)(93,233,111,222)(94,229,112,218)(95,240,113,214)(96,236,114,225)(97,232,115,221)(98,228,116,217)(99,239,117,213)(100,235,118,224)(101,231,119,220)(102,227,120,216)(103,238,106,212)(104,234,107,223)(105,230,108,219)(241,368,262,390)(242,364,263,386)(243,375,264,382)(244,371,265,378)(245,367,266,389)(246,363,267,385)(247,374,268,381)(248,370,269,377)(249,366,270,388)(250,362,256,384)(251,373,257,380)(252,369,258,376)(253,365,259,387)(254,361,260,383)(255,372,261,379)(271,402,289,410)(272,398,290,406)(273,394,291,417)(274,405,292,413)(275,401,293,409)(276,397,294,420)(277,393,295,416)(278,404,296,412)(279,400,297,408)(280,396,298,419)(281,392,299,415)(282,403,300,411)(283,399,286,407)(284,395,287,418)(285,391,288,414)(301,432,318,444)(302,428,319,440)(303,424,320,436)(304,435,321,447)(305,431,322,443)(306,427,323,439)(307,423,324,450)(308,434,325,446)(309,430,326,442)(310,426,327,438)(311,422,328,449)(312,433,329,445)(313,429,330,441)(314,425,316,437)(315,421,317,448)(331,455,358,466)(332,451,359,477)(333,462,360,473)(334,458,346,469)(335,454,347,480)(336,465,348,476)(337,461,349,472)(338,457,350,468)(339,453,351,479)(340,464,352,475)(341,460,353,471)(342,456,354,467)(343,452,355,478)(344,463,356,474)(345,459,357,470), (1,256,29,250)(2,260,30,254)(3,264,16,243)(4,268,17,247)(5,257,18,251)(6,261,19,255)(7,265,20,244)(8,269,21,248)(9,258,22,252)(10,262,23,241)(11,266,24,245)(12,270,25,249)(13,259,26,253)(14,263,27,242)(15,267,28,246)(31,297,59,279)(32,286,60,283)(33,290,46,272)(34,294,47,276)(35,298,48,280)(36,287,49,284)(37,291,50,273)(38,295,51,277)(39,299,52,281)(40,288,53,285)(41,292,54,274)(42,296,55,278)(43,300,56,282)(44,289,57,271)(45,293,58,275)(61,323,85,306)(62,327,86,310)(63,316,87,314)(64,320,88,303)(65,324,89,307)(66,328,90,311)(67,317,76,315)(68,321,77,304)(69,325,78,308)(70,329,79,312)(71,318,80,301)(72,322,81,305)(73,326,82,309)(74,330,83,313)(75,319,84,302)(91,352,109,340)(92,356,110,344)(93,360,111,333)(94,349,112,337)(95,353,113,341)(96,357,114,345)(97,346,115,334)(98,350,116,338)(99,354,117,342)(100,358,118,331)(101,347,119,335)(102,351,120,339)(103,355,106,343)(104,359,107,332)(105,348,108,336)(121,385,140,363)(122,389,141,367)(123,378,142,371)(124,382,143,375)(125,386,144,364)(126,390,145,368)(127,379,146,372)(128,383,147,361)(129,387,148,365)(130,376,149,369)(131,380,150,373)(132,384,136,362)(133,388,137,366)(134,377,138,370)(135,381,139,374)(151,408,179,400)(152,412,180,404)(153,416,166,393)(154,420,167,397)(155,409,168,401)(156,413,169,405)(157,417,170,394)(158,406,171,398)(159,410,172,402)(160,414,173,391)(161,418,174,395)(162,407,175,399)(163,411,176,403)(164,415,177,392)(165,419,178,396)(181,449,209,422)(182,438,210,426)(183,442,196,430)(184,446,197,434)(185,450,198,423)(186,439,199,427)(187,443,200,431)(188,447,201,435)(189,436,202,424)(190,440,203,428)(191,444,204,432)(192,448,205,421)(193,437,206,425)(194,441,207,429)(195,445,208,433)(211,474,237,463)(212,478,238,452)(213,467,239,456)(214,471,240,460)(215,475,226,464)(216,479,227,453)(217,468,228,457)(218,472,229,461)(219,476,230,465)(220,480,231,454)(221,469,232,458)(222,473,233,462)(223,477,234,451)(224,466,235,455)(225,470,236,459) );
G=PermutationGroup([[(1,100,40,67),(2,101,41,68),(3,102,42,69),(4,103,43,70),(5,104,44,71),(6,105,45,72),(7,91,31,73),(8,92,32,74),(9,93,33,75),(10,94,34,61),(11,95,35,62),(12,96,36,63),(13,97,37,64),(14,98,38,65),(15,99,39,66),(16,120,55,78),(17,106,56,79),(18,107,57,80),(19,108,58,81),(20,109,59,82),(21,110,60,83),(22,111,46,84),(23,112,47,85),(24,113,48,86),(25,114,49,87),(26,115,50,88),(27,116,51,89),(28,117,52,90),(29,118,53,76),(30,119,54,77),(121,213,164,181),(122,214,165,182),(123,215,151,183),(124,216,152,184),(125,217,153,185),(126,218,154,186),(127,219,155,187),(128,220,156,188),(129,221,157,189),(130,222,158,190),(131,223,159,191),(132,224,160,192),(133,225,161,193),(134,211,162,194),(135,212,163,195),(136,235,173,205),(137,236,174,206),(138,237,175,207),(139,238,176,208),(140,239,177,209),(141,240,178,210),(142,226,179,196),(143,227,180,197),(144,228,166,198),(145,229,167,199),(146,230,168,200),(147,231,169,201),(148,232,170,202),(149,233,171,203),(150,234,172,204),(241,337,276,306),(242,338,277,307),(243,339,278,308),(244,340,279,309),(245,341,280,310),(246,342,281,311),(247,343,282,312),(248,344,283,313),(249,345,284,314),(250,331,285,315),(251,332,271,301),(252,333,272,302),(253,334,273,303),(254,335,274,304),(255,336,275,305),(256,358,288,317),(257,359,289,318),(258,360,290,319),(259,346,291,320),(260,347,292,321),(261,348,293,322),(262,349,294,323),(263,350,295,324),(264,351,296,325),(265,352,297,326),(266,353,298,327),(267,354,299,328),(268,355,300,329),(269,356,286,330),(270,357,287,316),(361,454,405,435),(362,455,391,421),(363,456,392,422),(364,457,393,423),(365,458,394,424),(366,459,395,425),(367,460,396,426),(368,461,397,427),(369,462,398,428),(370,463,399,429),(371,464,400,430),(372,465,401,431),(373,451,402,432),(374,452,403,433),(375,453,404,434),(376,473,406,440),(377,474,407,441),(378,475,408,442),(379,476,409,443),(380,477,410,444),(381,478,411,445),(382,479,412,446),(383,480,413,447),(384,466,414,448),(385,467,415,449),(386,468,416,450),(387,469,417,436),(388,470,418,437),(389,471,419,438),(390,472,420,439)], [(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)], [(1,136,29,132),(2,147,30,128),(3,143,16,124),(4,139,17,135),(5,150,18,131),(6,146,19,127),(7,142,20,123),(8,138,21,134),(9,149,22,130),(10,145,23,126),(11,141,24,122),(12,137,25,133),(13,148,26,129),(14,144,27,125),(15,140,28,121),(31,179,59,151),(32,175,60,162),(33,171,46,158),(34,167,47,154),(35,178,48,165),(36,174,49,161),(37,170,50,157),(38,166,51,153),(39,177,52,164),(40,173,53,160),(41,169,54,156),(42,180,55,152),(43,176,56,163),(44,172,57,159),(45,168,58,155),(61,199,85,186),(62,210,86,182),(63,206,87,193),(64,202,88,189),(65,198,89,185),(66,209,90,181),(67,205,76,192),(68,201,77,188),(69,197,78,184),(70,208,79,195),(71,204,80,191),(72,200,81,187),(73,196,82,183),(74,207,83,194),(75,203,84,190),(91,226,109,215),(92,237,110,211),(93,233,111,222),(94,229,112,218),(95,240,113,214),(96,236,114,225),(97,232,115,221),(98,228,116,217),(99,239,117,213),(100,235,118,224),(101,231,119,220),(102,227,120,216),(103,238,106,212),(104,234,107,223),(105,230,108,219),(241,368,262,390),(242,364,263,386),(243,375,264,382),(244,371,265,378),(245,367,266,389),(246,363,267,385),(247,374,268,381),(248,370,269,377),(249,366,270,388),(250,362,256,384),(251,373,257,380),(252,369,258,376),(253,365,259,387),(254,361,260,383),(255,372,261,379),(271,402,289,410),(272,398,290,406),(273,394,291,417),(274,405,292,413),(275,401,293,409),(276,397,294,420),(277,393,295,416),(278,404,296,412),(279,400,297,408),(280,396,298,419),(281,392,299,415),(282,403,300,411),(283,399,286,407),(284,395,287,418),(285,391,288,414),(301,432,318,444),(302,428,319,440),(303,424,320,436),(304,435,321,447),(305,431,322,443),(306,427,323,439),(307,423,324,450),(308,434,325,446),(309,430,326,442),(310,426,327,438),(311,422,328,449),(312,433,329,445),(313,429,330,441),(314,425,316,437),(315,421,317,448),(331,455,358,466),(332,451,359,477),(333,462,360,473),(334,458,346,469),(335,454,347,480),(336,465,348,476),(337,461,349,472),(338,457,350,468),(339,453,351,479),(340,464,352,475),(341,460,353,471),(342,456,354,467),(343,452,355,478),(344,463,356,474),(345,459,357,470)], [(1,256,29,250),(2,260,30,254),(3,264,16,243),(4,268,17,247),(5,257,18,251),(6,261,19,255),(7,265,20,244),(8,269,21,248),(9,258,22,252),(10,262,23,241),(11,266,24,245),(12,270,25,249),(13,259,26,253),(14,263,27,242),(15,267,28,246),(31,297,59,279),(32,286,60,283),(33,290,46,272),(34,294,47,276),(35,298,48,280),(36,287,49,284),(37,291,50,273),(38,295,51,277),(39,299,52,281),(40,288,53,285),(41,292,54,274),(42,296,55,278),(43,300,56,282),(44,289,57,271),(45,293,58,275),(61,323,85,306),(62,327,86,310),(63,316,87,314),(64,320,88,303),(65,324,89,307),(66,328,90,311),(67,317,76,315),(68,321,77,304),(69,325,78,308),(70,329,79,312),(71,318,80,301),(72,322,81,305),(73,326,82,309),(74,330,83,313),(75,319,84,302),(91,352,109,340),(92,356,110,344),(93,360,111,333),(94,349,112,337),(95,353,113,341),(96,357,114,345),(97,346,115,334),(98,350,116,338),(99,354,117,342),(100,358,118,331),(101,347,119,335),(102,351,120,339),(103,355,106,343),(104,359,107,332),(105,348,108,336),(121,385,140,363),(122,389,141,367),(123,378,142,371),(124,382,143,375),(125,386,144,364),(126,390,145,368),(127,379,146,372),(128,383,147,361),(129,387,148,365),(130,376,149,369),(131,380,150,373),(132,384,136,362),(133,388,137,366),(134,377,138,370),(135,381,139,374),(151,408,179,400),(152,412,180,404),(153,416,166,393),(154,420,167,397),(155,409,168,401),(156,413,169,405),(157,417,170,394),(158,406,171,398),(159,410,172,402),(160,414,173,391),(161,418,174,395),(162,407,175,399),(163,411,176,403),(164,415,177,392),(165,419,178,396),(181,449,209,422),(182,438,210,426),(183,442,196,430),(184,446,197,434),(185,450,198,423),(186,439,199,427),(187,443,200,431),(188,447,201,435),(189,436,202,424),(190,440,203,428),(191,444,204,432),(192,448,205,421),(193,437,206,425),(194,441,207,429),(195,445,208,433),(211,474,237,463),(212,478,238,452),(213,467,239,456),(214,471,240,460),(215,475,226,464),(216,479,227,453),(217,468,228,457),(218,472,229,461),(219,476,230,465),(220,480,231,454),(221,469,232,458),(222,473,233,462),(223,477,234,451),(224,466,235,455),(225,470,236,459)]])
84 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 5A | 5B | 6A | 6B | 6C | 10A | ··· | 10F | 12A | 12B | 12C | 12D | 12E | ··· | 12L | 15A | 15B | 20A | ··· | 20H | 20I | ··· | 20X | 30A | ··· | 30F | 60A | ··· | 60H |
| order | 1 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 10 | ··· | 10 | 12 | 12 | 12 | 12 | 12 | ··· | 12 | 15 | 15 | 20 | ··· | 20 | 20 | ··· | 20 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 6 | 6 | 6 | 6 | 10 | 10 | 10 | 10 | 30 | 30 | 30 | 30 | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 10 | ··· | 10 | 4 | 4 | 2 | ··· | 2 | 6 | ··· | 6 | 4 | ··· | 4 | 4 | ··· | 4 |
84 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | - | + | + | + | + | + | - | - | + | - | + | ||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | S3 | Q8 | D5 | D6 | D6 | C4○D4 | D10 | D10 | C4×S3 | Dic6 | C4×D5 | Dic10 | C4○D12 | C4○D20 | S3×D5 | C15⋊Q8 | C2×S3×D5 | D6.D10 | C4×S3×D5 |
| kernel | C4×C15⋊Q8 | C30.Q8 | Dic15⋊5C4 | C6.Dic10 | C12×Dic5 | Dic3×C20 | C4×Dic15 | C2×C15⋊Q8 | C15⋊Q8 | C4×Dic5 | C60 | C4×Dic3 | C2×Dic5 | C2×C20 | C30 | C2×Dic3 | C2×C12 | Dic5 | C20 | Dic3 | C12 | C10 | C6 | C2×C4 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 8 | 1 | 2 | 2 | 2 | 1 | 2 | 4 | 2 | 4 | 4 | 8 | 8 | 4 | 8 | 2 | 4 | 2 | 4 | 4 |
Matrix representation of C4×C15⋊Q8 ►in GL5(𝔽61)
| 50 | 0 | 0 | 0 | 0 |
| 0 | 11 | 0 | 0 | 0 |
| 0 | 0 | 11 | 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 | 18 |
| 0 | 0 | 0 | 44 | 17 |
| 60 | 0 | 0 | 0 | 0 |
| 0 | 21 | 59 | 0 | 0 |
| 0 | 38 | 40 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 38 | 15 | 0 | 0 |
| 0 | 46 | 23 | 0 | 0 |
| 0 | 0 | 0 | 14 | 52 |
| 0 | 0 | 0 | 42 | 47 |
G:=sub<GL(5,GF(61))| [50,0,0,0,0,0,11,0,0,0,0,0,11,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,60,1,0,0,0,60,0,0,0,0,0,0,0,44,0,0,0,18,17],[60,0,0,0,0,0,21,38,0,0,0,59,40,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,38,46,0,0,0,15,23,0,0,0,0,0,14,42,0,0,0,52,47] >;
C4×C15⋊Q8 in GAP, Magma, Sage, TeX
C_4\times C_{15}\rtimes Q_8 % in TeX
G:=Group("C4xC15:Q8"); // GroupNames label
G:=SmallGroup(480,543);
// by ID
G=gap.SmallGroup(480,543);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,112,253,120,58,1356,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^15=c^4=1,d^2=c^2,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^11,d*b*d^-1=b^4,d*c*d^-1=c^-1>;
// generators/relations