Groups of order 500

Statistics at a glance
The number 500 has prime factors 2 and 5. The prime factorization is as follows:

$$\! 500 = 2^2 \cdot 5^3 = 4 \cdot 125$$

GAP implementation
gap> SmallGroupsInformation(500);

There are 56 groups of order 500. 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 has Frattini factor [ 20, 4 ]. 5 has Frattini factor [ 20, 5 ]. 6 - 9 have Frattini factor [ 50, 3 ]. 10 - 11 have Frattini factor [ 50, 4 ]. 12 - 14 have Frattini factor [ 50, 5 ]. 15 - 18 have Frattini factor [ 100, 9 ]. 19 - 21 have Frattini factor [ 100, 10 ]. 22 - 23 have Frattini factor [ 100, 11 ]. 24 - 25 have Frattini factor [ 100, 12 ]. 26 - 27 have Frattini factor [ 100, 13 ]. 28 - 31 have Frattini factor [ 100, 14 ]. 32 - 33 have Frattini factor [ 100, 15 ]. 34 - 36 have Frattini factor [ 100, 16 ]. 37 has Frattini factor [ 250, 12 ]. 38 has Frattini factor [ 250, 13 ]. 39 has Frattini factor [ 250, 14 ]. 40 has Frattini factor [ 250, 15 ]. 41 - 56 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.