Groups of order 1080

Statistics at a glance
The prime factorization of 1080 is:

$$\! 1080 = 2^3 \cdot 3^3 \cdot 5^1 = 8 \cdot 27 \cdot 5$$

GAP implementation
gap> SmallGroupsInformation(1080);

There are 583 groups of order 1080. They are sorted by their Frattini factors. 1 has Frattini factor [ 30, 1 ]. 2 has Frattini factor [ 30, 2 ]. 3 has Frattini factor [ 30, 3 ]. 4 has Frattini factor [ 30, 4 ]. 5 has Frattini factor [ 60, 6 ]. 6 has Frattini factor [ 60, 7 ]. 7 - 13 have Frattini factor [ 60, 8 ]. 14 has Frattini factor [ 60, 9 ]. 15 - 19 have Frattini factor [ 60, 10 ]. 20 - 24 have Frattini factor [ 60, 11 ]. 25 - 29 have Frattini factor [ 60, 12 ]. 30 - 32 have Frattini factor [ 60, 13 ]. 33 - 35 have Frattini factor [ 90, 5 ]. 36 - 39 have Frattini factor [ 90, 6 ]. 40 - 43 have Frattini factor [ 90, 7 ]. 44 - 45 have Frattini factor [ 90, 8 ]. 46 - 47 have Frattini factor [ 90, 9 ]. 48 - 50 have Frattini factor [ 90, 10 ]. 51 has Frattini factor [ 120, 36 ]. 52 has Frattini factor [ 120, 37 ]. 53 has Frattini factor [ 120, 38 ]. 54 has Frattini factor [ 120, 39 ]. 55 has Frattini factor [ 120, 40 ]. 56 has Frattini factor [ 120, 41 ]. 57 has Frattini factor [ 120, 42 ]. 58 has Frattini factor [ 120, 43 ]. 59 has Frattini factor [ 120, 44 ]. 60 has Frattini factor [ 120, 45 ]. 61 has Frattini factor [ 120, 46 ]. 62 has Frattini factor [ 120, 47 ]. 63 has Frattini factor [ 180, 19 ]. 64 - 66 have Frattini factor [ 180, 20 ]. 67 - 70 have Frattini factor [ 180, 21 ]. 71 - 72 have Frattini factor [ 180, 22 ]. 73 has Frattini factor [ 180, 23 ]. 74 has Frattini factor [ 180, 24 ]. 75 has Frattini factor [ 180, 25 ]. 76 - 103 have Frattini factor [ 180, 26 ]. 104 - 117 have Frattini factor [ 180, 27 ]. 118 - 129 have Frattini factor [ 180, 28 ]. 130 - 150 have Frattini factor [ 180, 29 ]. 151 - 162 have Frattini factor [ 180, 30 ]. 163 - 167 have Frattini factor [ 180, 31 ]. 168 - 182 have Frattini factor [ 180, 32 ]. 183 - 202 have Frattini factor [ 180, 33 ]. 203 - 222 have Frattini factor [ 180, 34 ]. 223 - 232 have Frattini factor [ 180, 35 ]. 233 - 242 have Frattini factor [ 180, 36 ]. 243 - 251 have Frattini factor [ 180, 37 ]. 252 has Frattini factor [ 270, 23 ]. 253 has Frattini factor [ 270, 24 ]. 254 has Frattini factor [ 270, 25 ]. 255 has Frattini factor [ 270, 26 ]. 256 has Frattini factor [ 270, 27 ]. 257 has Frattini factor [ 270, 28 ]. 258 has Frattini factor [ 270, 29 ]. 259 has Frattini factor [ 270, 30 ]. 260 has Frattini factor [ 360, 118 ]. 261 has Frattini factor [ 360, 119 ]. 262 has Frattini factor [ 360, 120 ]. 263 has Frattini factor [ 360, 121 ]. 264 has Frattini factor [ 360, 122 ]. 265 has Frattini factor [ 360, 123 ]. 266 has Frattini factor [ 360, 124 ]. 267 has Frattini factor [ 360, 125 ]. 268 - 271 have Frattini factor [ 360, 126 ]. 272 - 273 have Frattini factor [ 360, 127 ]. 274 - 276 have Frattini factor [ 360, 128 ]. 277 - 278 have Frattini factor [ 360, 129 ]. 279 has Frattini factor [ 360, 130 ]. 280 has Frattini factor [ 360, 131 ]. 281 has Frattini factor [ 360, 132 ]. 282 has Frattini factor [ 360, 133 ]. 283 has Frattini factor [ 360, 134 ]. 284 has Frattini factor [ 360, 135 ]. 285 has Frattini factor [ 360, 136 ]. 286 - 287 have Frattini factor [ 360, 137 ]. 288 - 291 have Frattini factor [ 360, 138 ]. 292 - 295 have Frattini factor [ 360, 139 ]. 296 - 298 have Frattini factor [ 360, 140 ]. 299 - 301 have Frattini factor [ 360, 141 ]. 302 - 306 have Frattini factor [ 360, 142 ]. 307 - 310 have Frattini factor [ 360, 143 ]. 311 - 314 have Frattini factor [ 360, 144 ]. 315 - 317 have Frattini factor [ 360, 145 ]. 318 - 321 have Frattini factor [ 360, 146 ]. 322 - 323 have Frattini factor [ 360, 147 ]. 324 has Frattini factor [ 360, 148 ]. 325 has Frattini factor [ 360, 149 ]. 326 has Frattini factor [ 360, 150 ]. 327 - 330 have Frattini factor [ 360, 151 ]. 331 - 332 have Frattini factor [ 360, 152 ]. 333 - 334 have Frattini factor [ 360, 153 ]. 335 - 337 have Frattini factor [ 360, 154 ]. 338 - 339 have Frattini factor [ 360, 155 ]. 340 - 344 have Frattini factor [ 360, 156 ]. 345 - 347 have Frattini factor [ 360, 157 ]. 348 - 351 have Frattini factor [ 360, 158 ]. 352 - 355 have Frattini factor [ 360, 159 ]. 356 - 357 have Frattini factor [ 360, 160 ]. 358 - 359 have Frattini factor [ 360, 161 ]. 360 - 362 have Frattini factor [ 360, 162 ]. 363 has Frattini factor [ 540, 88 ]. 364 has Frattini factor [ 540, 89 ]. 365 has Frattini factor [ 540, 90 ]. 366 has Frattini factor [ 540, 91 ]. 367 has Frattini factor [ 540, 92 ]. 368 has Frattini factor [ 540, 93 ]. 369 has Frattini factor [ 540, 94 ]. 370 has Frattini factor [ 540, 95 ]. 371 has Frattini factor [ 540, 96 ]. 372 has Frattini factor [ 540, 97 ]. 373 has Frattini factor [ 540, 98 ]. 374 - 380 have Frattini factor [ 540, 99 ]. 381 - 387 have Frattini factor [ 540, 100 ]. 388 - 392 have Frattini factor [ 540, 101 ]. 393 - 399 have Frattini factor [ 540, 102 ]. 400 - 404 have Frattini factor [ 540, 103 ]. 405 - 411 have Frattini factor [ 540, 104 ]. 412 - 418 have Frattini factor [ 540, 105 ]. 419 - 425 have Frattini factor [ 540, 106 ]. 426 - 432 have Frattini factor [ 540, 107 ]. 433 - 439 have Frattini factor [ 540, 108 ]. 440 - 442 have Frattini factor [ 540, 109 ]. 443 - 447 have Frattini factor [ 540, 110 ]. 448 has Frattini factor [ 540, 111 ]. 449 - 453 have Frattini factor [ 540, 112 ]. 454 - 458 have Frattini factor [ 540, 113 ]. 459 - 463 have Frattini factor [ 540, 114 ]. 464 - 468 have Frattini factor [ 540, 115 ]. 469 - 473 have Frattini factor [ 540, 116 ]. 474 - 478 have Frattini factor [ 540, 117 ]. 479 - 483 have Frattini factor [ 540, 118 ]. 484 - 486 have Frattini factor [ 540, 119 ]. 487 - 583 have trivial Frattini subgroup.

For the selection functions the values of the following attributes are precomputed and stored: IsAbelian, IsNilpotentGroup, IsSupersolvableGroup, IsSolvableGroup, LGLength, FrattinifactorSize and FrattinifactorId.

This size belongs to layer 5 of the SmallGroups library. IdSmallGroup is available for this size.