Groups of order 1512

Statistics at a glance
The number 1512 has prime factors 2, 3, and 7. The prime factorization is as follows:

$$\! 1512 = 2^3 \cdot 3^3 \cdot 7^1 = 8 \cdot 27 \cdot 7$$

There are both solvable and non-solvable groups of this order.

For a non-solvable group, there are two possibilities for the collection of composition factors. One possibility is that the non-abelian composition factor is projective special linear group:PSL(3,2) (order 168), and there are two copies of cyclic group:Z3. The other is that the non-abelian composition factor is projective special linear group:PSL(2,8) (order 504), and there is one copy of cyclic group:Z3.

GAP implementation
gap> SmallGroupsInformation(1512);

There are 889 groups of order 1512. They are sorted by their Frattini factors. 1 has Frattini factor [ 42, 1 ]. 2 has Frattini factor [ 42, 2 ]. 3 has Frattini factor [ 42, 3 ]. 4 has Frattini factor [ 42, 4 ]. 5 has Frattini factor [ 42, 5 ]. 6 has Frattini factor [ 42, 6 ]. 7 - 11 have Frattini factor [ 84, 7 ]. 12 - 18 have Frattini factor [ 84, 8 ]. 19 - 21 have Frattini factor [ 84, 9 ]. 22 has Frattini factor [ 84, 10 ]. 23 has Frattini factor [ 84, 11 ]. 24 - 28 have Frattini factor [ 84, 12 ]. 29 - 33 have Frattini factor [ 84, 13 ]. 34 - 38 have Frattini factor [ 84, 14 ]. 39 - 41 have Frattini factor [ 84, 15 ]. 42 - 47 have Frattini factor [ 126, 7 ]. 48 - 52 have Frattini factor [ 126, 8 ]. 53 - 57 have Frattini factor [ 126, 9 ]. 58 - 63 have Frattini factor [ 126, 10 ]. 64 - 66 have Frattini factor [ 126, 11 ]. 67 - 70 have Frattini factor [ 126, 12 ]. 71 - 74 have Frattini factor [ 126, 13 ]. 75 - 76 have Frattini factor [ 126, 14 ]. 77 - 78 have Frattini factor [ 126, 15 ]. 79 - 81 have Frattini factor [ 126, 16 ]. 82 has Frattini factor [ 168, 43 ]. 83 has Frattini factor [ 168, 44 ]. 84 has Frattini factor [ 168, 45 ]. 85 has Frattini factor [ 168, 46 ]. 86 has Frattini factor [ 168, 47 ]. 87 has Frattini factor [ 168, 48 ]. 88 has Frattini factor [ 168, 49 ]. 89 has Frattini factor [ 168, 50 ]. 90 has Frattini factor [ 168, 51 ]. 91 has Frattini factor [ 168, 52 ]. 92 has Frattini factor [ 168, 53 ]. 93 has Frattini factor [ 168, 54 ]. 94 has Frattini factor [ 168, 55 ]. 95 has Frattini factor [ 168, 56 ]. 96 has Frattini factor [ 168, 57 ]. 97 - 131 have Frattini factor [ 252, 26 ]. 132 - 140 have Frattini factor [ 252, 27 ]. 141 - 170 have Frattini factor [ 252, 28 ]. 171 - 195 have Frattini factor [ 252, 29 ]. 196 - 220 have Frattini factor [ 252, 30 ]. 221 has Frattini factor [ 252, 31 ]. 222 has Frattini factor [ 252, 32 ]. 223 - 250 have Frattini factor [ 252, 33 ]. 251 - 264 have Frattini factor [ 252, 34 ]. 265 - 276 have Frattini factor [ 252, 35 ]. 277 - 297 have Frattini factor [ 252, 36 ]. 298 - 309 have Frattini factor [ 252, 37 ]. 310 - 327 have Frattini factor [ 252, 38 ]. 328 - 332 have Frattini factor [ 252, 39 ]. 333 - 338 have Frattini factor [ 252, 40 ]. 339 - 353 have Frattini factor [ 252, 41 ]. 354 - 373 have Frattini factor [ 252, 42 ]. 374 - 393 have Frattini factor [ 252, 43 ]. 394 - 403 have Frattini factor [ 252, 44 ]. 404 - 413 have Frattini factor [ 252, 45 ]. 414 - 422 have Frattini factor [ 252, 46 ]. 423 has Frattini factor [ 378, 47 ]. 424 has Frattini factor [ 378, 48 ]. 425 has Frattini factor [ 378, 49 ]. 426 has Frattini factor [ 378, 50 ]. 427 has Frattini factor [ 378, 51 ]. 428 has Frattini factor [ 378, 52 ]. 429 has Frattini factor [ 378, 53 ]. 430 has Frattini factor [ 378, 54 ]. 431 has Frattini factor [ 378, 55 ]. 432 has Frattini factor [ 378, 56 ]. 433 has Frattini factor [ 378, 57 ]. 434 has Frattini factor [ 378, 58 ]. 435 has Frattini factor [ 378, 59 ]. 436 has Frattini factor [ 378, 60 ]. 437 has Frattini factor [ 504, 157 ]. 438 - 443 have Frattini factor [ 504, 158 ]. 444 - 448 have Frattini factor [ 504, 159 ]. 449 - 453 have Frattini factor [ 504, 160 ]. 454 - 462 have Frattini factor [ 504, 161 ]. 463 - 467 have Frattini factor [ 504, 162 ]. 468 - 476 have Frattini factor [ 504, 163 ]. 477 has Frattini factor [ 504, 164 ]. 478 has Frattini factor [ 504, 165 ]. 479 has Frattini factor [ 504, 166 ]. 480 has Frattini factor [ 504, 167 ]. 481 has Frattini factor [ 504, 168 ]. 482 has Frattini factor [ 504, 169 ]. 483 has Frattini factor [ 504, 170 ]. 484 has Frattini factor [ 504, 171 ]. 485 - 486 have Frattini factor [ 504, 172 ]. 487 - 489 have Frattini factor [ 504, 173 ]. 490 - 493 have Frattini factor [ 504, 174 ]. 494 - 497 have Frattini factor [ 504, 175 ]. 498 - 500 have Frattini factor [ 504, 176 ]. 501 - 503 have Frattini factor [ 504, 177 ]. 504 - 509 have Frattini factor [ 504, 178 ]. 510 - 514 have Frattini factor [ 504, 179 ]. 515 - 519 have Frattini factor [ 504, 180 ]. 520 - 524 have Frattini factor [ 504, 181 ]. 525 - 530 have Frattini factor [ 504, 182 ]. 531 - 534 have Frattini factor [ 504, 183 ]. 535 - 538 have Frattini factor [ 504, 184 ]. 539 - 543 have Frattini factor [ 504, 185 ]. 544 - 548 have Frattini factor [ 504, 186 ]. 549 has Frattini factor [ 504, 187 ]. 550 has Frattini factor [ 504, 188 ]. 551 - 554 have Frattini factor [ 504, 189 ]. 555 - 556 have Frattini factor [ 504, 190 ]. 557 - 558 have Frattini factor [ 504, 191 ]. 559 - 561 have Frattini factor [ 504, 192 ]. 562 - 563 have Frattini factor [ 504, 193 ]. 564 - 569 have Frattini factor [ 504, 194 ]. 570 - 574 have Frattini factor [ 504, 195 ]. 575 - 580 have Frattini factor [ 504, 196 ]. 581 - 583 have Frattini factor [ 504, 197 ]. 584 - 587 have Frattini factor [ 504, 198 ]. 588 - 591 have Frattini factor [ 504, 199 ]. 592 - 593 have Frattini factor [ 504, 200 ]. 594 - 595 have Frattini factor [ 504, 201 ]. 596 - 598 have Frattini factor [ 504, 202 ]. 599 has Frattini factor [ 756, 150 ]. 600 has Frattini factor [ 756, 151 ]. 601 - 607 have Frattini factor [ 756, 152 ]. 608 - 614 have Frattini factor [ 756, 153 ]. 615 - 619 have Frattini factor [ 756, 154 ]. 620 - 626 have Frattini factor [ 756, 155 ]. 627 - 631 have Frattini factor [ 756, 156 ]. 632 has Frattini factor [ 756, 157 ]. 633 - 637 have Frattini factor [ 756, 158 ]. 638 - 642 have Frattini factor [ 756, 159 ]. 643 - 647 have Frattini factor [ 756, 160 ]. 648 - 652 have Frattini factor [ 756, 161 ]. 653 - 657 have Frattini factor [ 756, 162 ]. 658 has Frattini factor [ 756, 163 ]. 659 has Frattini factor [ 756, 164 ]. 660 has Frattini factor [ 756, 165 ]. 661 has Frattini factor [ 756, 166 ]. 662 - 668 have Frattini factor [ 756, 167 ]. 669 - 675 have Frattini factor [ 756, 168 ]. 676 - 680 have Frattini factor [ 756, 169 ]. 681 - 687 have Frattini factor [ 756, 170 ]. 688 - 692 have Frattini factor [ 756, 171 ]. 693 - 699 have Frattini factor [ 756, 172 ]. 700 - 706 have Frattini factor [ 756, 173 ]. 707 - 713 have Frattini factor [ 756, 174 ]. 714 - 720 have Frattini factor [ 756, 175 ]. 721 - 727 have Frattini factor [ 756, 176 ]. 728 - 730 have Frattini factor [ 756, 177 ]. 731 - 735 have Frattini factor [ 756, 178 ]. 736 - 738 have Frattini factor [ 756, 179 ]. 739 has Frattini factor [ 756, 180 ]. 740 has Frattini factor [ 756, 181 ]. 741 - 745 have Frattini factor [ 756, 182 ]. 746 - 750 have Frattini factor [ 756, 183 ]. 751 - 755 have Frattini factor [ 756, 184 ]. 756 - 760 have Frattini factor [ 756, 185 ]. 761 - 765 have Frattini factor [ 756, 186 ]. 766 - 770 have Frattini factor [ 756, 187 ]. 771 - 775 have Frattini factor [ 756, 188 ]. 776 - 778 have Frattini factor [ 756, 189 ]. 779 - 889 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.