Groups of order 2000

Statistics at a glance
The number 2000 has prime factors 2 and 5. The prime factorization is as follows:

$$\! 2000 = 2^4 \cdot 5^3 = 16 \cdot 125$$

GAP implementation
gap> SmallGroupsInformation(2000);

There are 963 groups of order 2000. They are sorted by their Frattini factors. 1 has Frattini factor [ 10, 1 ]. 2 has Frattini factor [ 10, 2 ]. 3 has Frattini factor [ 20, 3 ]. 4 - 19 have Frattini factor [ 20, 4 ]. 20 - 27 have Frattini factor [ 20, 5 ]. 28 - 34 have Frattini factor [ 40, 12 ]. 35 - 44 have Frattini factor [ 40, 13 ]. 45 - 48 have Frattini factor [ 40, 14 ]. 49 - 52 have Frattini factor [ 50, 3 ]. 53 - 54 have Frattini factor [ 50, 4 ]. 55 - 57 have Frattini factor [ 50, 5 ]. 58 has Frattini factor [ 80, 49 ]. 59 has Frattini factor [ 80, 50 ]. 60 has Frattini factor [ 80, 51 ]. 61 has Frattini factor [ 80, 52 ]. 62 - 65 have Frattini factor [ 100, 9 ]. 66 - 68 have Frattini factor [ 100, 10 ]. 69 - 70 have Frattini factor [ 100, 11 ]. 71 - 72 have Frattini factor [ 100, 12 ]. 73 - 113 have Frattini factor [ 100, 13 ]. 114 - 177 have Frattini factor [ 100, 14 ]. 178 - 209 have Frattini factor [ 100, 15 ]. 210 - 233 have Frattini factor [ 100, 16 ]. 234 has Frattini factor [ 200, 40 ]. 235 - 255 have Frattini factor [ 200, 41 ]. 256 - 267 have Frattini factor [ 200, 42 ]. 268 - 272 have Frattini factor [ 200, 43 ]. 273 has Frattini factor [ 200, 44 ]. 274 - 301 have Frattini factor [ 200, 45 ]. 302 - 322 have Frattini factor [ 200, 46 ]. 323 - 336 have Frattini factor [ 200, 47 ]. 337 - 350 have Frattini factor [ 200, 48 ]. 351 - 395 have Frattini factor [ 200, 49 ]. 396 - 435 have Frattini factor [ 200, 50 ]. 436 - 455 have Frattini factor [ 200, 51 ]. 456 - 467 have Frattini factor [ 200, 52 ]. 468 has Frattini factor [ 250, 12 ]. 469 has Frattini factor [ 250, 13 ]. 470 has Frattini factor [ 250, 14 ]. 471 has Frattini factor [ 250, 15 ]. 472 - 473 have Frattini factor [ 400, 205 ]. 474 has Frattini factor [ 400, 206 ]. 475 has Frattini factor [ 400, 207 ]. 476 has Frattini factor [ 400, 208 ]. 477 - 479 have Frattini factor [ 400, 209 ]. 480 - 481 have Frattini factor [ 400, 210 ]. 482 has Frattini factor [ 400, 211 ]. 483 has Frattini factor [ 400, 212 ]. 484 - 488 have Frattini factor [ 400, 213 ]. 489 - 492 have Frattini factor [ 400, 214 ]. 493 - 495 have Frattini factor [ 400, 215 ]. 496 - 497 have Frattini factor [ 400, 216 ]. 498 - 499 have Frattini factor [ 400, 217 ]. 500 - 501 have Frattini factor [ 400, 218 ]. 502 - 505 have Frattini factor [ 400, 219 ]. 506 - 507 have Frattini factor [ 400, 220 ]. 508 - 510 have Frattini factor [ 400, 221 ]. 511 has Frattini factor [ 500, 41 ]. 512 has Frattini factor [ 500, 42 ]. 513 has Frattini factor [ 500, 43 ]. 514 has Frattini factor [ 500, 44 ]. 515 has Frattini factor [ 500, 45 ]. 516 has Frattini factor [ 500, 46 ]. 517 has Frattini factor [ 500, 47 ]. 518 has Frattini factor [ 500, 48 ]. 519 has Frattini factor [ 500, 49 ]. 520 - 535 have Frattini factor [ 500, 50 ]. 536 - 560 have Frattini factor [ 500, 51 ]. 561 - 568 have Frattini factor [ 500, 52 ]. 569 - 584 have Frattini factor [ 500, 53 ]. 585 - 600 have Frattini factor [ 500, 54 ]. 601 - 616 have Frattini factor [ 500, 55 ]. 617 - 624 have Frattini factor [ 500, 56 ]. 625 has Frattini factor [ 1000, 162 ]. 626 has Frattini factor [ 1000, 163 ]. 627 has Frattini factor [ 1000, 164 ]. 628 has Frattini factor [ 1000, 165 ]. 629 - 633 have Frattini factor [ 1000, 166 ]. 634 - 640 have Frattini factor [ 1000, 167 ]. 641 - 647 have Frattini factor [ 1000, 168 ]. 648 - 654 have Frattini factor [ 1000, 169 ]. 655 - 661 have Frattini factor [ 1000, 170 ]. 662 - 668 have Frattini factor [ 1000, 171 ]. 669 - 673 have Frattini factor [ 1000, 172 ]. 674 - 678 have Frattini factor [ 1000, 173 ]. 679 - 683 have Frattini factor [ 1000, 174 ]. 684 - 690 have Frattini factor [ 1000, 175 ]. 691 - 697 have Frattini factor [ 1000, 176 ]. 698 - 704 have Frattini factor [ 1000, 177 ]. 705 - 709 have Frattini factor [ 1000, 178 ]. 710 - 714 have Frattini factor [ 1000, 179 ]. 715 - 721 have Frattini factor [ 1000, 180 ]. 722 has Frattini factor [ 1000, 181 ]. 723 - 724 have Frattini factor [ 1000, 182 ]. 725 - 743 have Frattini factor [ 1000, 183 ]. 744 - 750 have Frattini factor [ 1000, 184 ]. 751 - 757 have Frattini factor [ 1000, 185 ]. 758 - 764 have Frattini factor [ 1000, 186 ]. 765 - 771 have Frattini factor [ 1000, 187 ]. 772 - 778 have Frattini factor [ 1000, 188 ]. 779 - 785 have Frattini factor [ 1000, 189 ]. 786 - 792 have Frattini factor [ 1000, 190 ]. 793 - 799 have Frattini factor [ 1000, 191 ]. 800 - 806 have Frattini factor [ 1000, 192 ]. 807 - 824 have Frattini factor [ 1000, 193 ]. 825 - 851 have Frattini factor [ 1000, 194 ]. 852 - 861 have Frattini factor [ 1000, 195 ]. 862 - 871 have Frattini factor [ 1000, 196 ]. 872 - 881 have Frattini factor [ 1000, 197 ]. 882 - 891 have Frattini factor [ 1000, 198 ]. 892 - 895 have Frattini factor [ 1000, 199 ]. 896 - 963 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.