Groups of order 864

Statistics at a glance
The number 864 has the following prime factorization

$$\! 864 = 2^5 \cdot 3^3 = 32 \cdot 27$$

GAP implementation
gap> SmallGroupsInformation(864);

There are 4725 groups of order 864. 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 - 44 have Frattini factor [ 12, 4 ]. 45 - 63 have Frattini factor [ 12, 5 ]. 64 - 67 have Frattini factor [ 18, 3 ]. 68 - 69 have Frattini factor [ 18, 4 ]. 70 - 72 have Frattini factor [ 18, 5 ]. 73 - 76 have Frattini factor [ 24, 12 ]. 77 - 83 have Frattini factor [ 24, 13 ]. 84 - 169 have Frattini factor [ 24, 14 ]. 170 - 193 have Frattini factor [ 24, 15 ]. 194 has Frattini factor [ 36, 9 ]. 195 - 302 have Frattini factor [ 36, 10 ]. 303 - 307 have Frattini factor [ 36, 11 ]. 308 - 471 have Frattini factor [ 36, 12 ]. 472 - 553 have Frattini factor [ 36, 13 ]. 554 - 610 have Frattini factor [ 36, 14 ]. 611 - 621 have Frattini factor [ 48, 48 ]. 622 - 628 have Frattini factor [ 48, 49 ]. 629 - 630 have Frattini factor [ 48, 50 ]. 631 - 645 have Frattini factor [ 48, 51 ]. 646 - 651 have Frattini factor [ 48, 52 ]. 652 has Frattini factor [ 54, 12 ]. 653 has Frattini factor [ 54, 13 ]. 654 has Frattini factor [ 54, 14 ]. 655 has Frattini factor [ 54, 15 ]. 656 has Frattini factor [ 72, 39 ]. 657 - 674 have Frattini factor [ 72, 40 ]. 675 - 679 have Frattini factor [ 72, 41 ]. 680 - 695 have Frattini factor [ 72, 42 ]. 696 - 707 have Frattini factor [ 72, 43 ]. 708 - 736 have Frattini factor [ 72, 44 ]. 737 - 761 have Frattini factor [ 72, 45 ]. 762 - 1291 have Frattini factor [ 72, 46 ]. 1292 - 1327 have Frattini factor [ 72, 47 ]. 1328 - 1671 have Frattini factor [ 72, 48 ]. 1672 - 1843 have Frattini factor [ 72, 49 ]. 1844 - 1915 have Frattini factor [ 72, 50 ]. 1916 has Frattini factor [ 96, 226 ]. 1917 has Frattini factor [ 96, 227 ]. 1918 has Frattini factor [ 96, 228 ]. 1919 has Frattini factor [ 96, 229 ]. 1920 has Frattini factor [ 96, 230 ]. 1921 has Frattini factor [ 96, 231 ]. 1922 has Frattini factor [ 108, 36 ]. 1923 has Frattini factor [ 108, 37 ]. 1924 - 1964 have Frattini factor [ 108, 38 ]. 1965 - 2031 have Frattini factor [ 108, 39 ]. 2032 - 2050 have Frattini factor [ 108, 40 ]. 2051 has Frattini factor [ 108, 41 ]. 2052 - 2092 have Frattini factor [ 108, 42 ]. 2093 - 2133 have Frattini factor [ 108, 43 ]. 2134 - 2174 have Frattini factor [ 108, 44 ]. 2175 - 2193 have Frattini factor [ 108, 45 ]. 2194 - 2196 have Frattini factor [ 144, 182 ]. 2197 - 2241 have Frattini factor [ 144, 183 ]. 2242 - 2253 have Frattini factor [ 144, 184 ]. 2254 - 2260 have Frattini factor [ 144, 185 ]. 2261 - 2283 have Frattini factor [ 144, 186 ]. 2284 - 2288 have Frattini factor [ 144, 187 ]. 2289 - 2332 have Frattini factor [ 144, 188 ]. 2333 - 2365 have Frattini factor [ 144, 189 ]. 2366 - 2409 have Frattini factor [ 144, 190 ]. 2410 - 2422 have Frattini factor [ 144, 191 ]. 2423 - 2512 have Frattini factor [ 144, 192 ]. 2513 - 2547 have Frattini factor [ 144, 193 ]. 2548 - 2557 have Frattini factor [ 144, 194 ]. 2558 - 2617 have Frattini factor [ 144, 195 ]. 2618 - 2647 have Frattini factor [ 144, 196 ]. 2648 - 2665 have Frattini factor [ 144, 197 ]. 2666 has Frattini factor [ 216, 153 ]. 2667 has Frattini factor [ 216, 154 ]. 2668 has Frattini factor [ 216, 155 ]. 2669 - 2699 have Frattini factor [ 216, 156 ]. 2700 - 2717 have Frattini factor [ 216, 157 ]. 2718 - 2746 have Frattini factor [ 216, 158 ]. 2747 - 2764 have Frattini factor [ 216, 159 ]. 2765 - 2769 have Frattini factor [ 216, 160 ]. 2770 - 2778 have Frattini factor [ 216, 161 ]. 2779 - 3004 have Frattini factor [ 216, 162 ]. 3005 - 3008 have Frattini factor [ 216, 163 ]. 3009 - 3012 have Frattini factor [ 216, 164 ]. 3013 - 3016 have Frattini factor [ 216, 165 ]. 3017 - 3023 have Frattini factor [ 216, 166 ]. 3024 - 3030 have Frattini factor [ 216, 167 ]. 3031 - 3055 have Frattini factor [ 216, 168 ]. 3056 - 3080 have Frattini factor [ 216, 169 ]. 3081 - 3275 have Frattini factor [ 216, 170 ]. 3276 - 3610 have Frattini factor [ 216, 171 ]. 3611 - 3696 have Frattini factor [ 216, 172 ]. 3697 - 3703 have Frattini factor [ 216, 173 ]. 3704 - 3789 have Frattini factor [ 216, 174 ]. 3790 - 3875 have Frattini factor [ 216, 175 ]. 3876 - 3961 have Frattini factor [ 216, 176 ]. 3962 - 3985 have Frattini factor [ 216, 177 ]. 3986 - 3989 have Frattini factor [ 288, 1024 ]. 3990 - 3993 have Frattini factor [ 288, 1025 ]. 3994 - 3996 have Frattini factor [ 288, 1026 ]. 3997 has Frattini factor [ 288, 1027 ]. 3998 - 4000 have Frattini factor [ 288, 1028 ]. 4001 - 4005 have Frattini factor [ 288, 1029 ]. 4006 has Frattini factor [ 288, 1030 ]. 4007 has Frattini factor [ 288, 1031 ]. 4008 has Frattini factor [ 288, 1032 ]. 4009 - 4012 have Frattini factor [ 288, 1033 ]. 4013 - 4015 have Frattini factor [ 288, 1034 ]. 4016 - 4019 have Frattini factor [ 288, 1035 ]. 4020 - 4022 have Frattini factor [ 288, 1036 ]. 4023 - 4026 have Frattini factor [ 288, 1037 ]. 4027 - 4030 have Frattini factor [ 288, 1038 ]. 4031 has Frattini factor [ 288, 1039 ]. 4032 - 4033 have Frattini factor [ 288, 1040 ]. 4034 - 4038 have Frattini factor [ 288, 1041 ]. 4039 - 4043 have Frattini factor [ 288, 1042 ]. 4044 - 4047 have Frattini factor [ 288, 1043 ]. 4048 - 4049 have Frattini factor [ 288, 1044 ]. 4050 - 4052 have Frattini factor [ 288, 1045 ]. 4053 has Frattini factor [ 432, 734 ]. 4054 has Frattini factor [ 432, 735 ]. 4055 - 4061 have Frattini factor [ 432, 736 ]. 4062 - 4064 have Frattini factor [ 432, 737 ]. 4065 - 4067 have Frattini factor [ 432, 738 ]. 4068 - 4070 have Frattini factor [ 432, 739 ]. 4071 - 4073 have Frattini factor [ 432, 740 ]. 4074 - 4112 have Frattini factor [ 432, 741 ]. 4113 - 4121 have Frattini factor [ 432, 742 ]. 4122 - 4124 have Frattini factor [ 432, 743 ]. 4125 - 4127 have Frattini factor [ 432, 744 ]. 4128 - 4142 have Frattini factor [ 432, 745 ]. 4143 - 4157 have Frattini factor [ 432, 746 ]. 4158 - 4172 have Frattini factor [ 432, 747 ]. 4173 - 4183 have Frattini factor [ 432, 748 ]. 4184 - 4194 have Frattini factor [ 432, 749 ]. 4195 - 4196 have Frattini factor [ 432, 750 ]. 4197 - 4203 have Frattini factor [ 432, 751 ]. 4204 - 4210 have Frattini factor [ 432, 752 ]. 4211 - 4241 have Frattini factor [ 432, 753 ]. 4242 - 4264 have Frattini factor [ 432, 754 ]. 4265 - 4299 have Frattini factor [ 432, 755 ]. 4300 - 4322 have Frattini factor [ 432, 756 ]. 4323 - 4327 have Frattini factor [ 432, 757 ]. 4328 - 4336 have Frattini factor [ 432, 758 ]. 4337 - 4407 have Frattini factor [ 432, 759 ]. 4408 - 4418 have Frattini factor [ 432, 760 ]. 4419 - 4429 have Frattini factor [ 432, 761 ]. 4430 - 4440 have Frattini factor [ 432, 762 ]. 4441 - 4451 have Frattini factor [ 432, 763 ]. 4452 - 4462 have Frattini factor [ 432, 764 ]. 4463 - 4475 have Frattini factor [ 432, 765 ]. 4476 - 4488 have Frattini factor [ 432, 766 ]. 4489 - 4525 have Frattini factor [ 432, 767 ]. 4526 - 4578 have Frattini factor [ 432, 768 ]. 4579 - 4600 have Frattini factor [ 432, 769 ]. 4601 - 4607 have Frattini factor [ 432, 770 ]. 4608 - 4609 have Frattini factor [ 432, 771 ]. 4610 - 4624 have Frattini factor [ 432, 772 ]. 4625 - 4639 have Frattini factor [ 432, 773 ]. 4640 - 4654 have Frattini factor [ 432, 774 ]. 4655 - 4660 have Frattini factor [ 432, 775 ]. 4661 - 4725 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.