Groups of order 648

Statistics at a glance
The number 648 has 2 and 3 as its only prime factors, and it has prime factorization:

$$\! 648 = 2^3 \cdot 3^4$$

Interesting groups

 * Special linear group:SL(2,Z9)
 * Projective general linear group:PGL(2,Z9)

GAP implementation
gap> SmallGroupsInformation(648);

There are 757 groups of order 648. 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 - 8 have Frattini factor [ 12, 4 ]. 9 - 11 have Frattini factor [ 12, 5 ]. 12 - 24 have Frattini factor [ 18, 3 ]. 25 - 31 have Frattini factor [ 18, 4 ]. 32 - 40 have Frattini factor [ 18, 5 ]. 41 has Frattini factor [ 24, 12 ]. 42 has Frattini factor [ 24, 13 ]. 43 has Frattini factor [ 24, 14 ]. 44 has Frattini factor [ 24, 15 ]. 45 has Frattini factor [ 36, 9 ]. 46 - 85 have Frattini factor [ 36, 10 ]. 86 - 104 have Frattini factor [ 36, 11 ]. 105 - 169 have Frattini factor [ 36, 12 ]. 170 - 204 have Frattini factor [ 36, 13 ]. 205 - 231 have Frattini factor [ 36, 14 ]. 232 - 237 have Frattini factor [ 54, 12 ]. 238 - 244 have Frattini factor [ 54, 13 ]. 245 - 246 have Frattini factor [ 54, 14 ]. 247 - 250 have Frattini factor [ 54, 15 ]. 251 has Frattini factor [ 72, 39 ]. 252 has Frattini factor [ 72, 40 ]. 253 has Frattini factor [ 72, 41 ]. 254 - 266 have Frattini factor [ 72, 42 ]. 267 - 281 have Frattini factor [ 72, 43 ]. 282 - 294 have Frattini factor [ 72, 44 ]. 295 has Frattini factor [ 72, 45 ]. 296 - 301 have Frattini factor [ 72, 46 ]. 302 - 320 have Frattini factor [ 72, 47 ]. 321 - 333 have Frattini factor [ 72, 48 ]. 334 - 340 have Frattini factor [ 72, 49 ]. 341 - 349 have Frattini factor [ 72, 50 ]. 350 - 352 have Frattini factor [ 108, 36 ]. 353 - 354 have Frattini factor [ 108, 37 ]. 355 - 385 have Frattini factor [ 108, 38 ]. 386 - 413 have Frattini factor [ 108, 39 ]. 414 - 428 have Frattini factor [ 108, 40 ]. 429 - 438 have Frattini factor [ 108, 41 ]. 439 - 468 have Frattini factor [ 108, 42 ]. 469 - 503 have Frattini factor [ 108, 43 ]. 504 - 513 have Frattini factor [ 108, 44 ]. 514 - 525 have Frattini factor [ 108, 45 ]. 526 has Frattini factor [ 162, 51 ]. 527 has Frattini factor [ 162, 52 ]. 528 has Frattini factor [ 162, 53 ]. 529 has Frattini factor [ 162, 54 ]. 530 has Frattini factor [ 162, 55 ]. 531 - 534 have Frattini factor [ 216, 153 ]. 535 - 536 have Frattini factor [ 216, 154 ]. 537 - 539 have Frattini factor [ 216, 155 ]. 540 - 541 have Frattini factor [ 216, 156 ]. 542 - 543 have Frattini factor [ 216, 157 ]. 544 - 545 have Frattini factor [ 216, 158 ]. 546 - 548 have Frattini factor [ 216, 159 ]. 549 - 551 have Frattini factor [ 216, 160 ]. 552 - 553 have Frattini factor [ 216, 161 ]. 554 - 555 have Frattini factor [ 216, 162 ]. 556 - 561 have Frattini factor [ 216, 163 ]. 562 - 573 have Frattini factor [ 216, 164 ]. 574 - 577 have Frattini factor [ 216, 165 ]. 578 - 587 have Frattini factor [ 216, 166 ]. 588 - 594 have Frattini factor [ 216, 167 ]. 595 - 597 have Frattini factor [ 216, 168 ]. 598 - 599 have Frattini factor [ 216, 169 ]. 600 - 604 have Frattini factor [ 216, 170 ]. 605 - 608 have Frattini factor [ 216, 171 ]. 609 - 611 have Frattini factor [ 216, 172 ]. 612 - 621 have Frattini factor [ 216, 173 ]. 622 - 627 have Frattini factor [ 216, 174 ]. 628 - 634 have Frattini factor [ 216, 175 ]. 635 - 636 have Frattini factor [ 216, 176 ]. 637 - 640 have Frattini factor [ 216, 177 ]. 641 has Frattini factor [ 324, 160 ]. 642 has Frattini factor [ 324, 161 ]. 643 has Frattini factor [ 324, 162 ]. 644 has Frattini factor [ 324, 163 ]. 645 has Frattini factor [ 324, 164 ]. 646 - 650 have Frattini factor [ 324, 165 ]. 651 - 657 have Frattini factor [ 324, 166 ]. 658 - 660 have Frattini factor [ 324, 167 ]. 661 - 667 have Frattini factor [ 324, 168 ]. 668 - 672 have Frattini factor [ 324, 169 ]. 673 - 677 have Frattini factor [ 324, 170 ]. 678 has Frattini factor [ 324, 171 ]. 679 - 683 have Frattini factor [ 324, 172 ]. 684 - 688 have Frattini factor [ 324, 173 ]. 689 - 693 have Frattini factor [ 324, 174 ]. 694 - 698 have Frattini factor [ 324, 175 ]. 699 - 701 have Frattini factor [ 324, 176 ]. 702 - 757 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.