Groups of order 1000

Statistics at a glance
The number 1000 has prime factors 2 and 5. The prime factorization is:

$$\! 1000 = 2^3 \cdot 5^3 = 8 \cdot 125$$

GAP implementation
gap> SmallGroupsInformation(1000);

There are 199 groups of order 1000. They are sorted by their Frattini factors. 1 has Frattini factor [ 10, 1 ]. 2 has Frattini factor [ 10, 2 ]. 3 has Frattini factor [ 20, 3 ]. 4 - 8 have Frattini factor [ 20, 4 ]. 9 - 11 have Frattini factor [ 20, 5 ]. 12 has Frattini factor [ 40, 12 ]. 13 has Frattini factor [ 40, 13 ]. 14 has Frattini factor [ 40, 14 ]. 15 - 18 have Frattini factor [ 50, 3 ]. 19 - 20 have Frattini factor [ 50, 4 ]. 21 - 23 have Frattini factor [ 50, 5 ]. 24 - 27 have Frattini factor [ 100, 9 ]. 28 - 30 have Frattini factor [ 100, 10 ]. 31 - 32 have Frattini factor [ 100, 11 ]. 33 - 34 have Frattini factor [ 100, 12 ]. 35 - 46 have Frattini factor [ 100, 13 ]. 47 - 66 have Frattini factor [ 100, 14 ]. 67 - 76 have Frattini factor [ 100, 15 ]. 77 - 85 have Frattini factor [ 100, 16 ]. 86 has Frattini factor [ 200, 40 ]. 87 - 89 have Frattini factor [ 200, 41 ]. 90 - 91 have Frattini factor [ 200, 42 ]. 92 has Frattini factor [ 200, 43 ]. 93 has Frattini factor [ 200, 44 ]. 94 - 97 have Frattini factor [ 200, 45 ]. 98 - 100 have Frattini factor [ 200, 46 ]. 101 - 102 have Frattini factor [ 200, 47 ]. 103 - 104 have Frattini factor [ 200, 48 ]. 105 - 106 have Frattini factor [ 200, 49 ]. 107 - 110 have Frattini factor [ 200, 50 ]. 111 - 112 have Frattini factor [ 200, 51 ]. 113 - 115 have Frattini factor [ 200, 52 ]. 116 has Frattini factor [ 250, 12 ]. 117 has Frattini factor [ 250, 13 ]. 118 has Frattini factor [ 250, 14 ]. 119 has Frattini factor [ 250, 15 ]. 120 has Frattini factor [ 500, 41 ]. 121 has Frattini factor [ 500, 42 ]. 122 has Frattini factor [ 500, 43 ]. 123 has Frattini factor [ 500, 44 ]. 124 has Frattini factor [ 500, 45 ]. 125 has Frattini factor [ 500, 46 ]. 126 has Frattini factor [ 500, 47 ]. 127 has Frattini factor [ 500, 48 ]. 128 has Frattini factor [ 500, 49 ]. 129 - 133 have Frattini factor [ 500, 50 ]. 134 - 140 have Frattini factor [ 500, 51 ]. 141 - 143 have Frattini factor [ 500, 52 ]. 144 - 148 have Frattini factor [ 500, 53 ]. 149 - 153 have Frattini factor [ 500, 54 ]. 154 - 158 have Frattini factor [ 500, 55 ]. 159 - 161 have Frattini factor [ 500, 56 ]. 162 - 199 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.