metacyclic, supersoluble, monomial, 2-hyperelementary
Aliases: C60⋊1C8, C30.6M4(2), Dic5.12D12, Dic5.10Dic6, C12⋊1(C5⋊C8), C15⋊3(C4⋊C8), C20⋊1(C3⋊C8), C4⋊(C15⋊C8), (C2×C60).3C4, C5⋊1(C12⋊C8), C3⋊1(C20⋊C8), C6.5(C4⋊F5), (C2×C12).9F5, C30.37(C2×C8), C30.12(C4⋊C4), C6.4(C4.F5), (C2×C20).5Dic3, C2.1(C60⋊C4), C10.5(C4⋊Dic3), (C6×Dic5).18C4, (C4×Dic5).13S3, (C3×Dic5).11Q8, (C3×Dic5).59D4, C2.1(C12.F5), (C12×Dic5).15C2, (C2×Dic5).9Dic3, (C2×Dic5).201D6, C10.1(C4.Dic3), (C6×Dic5).260C22, C6.9(C2×C5⋊C8), C10.8(C2×C3⋊C8), (C2×C4).6(C3⋊F5), C2.4(C2×C15⋊C8), (C2×C6).34(C2×F5), (C2×C15⋊C8).5C2, (C2×C30).28(C2×C4), C22.10(C2×C3⋊F5), (C2×C10).4(C2×Dic3), SmallGroup(480,306)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C60⋊C8
G = < a,b | a60=b8=1, bab-1=a47 >
Subgroups: 284 in 76 conjugacy classes, 45 normal (35 characteristic)
C1, C2, C3, C4, C4, C22, C5, C6, C8, C2×C4, C2×C4, C10, C12, C12, C2×C6, C15, C42, C2×C8, Dic5, Dic5, C20, C2×C10, C3⋊C8, C2×C12, C2×C12, C30, C4⋊C8, C5⋊C8, C2×Dic5, C2×C20, C2×C3⋊C8, C4×C12, C3×Dic5, C3×Dic5, C60, C2×C30, C4×Dic5, C2×C5⋊C8, C12⋊C8, C15⋊C8, C6×Dic5, C2×C60, C20⋊C8, C12×Dic5, C2×C15⋊C8, C60⋊C8
Quotients: C1, C2, C4, C22, S3, C8, C2×C4, D4, Q8, Dic3, D6, C4⋊C4, C2×C8, M4(2), F5, C3⋊C8, Dic6, D12, C2×Dic3, C4⋊C8, C5⋊C8, C2×F5, C2×C3⋊C8, C4.Dic3, C4⋊Dic3, C3⋊F5, C4.F5, C4⋊F5, C2×C5⋊C8, C12⋊C8, C15⋊C8, C2×C3⋊F5, C20⋊C8, C12.F5, C60⋊C4, C2×C15⋊C8, C60⋊C8
►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)
(1 267 346 173 91 208 395 439)(2 290 335 160 92 231 384 426)(3 253 324 147 93 194 373 473)(4 276 313 134 94 217 362 460)(5 299 302 121 95 240 411 447)(6 262 351 168 96 203 400 434)(7 285 340 155 97 226 389 421)(8 248 329 142 98 189 378 468)(9 271 318 129 99 212 367 455)(10 294 307 176 100 235 416 442)(11 257 356 163 101 198 405 429)(12 280 345 150 102 221 394 476)(13 243 334 137 103 184 383 463)(14 266 323 124 104 207 372 450)(15 289 312 171 105 230 361 437)(16 252 301 158 106 193 410 424)(17 275 350 145 107 216 399 471)(18 298 339 132 108 239 388 458)(19 261 328 179 109 202 377 445)(20 284 317 166 110 225 366 432)(21 247 306 153 111 188 415 479)(22 270 355 140 112 211 404 466)(23 293 344 127 113 234 393 453)(24 256 333 174 114 197 382 440)(25 279 322 161 115 220 371 427)(26 242 311 148 116 183 420 474)(27 265 360 135 117 206 409 461)(28 288 349 122 118 229 398 448)(29 251 338 169 119 192 387 435)(30 274 327 156 120 215 376 422)(31 297 316 143 61 238 365 469)(32 260 305 130 62 201 414 456)(33 283 354 177 63 224 403 443)(34 246 343 164 64 187 392 430)(35 269 332 151 65 210 381 477)(36 292 321 138 66 233 370 464)(37 255 310 125 67 196 419 451)(38 278 359 172 68 219 408 438)(39 241 348 159 69 182 397 425)(40 264 337 146 70 205 386 472)(41 287 326 133 71 228 375 459)(42 250 315 180 72 191 364 446)(43 273 304 167 73 214 413 433)(44 296 353 154 74 237 402 480)(45 259 342 141 75 200 391 467)(46 282 331 128 76 223 380 454)(47 245 320 175 77 186 369 441)(48 268 309 162 78 209 418 428)(49 291 358 149 79 232 407 475)(50 254 347 136 80 195 396 462)(51 277 336 123 81 218 385 449)(52 300 325 170 82 181 374 436)(53 263 314 157 83 204 363 423)(54 286 303 144 84 227 412 470)(55 249 352 131 85 190 401 457)(56 272 341 178 86 213 390 444)(57 295 330 165 87 236 379 431)(58 258 319 152 88 199 368 478)(59 281 308 139 89 222 417 465)(60 244 357 126 90 185 406 452)
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), (1,267,346,173,91,208,395,439)(2,290,335,160,92,231,384,426)(3,253,324,147,93,194,373,473)(4,276,313,134,94,217,362,460)(5,299,302,121,95,240,411,447)(6,262,351,168,96,203,400,434)(7,285,340,155,97,226,389,421)(8,248,329,142,98,189,378,468)(9,271,318,129,99,212,367,455)(10,294,307,176,100,235,416,442)(11,257,356,163,101,198,405,429)(12,280,345,150,102,221,394,476)(13,243,334,137,103,184,383,463)(14,266,323,124,104,207,372,450)(15,289,312,171,105,230,361,437)(16,252,301,158,106,193,410,424)(17,275,350,145,107,216,399,471)(18,298,339,132,108,239,388,458)(19,261,328,179,109,202,377,445)(20,284,317,166,110,225,366,432)(21,247,306,153,111,188,415,479)(22,270,355,140,112,211,404,466)(23,293,344,127,113,234,393,453)(24,256,333,174,114,197,382,440)(25,279,322,161,115,220,371,427)(26,242,311,148,116,183,420,474)(27,265,360,135,117,206,409,461)(28,288,349,122,118,229,398,448)(29,251,338,169,119,192,387,435)(30,274,327,156,120,215,376,422)(31,297,316,143,61,238,365,469)(32,260,305,130,62,201,414,456)(33,283,354,177,63,224,403,443)(34,246,343,164,64,187,392,430)(35,269,332,151,65,210,381,477)(36,292,321,138,66,233,370,464)(37,255,310,125,67,196,419,451)(38,278,359,172,68,219,408,438)(39,241,348,159,69,182,397,425)(40,264,337,146,70,205,386,472)(41,287,326,133,71,228,375,459)(42,250,315,180,72,191,364,446)(43,273,304,167,73,214,413,433)(44,296,353,154,74,237,402,480)(45,259,342,141,75,200,391,467)(46,282,331,128,76,223,380,454)(47,245,320,175,77,186,369,441)(48,268,309,162,78,209,418,428)(49,291,358,149,79,232,407,475)(50,254,347,136,80,195,396,462)(51,277,336,123,81,218,385,449)(52,300,325,170,82,181,374,436)(53,263,314,157,83,204,363,423)(54,286,303,144,84,227,412,470)(55,249,352,131,85,190,401,457)(56,272,341,178,86,213,390,444)(57,295,330,165,87,236,379,431)(58,258,319,152,88,199,368,478)(59,281,308,139,89,222,417,465)(60,244,357,126,90,185,406,452)>;
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), (1,267,346,173,91,208,395,439)(2,290,335,160,92,231,384,426)(3,253,324,147,93,194,373,473)(4,276,313,134,94,217,362,460)(5,299,302,121,95,240,411,447)(6,262,351,168,96,203,400,434)(7,285,340,155,97,226,389,421)(8,248,329,142,98,189,378,468)(9,271,318,129,99,212,367,455)(10,294,307,176,100,235,416,442)(11,257,356,163,101,198,405,429)(12,280,345,150,102,221,394,476)(13,243,334,137,103,184,383,463)(14,266,323,124,104,207,372,450)(15,289,312,171,105,230,361,437)(16,252,301,158,106,193,410,424)(17,275,350,145,107,216,399,471)(18,298,339,132,108,239,388,458)(19,261,328,179,109,202,377,445)(20,284,317,166,110,225,366,432)(21,247,306,153,111,188,415,479)(22,270,355,140,112,211,404,466)(23,293,344,127,113,234,393,453)(24,256,333,174,114,197,382,440)(25,279,322,161,115,220,371,427)(26,242,311,148,116,183,420,474)(27,265,360,135,117,206,409,461)(28,288,349,122,118,229,398,448)(29,251,338,169,119,192,387,435)(30,274,327,156,120,215,376,422)(31,297,316,143,61,238,365,469)(32,260,305,130,62,201,414,456)(33,283,354,177,63,224,403,443)(34,246,343,164,64,187,392,430)(35,269,332,151,65,210,381,477)(36,292,321,138,66,233,370,464)(37,255,310,125,67,196,419,451)(38,278,359,172,68,219,408,438)(39,241,348,159,69,182,397,425)(40,264,337,146,70,205,386,472)(41,287,326,133,71,228,375,459)(42,250,315,180,72,191,364,446)(43,273,304,167,73,214,413,433)(44,296,353,154,74,237,402,480)(45,259,342,141,75,200,391,467)(46,282,331,128,76,223,380,454)(47,245,320,175,77,186,369,441)(48,268,309,162,78,209,418,428)(49,291,358,149,79,232,407,475)(50,254,347,136,80,195,396,462)(51,277,336,123,81,218,385,449)(52,300,325,170,82,181,374,436)(53,263,314,157,83,204,363,423)(54,286,303,144,84,227,412,470)(55,249,352,131,85,190,401,457)(56,272,341,178,86,213,390,444)(57,295,330,165,87,236,379,431)(58,258,319,152,88,199,368,478)(59,281,308,139,89,222,417,465)(60,244,357,126,90,185,406,452) );
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)], [(1,267,346,173,91,208,395,439),(2,290,335,160,92,231,384,426),(3,253,324,147,93,194,373,473),(4,276,313,134,94,217,362,460),(5,299,302,121,95,240,411,447),(6,262,351,168,96,203,400,434),(7,285,340,155,97,226,389,421),(8,248,329,142,98,189,378,468),(9,271,318,129,99,212,367,455),(10,294,307,176,100,235,416,442),(11,257,356,163,101,198,405,429),(12,280,345,150,102,221,394,476),(13,243,334,137,103,184,383,463),(14,266,323,124,104,207,372,450),(15,289,312,171,105,230,361,437),(16,252,301,158,106,193,410,424),(17,275,350,145,107,216,399,471),(18,298,339,132,108,239,388,458),(19,261,328,179,109,202,377,445),(20,284,317,166,110,225,366,432),(21,247,306,153,111,188,415,479),(22,270,355,140,112,211,404,466),(23,293,344,127,113,234,393,453),(24,256,333,174,114,197,382,440),(25,279,322,161,115,220,371,427),(26,242,311,148,116,183,420,474),(27,265,360,135,117,206,409,461),(28,288,349,122,118,229,398,448),(29,251,338,169,119,192,387,435),(30,274,327,156,120,215,376,422),(31,297,316,143,61,238,365,469),(32,260,305,130,62,201,414,456),(33,283,354,177,63,224,403,443),(34,246,343,164,64,187,392,430),(35,269,332,151,65,210,381,477),(36,292,321,138,66,233,370,464),(37,255,310,125,67,196,419,451),(38,278,359,172,68,219,408,438),(39,241,348,159,69,182,397,425),(40,264,337,146,70,205,386,472),(41,287,326,133,71,228,375,459),(42,250,315,180,72,191,364,446),(43,273,304,167,73,214,413,433),(44,296,353,154,74,237,402,480),(45,259,342,141,75,200,391,467),(46,282,331,128,76,223,380,454),(47,245,320,175,77,186,369,441),(48,268,309,162,78,209,418,428),(49,291,358,149,79,232,407,475),(50,254,347,136,80,195,396,462),(51,277,336,123,81,218,385,449),(52,300,325,170,82,181,374,436),(53,263,314,157,83,204,363,423),(54,286,303,144,84,227,412,470),(55,249,352,131,85,190,401,457),(56,272,341,178,86,213,390,444),(57,295,330,165,87,236,379,431),(58,258,319,152,88,199,368,478),(59,281,308,139,89,222,417,465),(60,244,357,126,90,185,406,452)]])
60 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 5 | 6A | 6B | 6C | 8A | ··· | 8H | 10A | 10B | 10C | 12A | 12B | 12C | 12D | 12E | ··· | 12L | 15A | 15B | 20A | 20B | 20C | 20D | 30A | ··· | 30F | 60A | ··· | 60H |
| order | 1 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 6 | 6 | 6 | 8 | ··· | 8 | 10 | 10 | 10 | 12 | 12 | 12 | 12 | 12 | ··· | 12 | 15 | 15 | 20 | 20 | 20 | 20 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 5 | 5 | 5 | 5 | 10 | 10 | 4 | 2 | 2 | 2 | 30 | ··· | 30 | 4 | 4 | 4 | 2 | 2 | 2 | 2 | 10 | ··· | 10 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | ··· | 4 |
60 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | - | - | + | - | - | + | + | - | + | |||||||||||||
| image | C1 | C2 | C2 | C4 | C4 | C8 | S3 | D4 | Q8 | Dic3 | D6 | Dic3 | M4(2) | Dic6 | D12 | C3⋊C8 | C4.Dic3 | F5 | C5⋊C8 | C2×F5 | C3⋊F5 | C4.F5 | C4⋊F5 | C15⋊C8 | C2×C3⋊F5 | C12.F5 | C60⋊C4 |
| kernel | C60⋊C8 | C12×Dic5 | C2×C15⋊C8 | C6×Dic5 | C2×C60 | C60 | C4×Dic5 | C3×Dic5 | C3×Dic5 | C2×Dic5 | C2×Dic5 | C2×C20 | C30 | Dic5 | Dic5 | C20 | C10 | C2×C12 | C12 | C2×C6 | C2×C4 | C6 | C6 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 2 | 2 | 2 | 8 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 4 | 4 | 1 | 2 | 1 | 2 | 2 | 2 | 4 | 2 | 4 | 4 |
Matrix representation of C60⋊C8 ►in GL6(𝔽241)
| 15 | 155 | 0 | 0 | 0 | 0 |
| 0 | 225 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 34 | 224 | 17 |
| 0 | 0 | 207 | 34 | 17 | 0 |
| 0 | 0 | 224 | 0 | 17 | 34 |
| 0 | 0 | 207 | 17 | 224 | 34 |
| 41 | 107 | 0 | 0 | 0 | 0 |
| 40 | 200 | 0 | 0 | 0 | 0 |
| 0 | 0 | 148 | 98 | 50 | 51 |
| 0 | 0 | 199 | 233 | 198 | 149 |
| 0 | 0 | 56 | 42 | 8 | 43 |
| 0 | 0 | 191 | 190 | 106 | 93 |
G:=sub<GL(6,GF(241))| [15,0,0,0,0,0,155,225,0,0,0,0,0,0,0,207,224,207,0,0,34,34,0,17,0,0,224,17,17,224,0,0,17,0,34,34],[41,40,0,0,0,0,107,200,0,0,0,0,0,0,148,199,56,191,0,0,98,233,42,190,0,0,50,198,8,106,0,0,51,149,43,93] >;
C60⋊C8 in GAP, Magma, Sage, TeX
C_{60}\rtimes C_8 % in TeX
G:=Group("C60:C8"); // GroupNames label
G:=SmallGroup(480,306);
// by ID
G=gap.SmallGroup(480,306);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,28,141,64,100,2693,14118,4724]);
// Polycyclic
G:=Group<a,b|a^60=b^8=1,b*a*b^-1=a^47>;
// generators/relations