Groups of order 432

Statistics at a glance
The number 432 has prime factorization:

$$\! 432 = 2^4 \cdot 3^3 = 16 \cdot 27$$

GAP implementation
gap> SmallGroupsInformation(432);

There are 775 groups of order 432. They are sorted by their Frattini factors. 1 has Frattini factor [ 6, 1 ]. 2 has Frattini factor [ 6, 2 ]. 3 has Frattini factor [ 12, 3 ]. 4 - 19 have Frattini factor [ 12, 4 ]. 20 - 27 have Frattini factor [ 12, 5 ]. 28 - 31 have Frattini factor [ 18, 3 ]. 32 - 33 have Frattini factor [ 18, 4 ]. 34 - 36 have Frattini factor [ 18, 5 ]. 37 - 39 have Frattini factor [ 24, 12 ]. 40 - 42 have Frattini factor [ 24, 13 ]. 43 - 52 have Frattini factor [ 24, 14 ]. 53 - 56 have Frattini factor [ 24, 15 ]. 57 has Frattini factor [ 36, 9 ]. 58 - 98 have Frattini factor [ 36, 10 ]. 99 - 103 have Frattini factor [ 36, 11 ]. 104 - 167 have Frattini factor [ 36, 12 ]. 168 - 199 have Frattini factor [ 36, 13 ]. 200 - 223 have Frattini factor [ 36, 14 ]. 224 has Frattini factor [ 48, 48 ]. 225 has Frattini factor [ 48, 49 ]. 226 has Frattini factor [ 48, 50 ]. 227 has Frattini factor [ 48, 51 ]. 228 has Frattini factor [ 48, 52 ]. 229 has Frattini factor [ 54, 12 ]. 230 has Frattini factor [ 54, 13 ]. 231 has Frattini factor [ 54, 14 ]. 232 has Frattini factor [ 54, 15 ]. 233 has Frattini factor [ 72, 39 ]. 234 - 238 have Frattini factor [ 72, 40 ]. 239 has Frattini factor [ 72, 41 ]. 240 - 251 have Frattini factor [ 72, 42 ]. 252 - 260 have Frattini factor [ 72, 43 ]. 261 - 272 have Frattini factor [ 72, 44 ]. 273 - 279 have Frattini factor [ 72, 45 ]. 280 - 324 have Frattini factor [ 72, 46 ]. 325 - 339 have Frattini factor [ 72, 47 ]. 340 - 379 have Frattini factor [ 72, 48 ]. 380 - 399 have Frattini factor [ 72, 49 ]. 400 - 411 have Frattini factor [ 72, 50 ]. 412 has Frattini factor [ 108, 36 ]. 413 has Frattini factor [ 108, 37 ]. 414 - 429 have Frattini factor [ 108, 38 ]. 430 - 454 have Frattini factor [ 108, 39 ]. 455 - 462 have Frattini factor [ 108, 40 ]. 463 has Frattini factor [ 108, 41 ]. 464 - 479 have Frattini factor [ 108, 42 ]. 480 - 495 have Frattini factor [ 108, 43 ]. 496 - 511 have Frattini factor [ 108, 44 ]. 512 - 519 have Frattini factor [ 108, 45 ]. 520 has Frattini factor [ 144, 182 ]. 521 - 523 have Frattini factor [ 144, 183 ]. 524 - 528 have Frattini factor [ 144, 184 ]. 529 has Frattini factor [ 144, 185 ]. 530 has Frattini factor [ 144, 186 ]. 531 has Frattini factor [ 144, 187 ]. 532 - 535 have Frattini factor [ 144, 188 ]. 536 - 538 have Frattini factor [ 144, 189 ]. 539 - 542 have Frattini factor [ 144, 190 ]. 543 has Frattini factor [ 144, 191 ]. 544 - 545 have Frattini factor [ 144, 192 ]. 546 - 550 have Frattini factor [ 144, 193 ]. 551 - 555 have Frattini factor [ 144, 194 ]. 556 - 559 have Frattini factor [ 144, 195 ]. 560 - 561 have Frattini factor [ 144, 196 ]. 562 - 564 have Frattini factor [ 144, 197 ]. 565 has Frattini factor [ 216, 154 ]. 566 has Frattini factor [ 216, 155 ]. 567 - 573 have Frattini factor [ 216, 156 ]. 574 - 578 have Frattini factor [ 216, 157 ]. 579 - 585 have Frattini factor [ 216, 158 ]. 586 - 590 have Frattini factor [ 216, 159 ]. 591 has Frattini factor [ 216, 160 ]. 592 - 593 have Frattini factor [ 216, 161 ]. 594 - 612 have Frattini factor [ 216, 162 ]. 613 - 615 have Frattini factor [ 216, 163 ]. 616 - 618 have Frattini factor [ 216, 164 ]. 619 - 621 have Frattini factor [ 216, 165 ]. 622 - 624 have Frattini factor [ 216, 166 ]. 625 - 627 have Frattini factor [ 216, 167 ]. 628 - 634 have Frattini factor [ 216, 168 ]. 635 - 641 have Frattini factor [ 216, 169 ]. 642 - 659 have Frattini factor [ 216, 170 ]. 660 - 686 have Frattini factor [ 216, 171 ]. 687 - 696 have Frattini factor [ 216, 172 ]. 697 - 699 have Frattini factor [ 216, 173 ]. 700 - 709 have Frattini factor [ 216, 174 ]. 710 - 719 have Frattini factor [ 216, 175 ]. 720 - 729 have Frattini factor [ 216, 176 ]. 730 - 733 have Frattini factor [ 216, 177 ]. 734 - 775 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 2 of the SmallGroups library. IdSmallGroup is available for this size.