Groups of order 1944
This article gives information about, and links to more details on, groups of order 1944
See pages on algebraic structures of order 1944 | See pages on groups of a particular order
Statistics at a glance
The number 1944 has 2 and 3 as its only prime factors. It has prime factorization:
There are only two prime factors of this number. Order has only two prime factors implies solvable (by Burnside's -theorem) and hence all groups of this order are solvable groups (specifically, finite solvable groups). Another way of putting this is that the order is a solvability-forcing number. In particular, there is no simple non-abelian group of this order.
GAP implementation
The order 1944 is part of GAP's SmallGroup library. Hence, any group of order 1944 can be constructed using the SmallGroup function by specifying its group ID. Also, IdGroup is available, so the group ID of any group of this order can be queried.
Further, the collection of all groups of order 1944 can be accessed as a list using GAP's AllSmallGroups function.
Here is GAP's summary information about how it stores groups of this order, accessed using GAP's SmallGroupsInformation function:
gap> SmallGroupsInformation(1944);
There are 3973 groups of order 1944.
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 - 50 have Frattini factor [ 18, 3 ].
51 - 70 have Frattini factor [ 18, 4 ].
71 - 99 have Frattini factor [ 18, 5 ].
100 has Frattini factor [ 24, 12 ].
101 has Frattini factor [ 24, 13 ].
102 has Frattini factor [ 24, 14 ].
103 has Frattini factor [ 24, 15 ].
104 - 108 have Frattini factor [ 36, 9 ].
109 - 219 have Frattini factor [ 36, 10 ].
220 - 290 have Frattini factor [ 36, 11 ].
291 - 485 have Frattini factor [ 36, 12 ].
486 - 585 have Frattini factor [ 36, 13 ].
586 - 672 have Frattini factor [ 36, 14 ].
673 - 714 have Frattini factor [ 54, 12 ].
715 - 761 have Frattini factor [ 54, 13 ].
762 - 771 have Frattini factor [ 54, 14 ].
772 - 801 have Frattini factor [ 54, 15 ].
802 - 803 have Frattini factor [ 72, 39 ].
804 - 806 have Frattini factor [ 72, 40 ].
807 - 808 have Frattini factor [ 72, 41 ].
809 - 847 have Frattini factor [ 72, 42 ].
848 - 895 have Frattini factor [ 72, 43 ].
896 - 934 have Frattini factor [ 72, 44 ].
935 - 939 have Frattini factor [ 72, 45 ].
940 - 956 have Frattini factor [ 72, 46 ].
957 - 1027 have Frattini factor [ 72, 47 ].
1028 - 1066 have Frattini factor [ 72, 48 ].
1067 - 1086 have Frattini factor [ 72, 49 ].
1087 - 1115 have Frattini factor [ 72, 50 ].
1116 - 1123 have Frattini factor [ 108, 36 ].
1124 - 1129 have Frattini factor [ 108, 37 ].
1130 - 1327 have Frattini factor [ 108, 38 ].
1328 - 1481 have Frattini factor [ 108, 39 ].
1482 - 1558 have Frattini factor [ 108, 40 ].
1559 - 1667 have Frattini factor [ 108, 41 ].
1668 - 1877 have Frattini factor [ 108, 42 ].
1878 - 2112 have Frattini factor [ 108, 43 ].
2113 - 2162 have Frattini factor [ 108, 44 ].
2163 - 2252 have Frattini factor [ 108, 45 ].
2253 - 2259 have Frattini factor [ 162, 51 ].
2260 - 2272 have Frattini factor [ 162, 52 ].
2273 - 2279 have Frattini factor [ 162, 53 ].
2280 - 2282 have Frattini factor [ 162, 54 ].
2283 - 2288 have Frattini factor [ 162, 55 ].
2289 - 2295 have Frattini factor [ 216, 153 ].
2296 - 2302 have Frattini factor [ 216, 154 ].
2303 - 2307 have Frattini factor [ 216, 155 ].
2308 - 2311 have Frattini factor [ 216, 156 ].
2312 - 2316 have Frattini factor [ 216, 157 ].
2317 - 2321 have Frattini factor [ 216, 158 ].
2322 - 2327 have Frattini factor [ 216, 159 ].
2328 - 2333 have Frattini factor [ 216, 160 ].
2334 - 2338 have Frattini factor [ 216, 161 ].
2339 - 2346 have Frattini factor [ 216, 162 ].
2347 - 2388 have Frattini factor [ 216, 163 ].
2389 - 2488 have Frattini factor [ 216, 164 ].
2489 - 2520 have Frattini factor [ 216, 165 ].
2521 - 2611 have Frattini factor [ 216, 166 ].
2612 - 2658 have Frattini factor [ 216, 167 ].
2659 - 2666 have Frattini factor [ 216, 168 ].
2667 - 2672 have Frattini factor [ 216, 169 ].
2673 - 2702 have Frattini factor [ 216, 170 ].
2703 - 2724 have Frattini factor [ 216, 171 ].
2725 - 2737 have Frattini factor [ 216, 172 ].
2738 - 2846 have Frattini factor [ 216, 173 ].
2847 - 2888 have Frattini factor [ 216, 174 ].
2889 - 2935 have Frattini factor [ 216, 175 ].
2936 - 2945 have Frattini factor [ 216, 176 ].
2946 - 2975 have Frattini factor [ 216, 177 ].
2976 has Frattini factor [ 324, 160 ].
2977 - 2983 have Frattini factor [ 324, 161 ].
2984 - 2989 have Frattini factor [ 324, 162 ].
2990 - 2993 have Frattini factor [ 324, 163 ].
2994 - 2996 have Frattini factor [ 324, 164 ].
2997 - 3037 have Frattini factor [ 324, 165 ].
3038 - 3114 have Frattini factor [ 324, 166 ].
3115 - 3152 have Frattini factor [ 324, 167 ].
3153 - 3180 have Frattini factor [ 324, 168 ].
3181 - 3209 have Frattini factor [ 324, 169 ].
3210 - 3250 have Frattini factor [ 324, 170 ].
3251 - 3265 have Frattini factor [ 324, 171 ].
3266 - 3300 have Frattini factor [ 324, 172 ].
3301 - 3365 have Frattini factor [ 324, 173 ].
3366 - 3400 have Frattini factor [ 324, 174 ].
3401 - 3415 have Frattini factor [ 324, 175 ].
3416 - 3433 have Frattini factor [ 324, 176 ].
3434 has Frattini factor [ 486, 256 ].
3435 has Frattini factor [ 486, 257 ].
3436 has Frattini factor [ 486, 258 ].
3437 has Frattini factor [ 486, 259 ].
3438 has Frattini factor [ 486, 260 ].
3439 has Frattini factor [ 486, 261 ].
3440 - 3452 have Frattini factor [ 648, 702 ].
3453 has Frattini factor [ 648, 703 ].
3454 has Frattini factor [ 648, 704 ].
3455 has Frattini factor [ 648, 705 ].
3456 has Frattini factor [ 648, 706 ].
3457 - 3460 have Frattini factor [ 648, 707 ].
3461 - 3468 have Frattini factor [ 648, 708 ].
3469 - 3472 have Frattini factor [ 648, 709 ].
3473 - 3474 have Frattini factor [ 648, 710 ].
3475 - 3476 have Frattini factor [ 648, 711 ].
3477 - 3479 have Frattini factor [ 648, 712 ].
3480 - 3485 have Frattini factor [ 648, 713 ].
3486 - 3489 have Frattini factor [ 648, 714 ].
3490 - 3493 have Frattini factor [ 648, 715 ].
3494 - 3496 have Frattini factor [ 648, 716 ].
3497 - 3499 have Frattini factor [ 648, 717 ].
3500 - 3503 have Frattini factor [ 648, 718 ].
3504 - 3508 have Frattini factor [ 648, 719 ].
3509 - 3516 have Frattini factor [ 648, 720 ].
3517 - 3519 have Frattini factor [ 648, 721 ].
3520 - 3523 have Frattini factor [ 648, 722 ].
3524 - 3528 have Frattini factor [ 648, 723 ].
3529 - 3532 have Frattini factor [ 648, 724 ].
3533 - 3537 have Frattini factor [ 648, 725 ].
3538 - 3544 have Frattini factor [ 648, 726 ].
3545 - 3550 have Frattini factor [ 648, 727 ].
3551 - 3554 have Frattini factor [ 648, 728 ].
3555 - 3557 have Frattini factor [ 648, 729 ].
3558 - 3561 have Frattini factor [ 648, 730 ].
3562 - 3566 have Frattini factor [ 648, 731 ].
3567 - 3571 have Frattini factor [ 648, 732 ].
3572 - 3576 have Frattini factor [ 648, 733 ].
3577 - 3579 have Frattini factor [ 648, 734 ].
3580 - 3586 have Frattini factor [ 648, 735 ].
3587 - 3605 have Frattini factor [ 648, 736 ].
3606 - 3620 have Frattini factor [ 648, 737 ].
3621 - 3625 have Frattini factor [ 648, 738 ].
3626 - 3640 have Frattini factor [ 648, 739 ].
3641 - 3661 have Frattini factor [ 648, 740 ].
3662 - 3668 have Frattini factor [ 648, 741 ].
3669 - 3675 have Frattini factor [ 648, 742 ].
3676 - 3681 have Frattini factor [ 648, 743 ].
3682 - 3685 have Frattini factor [ 648, 744 ].
3686 - 3688 have Frattini factor [ 648, 745 ].
3689 - 3695 have Frattini factor [ 648, 746 ].
3696 - 3706 have Frattini factor [ 648, 747 ].
3707 - 3714 have Frattini factor [ 648, 748 ].
3715 - 3718 have Frattini factor [ 648, 749 ].
3719 - 3723 have Frattini factor [ 648, 750 ].
3724 - 3730 have Frattini factor [ 648, 751 ].
3731 - 3745 have Frattini factor [ 648, 752 ].
3746 - 3752 have Frattini factor [ 648, 753 ].
3753 - 3765 have Frattini factor [ 648, 754 ].
3766 - 3772 have Frattini factor [ 648, 755 ].
3773 - 3775 have Frattini factor [ 648, 756 ].
3776 - 3781 have Frattini factor [ 648, 757 ].
3782 has Frattini factor [ 972, 877 ].
3783 has Frattini factor [ 972, 878 ].
3784 has Frattini factor [ 972, 879 ].
3785 has Frattini factor [ 972, 880 ].
3786 has Frattini factor [ 972, 881 ].
3787 has Frattini factor [ 972, 882 ].
3788 has Frattini factor [ 972, 883 ].
3789 - 3793 have Frattini factor [ 972, 884 ].
3794 - 3800 have Frattini factor [ 972, 885 ].
3801 - 3803 have Frattini factor [ 972, 886 ].
3804 - 3810 have Frattini factor [ 972, 887 ].
3811 - 3815 have Frattini factor [ 972, 888 ].
3816 - 3820 have Frattini factor [ 972, 889 ].
3821 - 3827 have Frattini factor [ 972, 890 ].
3828 - 3834 have Frattini factor [ 972, 891 ].
3835 - 3839 have Frattini factor [ 972, 892 ].
3840 - 3844 have Frattini factor [ 972, 893 ].
3845 has Frattini factor [ 972, 894 ].
3846 - 3850 have Frattini factor [ 972, 895 ].
3851 - 3855 have Frattini factor [ 972, 896 ].
3856 - 3860 have Frattini factor [ 972, 897 ].
3861 - 3865 have Frattini factor [ 972, 898 ].
3866 - 3870 have Frattini factor [ 972, 899 ].
3871 - 3873 have Frattini factor [ 972, 900 ].
3874 - 3973 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.