Groups of order 1584

Statistics at a glance
The number 1584 has prime factors 2, 3, and 11, with the following prime factorization:

$$\! 1584 = 2^4 \cdot 3^2 \cdot 11^1 = 16 \cdot 9 \cdot 11$$

GAP implementation
gap> SmallGroupsInformation(1584);

There are 697 groups of order 1584. They are sorted by their Frattini factors. 1 has Frattini factor [ 66, 1 ]. 2 has Frattini factor [ 66, 2 ]. 3 has Frattini factor [ 66, 3 ]. 4 has Frattini factor [ 66, 4 ]. 5 - 29 have Frattini factor [ 132, 5 ]. 30 has Frattini factor [ 132, 6 ]. 31 - 46 have Frattini factor [ 132, 7 ]. 47 - 62 have Frattini factor [ 132, 8 ]. 63 - 78 have Frattini factor [ 132, 9 ]. 79 - 86 have Frattini factor [ 132, 10 ]. 87 has Frattini factor [ 198, 5 ]. 88 has Frattini factor [ 198, 6 ]. 89 has Frattini factor [ 198, 7 ]. 90 has Frattini factor [ 198, 8 ]. 91 has Frattini factor [ 198, 9 ]. 92 has Frattini factor [ 198, 10 ]. 93 - 95 have Frattini factor [ 264, 31 ]. 96 - 98 have Frattini factor [ 264, 32 ]. 99 - 101 have Frattini factor [ 264, 33 ]. 102 - 128 have Frattini factor [ 264, 34 ]. 129 - 131 have Frattini factor [ 264, 35 ]. 132 - 141 have Frattini factor [ 264, 36 ]. 142 - 151 have Frattini factor [ 264, 37 ]. 152 - 161 have Frattini factor [ 264, 38 ]. 162 - 165 have Frattini factor [ 264, 39 ]. 166 has Frattini factor [ 396, 17 ]. 167 has Frattini factor [ 396, 18 ]. 168 - 192 have Frattini factor [ 396, 19 ]. 193 - 217 have Frattini factor [ 396, 20 ]. 218 - 233 have Frattini factor [ 396, 21 ]. 234 - 258 have Frattini factor [ 396, 22 ]. 259 - 274 have Frattini factor [ 396, 23 ]. 275 has Frattini factor [ 396, 24 ]. 276 - 291 have Frattini factor [ 396, 25 ]. 292 - 307 have Frattini factor [ 396, 26 ]. 308 - 323 have Frattini factor [ 396, 27 ]. 324 - 339 have Frattini factor [ 396, 28 ]. 340 - 355 have Frattini factor [ 396, 29 ]. 356 - 363 have Frattini factor [ 396, 30 ]. 364 has Frattini factor [ 528, 160 ]. 365 has Frattini factor [ 528, 161 ]. 366 has Frattini factor [ 528, 162 ]. 367 has Frattini factor [ 528, 163 ]. 368 has Frattini factor [ 528, 164 ]. 369 has Frattini factor [ 528, 165 ]. 370 has Frattini factor [ 528, 166 ]. 371 has Frattini factor [ 528, 167 ]. 372 has Frattini factor [ 528, 168 ]. 373 has Frattini factor [ 528, 169 ]. 374 has Frattini factor [ 528, 170 ]. 375 has Frattini factor [ 792, 108 ]. 376 has Frattini factor [ 792, 109 ]. 377 - 383 have Frattini factor [ 792, 110 ]. 384 - 388 have Frattini factor [ 792, 111 ]. 389 - 395 have Frattini factor [ 792, 112 ]. 396 - 400 have Frattini factor [ 792, 113 ]. 401 has Frattini factor [ 792, 114 ]. 402 - 403 have Frattini factor [ 792, 115 ]. 404 - 442 have Frattini factor [ 792, 116 ]. 443 - 445 have Frattini factor [ 792, 117 ]. 446 - 448 have Frattini factor [ 792, 118 ]. 449 - 451 have Frattini factor [ 792, 119 ]. 452 - 454 have Frattini factor [ 792, 120 ]. 455 - 457 have Frattini factor [ 792, 121 ]. 458 - 460 have Frattini factor [ 792, 122 ]. 461 - 463 have Frattini factor [ 792, 123 ]. 464 - 470 have Frattini factor [ 792, 124 ]. 471 - 477 have Frattini factor [ 792, 125 ]. 478 - 504 have Frattini factor [ 792, 126 ]. 505 - 531 have Frattini factor [ 792, 127 ]. 532 - 549 have Frattini factor [ 792, 128 ]. 550 - 576 have Frattini factor [ 792, 129 ]. 577 - 594 have Frattini factor [ 792, 130 ]. 595 - 597 have Frattini factor [ 792, 131 ]. 598 - 607 have Frattini factor [ 792, 132 ]. 608 - 617 have Frattini factor [ 792, 133 ]. 618 - 627 have Frattini factor [ 792, 134 ]. 628 - 637 have Frattini factor [ 792, 135 ]. 638 - 647 have Frattini factor [ 792, 136 ]. 648 - 651 have Frattini factor [ 792, 137 ]. 652 - 697 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.