metacyclic, supersoluble, monomial, 2-hyperelementary
Aliases: C60⋊5C8, C4.16D60, C60.25Q8, C20.34D12, C12.34D20, C60.165D4, C4.7Dic30, C42.2D15, C20.22Dic6, C12.22Dic10, C30.35M4(2), C4⋊(C15⋊3C8), C20⋊3(C3⋊C8), C15⋊10(C4⋊C8), (C4×C20).4S3, (C4×C60).4C2, (C4×C12).4D5, C3⋊2(C20⋊3C8), C12⋊1(C5⋊2C8), C5⋊4(C12⋊C8), (C2×C60).33C4, C30.59(C2×C8), (C2×C4).90D30, C30.35(C4⋊C4), (C2×C20).404D6, C6.6(C4⋊Dic5), (C2×C12).6Dic5, (C2×C4).3Dic15, C2.1(C60⋊5C4), (C2×C12).408D10, (C2×C20).17Dic3, C6.5(C4.Dic5), C2.2(C60.7C4), (C2×C60).490C22, C10.13(C4⋊Dic3), C22.8(C2×Dic15), C10.10(C4.Dic3), C10.16(C2×C3⋊C8), C6.7(C2×C5⋊2C8), C2.3(C2×C15⋊3C8), (C2×C15⋊3C8).8C2, (C2×C30).171(C2×C4), (C2×C6).27(C2×Dic5), (C2×C10).47(C2×Dic3), SmallGroup(480,164)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C60⋊5C8
G = < a,b | a60=b8=1, bab-1=a-1 >
Subgroups: 228 in 76 conjugacy classes, 55 normal (45 characteristic)
C1, C2, C3, C4, C4, C4, C22, C5, C6, C8, C2×C4, C10, C12, C12, C12, C2×C6, C15, C42, C2×C8, C20, C20, C20, C2×C10, C3⋊C8, C2×C12, C30, C4⋊C8, C5⋊2C8, C2×C20, C2×C3⋊C8, C4×C12, C60, C60, C60, C2×C30, C2×C5⋊2C8, C4×C20, C12⋊C8, C15⋊3C8, C2×C60, C20⋊3C8, C2×C15⋊3C8, C4×C60, C60⋊5C8
Quotients: C1, C2, C4, C22, S3, C8, C2×C4, D4, Q8, D5, Dic3, D6, C4⋊C4, C2×C8, M4(2), Dic5, D10, C3⋊C8, Dic6, D12, C2×Dic3, D15, C4⋊C8, C5⋊2C8, Dic10, D20, C2×Dic5, C2×C3⋊C8, C4.Dic3, C4⋊Dic3, Dic15, D30, C2×C5⋊2C8, C4.Dic5, C4⋊Dic5, C12⋊C8, C15⋊3C8, Dic30, D60, C2×Dic15, C20⋊3C8, C2×C15⋊3C8, C60.7C4, C60⋊5C4, C60⋊5C8
►Regular action on 480 points
Generators in S480
(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)
(1 390 131 219 256 354 114 444)(2 389 132 218 257 353 115 443)(3 388 133 217 258 352 116 442)(4 387 134 216 259 351 117 441)(5 386 135 215 260 350 118 440)(6 385 136 214 261 349 119 439)(7 384 137 213 262 348 120 438)(8 383 138 212 263 347 61 437)(9 382 139 211 264 346 62 436)(10 381 140 210 265 345 63 435)(11 380 141 209 266 344 64 434)(12 379 142 208 267 343 65 433)(13 378 143 207 268 342 66 432)(14 377 144 206 269 341 67 431)(15 376 145 205 270 340 68 430)(16 375 146 204 271 339 69 429)(17 374 147 203 272 338 70 428)(18 373 148 202 273 337 71 427)(19 372 149 201 274 336 72 426)(20 371 150 200 275 335 73 425)(21 370 151 199 276 334 74 424)(22 369 152 198 277 333 75 423)(23 368 153 197 278 332 76 422)(24 367 154 196 279 331 77 421)(25 366 155 195 280 330 78 480)(26 365 156 194 281 329 79 479)(27 364 157 193 282 328 80 478)(28 363 158 192 283 327 81 477)(29 362 159 191 284 326 82 476)(30 361 160 190 285 325 83 475)(31 420 161 189 286 324 84 474)(32 419 162 188 287 323 85 473)(33 418 163 187 288 322 86 472)(34 417 164 186 289 321 87 471)(35 416 165 185 290 320 88 470)(36 415 166 184 291 319 89 469)(37 414 167 183 292 318 90 468)(38 413 168 182 293 317 91 467)(39 412 169 181 294 316 92 466)(40 411 170 240 295 315 93 465)(41 410 171 239 296 314 94 464)(42 409 172 238 297 313 95 463)(43 408 173 237 298 312 96 462)(44 407 174 236 299 311 97 461)(45 406 175 235 300 310 98 460)(46 405 176 234 241 309 99 459)(47 404 177 233 242 308 100 458)(48 403 178 232 243 307 101 457)(49 402 179 231 244 306 102 456)(50 401 180 230 245 305 103 455)(51 400 121 229 246 304 104 454)(52 399 122 228 247 303 105 453)(53 398 123 227 248 302 106 452)(54 397 124 226 249 301 107 451)(55 396 125 225 250 360 108 450)(56 395 126 224 251 359 109 449)(57 394 127 223 252 358 110 448)(58 393 128 222 253 357 111 447)(59 392 129 221 254 356 112 446)(60 391 130 220 255 355 113 445)
G:=sub<Sym(480)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60)(61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180)(181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240)(241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300)(301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360)(361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420)(421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480), (1,390,131,219,256,354,114,444)(2,389,132,218,257,353,115,443)(3,388,133,217,258,352,116,442)(4,387,134,216,259,351,117,441)(5,386,135,215,260,350,118,440)(6,385,136,214,261,349,119,439)(7,384,137,213,262,348,120,438)(8,383,138,212,263,347,61,437)(9,382,139,211,264,346,62,436)(10,381,140,210,265,345,63,435)(11,380,141,209,266,344,64,434)(12,379,142,208,267,343,65,433)(13,378,143,207,268,342,66,432)(14,377,144,206,269,341,67,431)(15,376,145,205,270,340,68,430)(16,375,146,204,271,339,69,429)(17,374,147,203,272,338,70,428)(18,373,148,202,273,337,71,427)(19,372,149,201,274,336,72,426)(20,371,150,200,275,335,73,425)(21,370,151,199,276,334,74,424)(22,369,152,198,277,333,75,423)(23,368,153,197,278,332,76,422)(24,367,154,196,279,331,77,421)(25,366,155,195,280,330,78,480)(26,365,156,194,281,329,79,479)(27,364,157,193,282,328,80,478)(28,363,158,192,283,327,81,477)(29,362,159,191,284,326,82,476)(30,361,160,190,285,325,83,475)(31,420,161,189,286,324,84,474)(32,419,162,188,287,323,85,473)(33,418,163,187,288,322,86,472)(34,417,164,186,289,321,87,471)(35,416,165,185,290,320,88,470)(36,415,166,184,291,319,89,469)(37,414,167,183,292,318,90,468)(38,413,168,182,293,317,91,467)(39,412,169,181,294,316,92,466)(40,411,170,240,295,315,93,465)(41,410,171,239,296,314,94,464)(42,409,172,238,297,313,95,463)(43,408,173,237,298,312,96,462)(44,407,174,236,299,311,97,461)(45,406,175,235,300,310,98,460)(46,405,176,234,241,309,99,459)(47,404,177,233,242,308,100,458)(48,403,178,232,243,307,101,457)(49,402,179,231,244,306,102,456)(50,401,180,230,245,305,103,455)(51,400,121,229,246,304,104,454)(52,399,122,228,247,303,105,453)(53,398,123,227,248,302,106,452)(54,397,124,226,249,301,107,451)(55,396,125,225,250,360,108,450)(56,395,126,224,251,359,109,449)(57,394,127,223,252,358,110,448)(58,393,128,222,253,357,111,447)(59,392,129,221,254,356,112,446)(60,391,130,220,255,355,113,445)>;
G:=Group( (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), (1,390,131,219,256,354,114,444)(2,389,132,218,257,353,115,443)(3,388,133,217,258,352,116,442)(4,387,134,216,259,351,117,441)(5,386,135,215,260,350,118,440)(6,385,136,214,261,349,119,439)(7,384,137,213,262,348,120,438)(8,383,138,212,263,347,61,437)(9,382,139,211,264,346,62,436)(10,381,140,210,265,345,63,435)(11,380,141,209,266,344,64,434)(12,379,142,208,267,343,65,433)(13,378,143,207,268,342,66,432)(14,377,144,206,269,341,67,431)(15,376,145,205,270,340,68,430)(16,375,146,204,271,339,69,429)(17,374,147,203,272,338,70,428)(18,373,148,202,273,337,71,427)(19,372,149,201,274,336,72,426)(20,371,150,200,275,335,73,425)(21,370,151,199,276,334,74,424)(22,369,152,198,277,333,75,423)(23,368,153,197,278,332,76,422)(24,367,154,196,279,331,77,421)(25,366,155,195,280,330,78,480)(26,365,156,194,281,329,79,479)(27,364,157,193,282,328,80,478)(28,363,158,192,283,327,81,477)(29,362,159,191,284,326,82,476)(30,361,160,190,285,325,83,475)(31,420,161,189,286,324,84,474)(32,419,162,188,287,323,85,473)(33,418,163,187,288,322,86,472)(34,417,164,186,289,321,87,471)(35,416,165,185,290,320,88,470)(36,415,166,184,291,319,89,469)(37,414,167,183,292,318,90,468)(38,413,168,182,293,317,91,467)(39,412,169,181,294,316,92,466)(40,411,170,240,295,315,93,465)(41,410,171,239,296,314,94,464)(42,409,172,238,297,313,95,463)(43,408,173,237,298,312,96,462)(44,407,174,236,299,311,97,461)(45,406,175,235,300,310,98,460)(46,405,176,234,241,309,99,459)(47,404,177,233,242,308,100,458)(48,403,178,232,243,307,101,457)(49,402,179,231,244,306,102,456)(50,401,180,230,245,305,103,455)(51,400,121,229,246,304,104,454)(52,399,122,228,247,303,105,453)(53,398,123,227,248,302,106,452)(54,397,124,226,249,301,107,451)(55,396,125,225,250,360,108,450)(56,395,126,224,251,359,109,449)(57,394,127,223,252,358,110,448)(58,393,128,222,253,357,111,447)(59,392,129,221,254,356,112,446)(60,391,130,220,255,355,113,445) );
G=PermutationGroup([[(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)], [(1,390,131,219,256,354,114,444),(2,389,132,218,257,353,115,443),(3,388,133,217,258,352,116,442),(4,387,134,216,259,351,117,441),(5,386,135,215,260,350,118,440),(6,385,136,214,261,349,119,439),(7,384,137,213,262,348,120,438),(8,383,138,212,263,347,61,437),(9,382,139,211,264,346,62,436),(10,381,140,210,265,345,63,435),(11,380,141,209,266,344,64,434),(12,379,142,208,267,343,65,433),(13,378,143,207,268,342,66,432),(14,377,144,206,269,341,67,431),(15,376,145,205,270,340,68,430),(16,375,146,204,271,339,69,429),(17,374,147,203,272,338,70,428),(18,373,148,202,273,337,71,427),(19,372,149,201,274,336,72,426),(20,371,150,200,275,335,73,425),(21,370,151,199,276,334,74,424),(22,369,152,198,277,333,75,423),(23,368,153,197,278,332,76,422),(24,367,154,196,279,331,77,421),(25,366,155,195,280,330,78,480),(26,365,156,194,281,329,79,479),(27,364,157,193,282,328,80,478),(28,363,158,192,283,327,81,477),(29,362,159,191,284,326,82,476),(30,361,160,190,285,325,83,475),(31,420,161,189,286,324,84,474),(32,419,162,188,287,323,85,473),(33,418,163,187,288,322,86,472),(34,417,164,186,289,321,87,471),(35,416,165,185,290,320,88,470),(36,415,166,184,291,319,89,469),(37,414,167,183,292,318,90,468),(38,413,168,182,293,317,91,467),(39,412,169,181,294,316,92,466),(40,411,170,240,295,315,93,465),(41,410,171,239,296,314,94,464),(42,409,172,238,297,313,95,463),(43,408,173,237,298,312,96,462),(44,407,174,236,299,311,97,461),(45,406,175,235,300,310,98,460),(46,405,176,234,241,309,99,459),(47,404,177,233,242,308,100,458),(48,403,178,232,243,307,101,457),(49,402,179,231,244,306,102,456),(50,401,180,230,245,305,103,455),(51,400,121,229,246,304,104,454),(52,399,122,228,247,303,105,453),(53,398,123,227,248,302,106,452),(54,397,124,226,249,301,107,451),(55,396,125,225,250,360,108,450),(56,395,126,224,251,359,109,449),(57,394,127,223,252,358,110,448),(58,393,128,222,253,357,111,447),(59,392,129,221,254,356,112,446),(60,391,130,220,255,355,113,445)]])
132 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 5A | 5B | 6A | 6B | 6C | 8A | ··· | 8H | 10A | ··· | 10F | 12A | ··· | 12L | 15A | 15B | 15C | 15D | 20A | ··· | 20X | 30A | ··· | 30L | 60A | ··· | 60AV |
| order | 1 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 8 | ··· | 8 | 10 | ··· | 10 | 12 | ··· | 12 | 15 | 15 | 15 | 15 | 20 | ··· | 20 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 30 | ··· | 30 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
132 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | - | + | - | + | - | + | - | + | + | - | + | - | + | - | + | |||||||||
| image | C1 | C2 | C2 | C4 | C8 | S3 | D4 | Q8 | D5 | Dic3 | D6 | M4(2) | Dic5 | D10 | C3⋊C8 | Dic6 | D12 | D15 | C5⋊2C8 | Dic10 | D20 | C4.Dic3 | Dic15 | D30 | C4.Dic5 | C15⋊3C8 | Dic30 | D60 | C60.7C4 |
| kernel | C60⋊5C8 | C2×C15⋊3C8 | C4×C60 | C2×C60 | C60 | C4×C20 | C60 | C60 | C4×C12 | C2×C20 | C2×C20 | C30 | C2×C12 | C2×C12 | C20 | C20 | C20 | C42 | C12 | C12 | C12 | C10 | C2×C4 | C2×C4 | C6 | C4 | C4 | C4 | C2 |
| # reps | 1 | 2 | 1 | 4 | 8 | 1 | 1 | 1 | 2 | 2 | 1 | 2 | 4 | 2 | 4 | 2 | 2 | 4 | 8 | 4 | 4 | 4 | 8 | 4 | 8 | 16 | 8 | 8 | 16 |
Matrix representation of C60⋊5C8 ►in GL4(𝔽241) generated by
| 198 | 99 | 0 | 0 |
| 142 | 99 | 0 | 0 |
| 0 | 0 | 163 | 57 |
| 0 | 0 | 112 | 51 |
| 38 | 164 | 0 | 0 |
| 126 | 203 | 0 | 0 |
| 0 | 0 | 190 | 57 |
| 0 | 0 | 77 | 51 |
G:=sub<GL(4,GF(241))| [198,142,0,0,99,99,0,0,0,0,163,112,0,0,57,51],[38,126,0,0,164,203,0,0,0,0,190,77,0,0,57,51] >;
C60⋊5C8 in GAP, Magma, Sage, TeX
C_{60}\rtimes_5C_8 % in TeX
G:=Group("C60:5C8"); // GroupNames label
G:=SmallGroup(480,164);
// by ID
G=gap.SmallGroup(480,164);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,28,141,64,100,2693,18822]);
// Polycyclic
G:=Group<a,b|a^60=b^8=1,b*a*b^-1=a^-1>;
// generators/relations