Groups of order 1296

Statistics at a glance
The number 1296 has the following prime factorization:

$$\! 1296 = 2^4 \cdot 3^4$$

GAP implementation
There are 3609 groups of order 1296. 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 - 40 have Frattini factor [ 18, 3 ]. 41 - 47 have Frattini factor [ 18, 4 ]. 48 - 56 have Frattini factor [ 18, 5 ]. 57 - 59 have Frattini factor [ 24, 12 ]. 60 - 62 have Frattini factor [ 24, 13 ]. 63 - 72 have Frattini factor [ 24, 14 ]. 73 - 76 have Frattini factor [ 24, 15 ]. 77 has Frattini factor [ 36, 9 ]. 78 - 218 have Frattini factor [ 36, 10 ]. 219 - 237 have Frattini factor [ 36, 11 ]. 238 - 445 have Frattini factor [ 36, 12 ]. 446 - 557 have Frattini factor [ 36, 13 ]. 558 - 629 have Frattini factor [ 36, 14 ]. 630 has Frattini factor [ 48, 48 ]. 631 has Frattini factor [ 48, 49 ]. 632 has Frattini factor [ 48, 50 ]. 633 has Frattini factor [ 48, 51 ]. 634 has Frattini factor [ 48, 52 ]. 635 - 640 have Frattini factor [ 54, 12 ]. 641 - 647 have Frattini factor [ 54, 13 ]. 648 - 649 have Frattini factor [ 54, 14 ]. 650 - 653 have Frattini factor [ 54, 15 ]. 654 has Frattini factor [ 72, 39 ]. 655 - 659 have Frattini factor [ 72, 40 ]. 660 has Frattini factor [ 72, 41 ]. 661 - 699 have Frattini factor [ 72, 42 ]. 700 - 744 have Frattini factor [ 72, 43 ]. 745 - 783 have Frattini factor [ 72, 44 ]. 784 - 790 have Frattini factor [ 72, 45 ]. 791 - 943 have Frattini factor [ 72, 46 ]. 944 - 1000 have Frattini factor [ 72, 47 ]. 1001 - 1130 have Frattini factor [ 72, 48 ]. 1131 - 1200 have Frattini factor [ 72, 49 ]. 1201 - 1236 have Frattini factor [ 72, 50 ]. 1237 - 1239 have Frattini factor [ 108, 36 ]. 1240 - 1241 have Frattini factor [ 108, 37 ]. 1242 - 1348 have Frattini factor [ 108, 38 ]. 1349 - 1448 have Frattini factor [ 108, 39 ]. 1449 - 1496 have Frattini factor [ 108, 40 ]. 1497 - 1506 have Frattini factor [ 108, 41 ]. 1507 - 1602 have Frattini factor [ 108, 42 ]. 1603 - 1714 have Frattini factor [ 108, 43 ]. 1715 - 1746 have Frattini factor [ 108, 44 ]. 1747 - 1778 have Frattini factor [ 108, 45 ]. 1779 has Frattini factor [ 144, 182 ]. 1780 - 1790 have Frattini factor [ 144, 183 ]. 1791 - 1811 have Frattini factor [ 144, 184 ]. 1812 has Frattini factor [ 144, 185 ]. 1813 has Frattini factor [ 144, 186 ]. 1814 has Frattini factor [ 144, 187 ]. 1815 - 1827 have Frattini factor [ 144, 188 ]. 1828 - 1842 have Frattini factor [ 144, 189 ]. 1843 - 1855 have Frattini factor [ 144, 190 ]. 1856 has Frattini factor [ 144, 191 ]. 1857 - 1862 have Frattini factor [ 144, 192 ]. 1863 - 1881 have Frattini factor [ 144, 193 ]. 1882 - 1900 have Frattini factor [ 144, 194 ]. 1901 - 1913 have Frattini factor [ 144, 195 ]. 1914 - 1920 have Frattini factor [ 144, 196 ]. 1921 - 1929 have Frattini factor [ 144, 197 ]. 1930 has Frattini factor [ 162, 51 ]. 1931 has Frattini factor [ 162, 52 ]. 1932 has Frattini factor [ 162, 53 ]. 1933 has Frattini factor [ 162, 54 ]. 1934 has Frattini factor [ 162, 55 ]. 1935 - 1936 have Frattini factor [ 216, 154 ]. 1937 - 1939 have Frattini factor [ 216, 155 ]. 1940 - 1953 have Frattini factor [ 216, 156 ]. 1954 - 1963 have Frattini factor [ 216, 157 ]. 1964 - 1977 have Frattini factor [ 216, 158 ]. 1978 - 1992 have Frattini factor [ 216, 159 ]. 1993 - 1995 have Frattini factor [ 216, 160 ]. 1996 - 1999 have Frattini factor [ 216, 161 ]. 2000 - 2077 have Frattini factor [ 216, 162 ]. 2078 - 2095 have Frattini factor [ 216, 163 ]. 2096 - 2131 have Frattini factor [ 216, 164 ]. 2132 - 2143 have Frattini factor [ 216, 165 ]. 2144 - 2173 have Frattini factor [ 216, 166 ]. 2174 - 2194 have Frattini factor [ 216, 167 ]. 2195 - 2215 have Frattini factor [ 216, 168 ]. 2216 - 2229 have Frattini factor [ 216, 169 ]. 2230 - 2346 have Frattini factor [ 216, 170 ]. 2347 - 2454 have Frattini factor [ 216, 171 ]. 2455 - 2508 have Frattini factor [ 216, 172 ]. 2509 - 2538 have Frattini factor [ 216, 173 ]. 2539 - 2598 have Frattini factor [ 216, 174 ]. 2599 - 2668 have Frattini factor [ 216, 175 ]. 2669 - 2688 have Frattini factor [ 216, 176 ]. 2689 - 2704 have Frattini factor [ 216, 177 ]. 2705 has Frattini factor [ 324, 160 ]. 2706 has Frattini factor [ 324, 161 ]. 2707 has Frattini factor [ 324, 162 ]. 2708 has Frattini factor [ 324, 163 ]. 2709 has Frattini factor [ 324, 164 ]. 2710 - 2725 have Frattini factor [ 324, 165 ]. 2726 - 2750 have Frattini factor [ 324, 166 ]. 2751 - 2758 have Frattini factor [ 324, 167 ]. 2759 - 2783 have Frattini factor [ 324, 168 ]. 2784 - 2799 have Frattini factor [ 324, 169 ]. 2800 - 2815 have Frattini factor [ 324, 170 ]. 2816 has Frattini factor [ 324, 171 ]. 2817 - 2832 have Frattini factor [ 324, 172 ]. 2833 - 2848 have Frattini factor [ 324, 173 ]. 2849 - 2864 have Frattini factor [ 324, 174 ]. 2865 - 2880 have Frattini factor [ 324, 175 ]. 2881 - 2888 have Frattini factor [ 324, 176 ]. 2889 - 2892 have Frattini factor [ 432, 734 ]. 2893 - 2896 have Frattini factor [ 432, 735 ]. 2897 - 2898 have Frattini factor [ 432, 736 ]. 2899 - 2900 have Frattini factor [ 432, 737 ]. 2901 - 2902 have Frattini factor [ 432, 738 ]. 2903 - 2905 have Frattini factor [ 432, 739 ]. 2906 - 2907 have Frattini factor [ 432, 740 ]. 2908 - 2909 have Frattini factor [ 432, 741 ]. 2910 - 2911 have Frattini factor [ 432, 742 ]. 2912 - 2913 have Frattini factor [ 432, 743 ]. 2914 - 2916 have Frattini factor [ 432, 744 ]. 2917 - 2924 have Frattini factor [ 432, 745 ]. 2925 - 2928 have Frattini factor [ 432, 746 ]. 2929 - 2934 have Frattini factor [ 432, 747 ]. 2935 - 2940 have Frattini factor [ 432, 748 ]. 2941 - 2945 have Frattini factor [ 432, 749 ]. 2946 - 2964 have Frattini factor [ 432, 750 ]. 2965 - 2966 have Frattini factor [ 432, 751 ]. 2967 - 2969 have Frattini factor [ 432, 752 ]. 2970 - 2971 have Frattini factor [ 432, 753 ]. 2972 - 2973 have Frattini factor [ 432, 754 ]. 2974 - 2975 have Frattini factor [ 432, 755 ]. 2976 - 2978 have Frattini factor [ 432, 756 ]. 2979 - 2981 have Frattini factor [ 432, 757 ]. 2982 - 2983 have Frattini factor [ 432, 758 ]. 2984 - 2985 have Frattini factor [ 432, 759 ]. 2986 - 2991 have Frattini factor [ 432, 760 ]. 2992 - 3003 have Frattini factor [ 432, 761 ]. 3004 - 3007 have Frattini factor [ 432, 762 ]. 3008 - 3017 have Frattini factor [ 432, 763 ]. 3018 - 3024 have Frattini factor [ 432, 764 ]. 3025 - 3027 have Frattini factor [ 432, 765 ]. 3028 - 3029 have Frattini factor [ 432, 766 ]. 3030 - 3034 have Frattini factor [ 432, 767 ]. 3035 - 3038 have Frattini factor [ 432, 768 ]. 3039 - 3041 have Frattini factor [ 432, 769 ]. 3042 - 3051 have Frattini factor [ 432, 770 ]. 3052 - 3061 have Frattini factor [ 432, 771 ]. 3062 - 3067 have Frattini factor [ 432, 772 ]. 3068 - 3074 have Frattini factor [ 432, 773 ]. 3075 - 3076 have Frattini factor [ 432, 774 ]. 3077 - 3080 have Frattini factor [ 432, 775 ]. 3081 - 3083 have Frattini factor [ 648, 703 ]. 3084 - 3086 have Frattini factor [ 648, 704 ]. 3087 - 3089 have Frattini factor [ 648, 705 ]. 3090 - 3092 have Frattini factor [ 648, 706 ]. 3093 has Frattini factor [ 648, 707 ]. 3094 has Frattini factor [ 648, 708 ]. 3095 has Frattini factor [ 648, 709 ]. 3096 has Frattini factor [ 648, 710 ]. 3097 has Frattini factor [ 648, 711 ]. 3098 has Frattini factor [ 648, 712 ]. 3099 - 3105 have Frattini factor [ 648, 713 ]. 3106 - 3112 have Frattini factor [ 648, 714 ]. 3113 - 3119 have Frattini factor [ 648, 715 ]. 3120 - 3126 have Frattini factor [ 648, 716 ]. 3127 - 3131 have Frattini factor [ 648, 717 ]. 3132 - 3136 have Frattini factor [ 648, 718 ]. 3137 - 3143 have Frattini factor [ 648, 719 ]. 3144 - 3148 have Frattini factor [ 648, 720 ]. 3149 - 3155 have Frattini factor [ 648, 721 ]. 3156 - 3160 have Frattini factor [ 648, 722 ]. 3161 - 3167 have Frattini factor [ 648, 723 ]. 3168 - 3172 have Frattini factor [ 648, 724 ]. 3173 - 3177 have Frattini factor [ 648, 725 ]. 3178 has Frattini factor [ 648, 726 ]. 3179 - 3180 have Frattini factor [ 648, 727 ]. 3181 - 3182 have Frattini factor [ 648, 728 ]. 3183 - 3184 have Frattini factor [ 648, 729 ]. 3185 has Frattini factor [ 648, 730 ]. 3186 - 3204 have Frattini factor [ 648, 731 ]. 3205 - 3243 have Frattini factor [ 648, 732 ]. 3244 - 3262 have Frattini factor [ 648, 733 ]. 3263 - 3272 have Frattini factor [ 648, 734 ]. 3273 - 3275 have Frattini factor [ 648, 735 ]. 3276 - 3278 have Frattini factor [ 648, 736 ]. 3279 - 3281 have Frattini factor [ 648, 737 ]. 3282 - 3284 have Frattini factor [ 648, 738 ]. 3285 - 3287 have Frattini factor [ 648, 739 ]. 3288 - 3290 have Frattini factor [ 648, 740 ]. 3291 - 3293 have Frattini factor [ 648, 741 ]. 3294 - 3300 have Frattini factor [ 648, 742 ]. 3301 - 3307 have Frattini factor [ 648, 743 ]. 3308 - 3314 have Frattini factor [ 648, 744 ]. 3315 - 3321 have Frattini factor [ 648, 745 ]. 3322 - 3339 have Frattini factor [ 648, 746 ]. 3340 - 3366 have Frattini factor [ 648, 747 ]. 3367 - 3376 have Frattini factor [ 648, 748 ]. 3377 - 3403 have Frattini factor [ 648, 749 ]. 3404 - 3421 have Frattini factor [ 648, 750 ]. 3422 - 3439 have Frattini factor [ 648, 751 ]. 3440 - 3442 have Frattini factor [ 648, 752 ]. 3443 - 3452 have Frattini factor [ 648, 753 ]. 3453 - 3462 have Frattini factor [ 648, 754 ]. 3463 - 3472 have Frattini factor [ 648, 755 ]. 3473 - 3482 have Frattini factor [ 648, 756 ]. 3483 - 3486 have Frattini factor [ 648, 757 ]. 3487 - 3609 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.