Groups of order 400

Statistics at a glance
The number 400 has prime factors 2 and 5. The prime factorization is as follows:

$$\! 400 = 2^4 \cdot 5^2 = 16 \cdot 25$$

GAP implementation
gap> SmallGroupsInformation(400);

There are 221 groups of order 400. 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 - 19 have Frattini factor [ 20, 4 ]. 20 - 27 have Frattini factor [ 20, 5 ]. 28 - 34 have Frattini factor [ 40, 12 ]. 35 - 44 have Frattini factor [ 40, 13 ]. 45 - 48 have Frattini factor [ 40, 14 ]. 49 has Frattini factor [ 50, 3 ]. 50 has Frattini factor [ 50, 4 ]. 51 has Frattini factor [ 50, 5 ]. 52 has Frattini factor [ 80, 49 ]. 53 has Frattini factor [ 80, 50 ]. 54 has Frattini factor [ 80, 51 ]. 55 has Frattini factor [ 80, 52 ]. 56 has Frattini factor [ 100, 9 ]. 57 has Frattini factor [ 100, 10 ]. 58 has Frattini factor [ 100, 11 ]. 59 has Frattini factor [ 100, 12 ]. 60 - 75 have Frattini factor [ 100, 13 ]. 76 - 91 have Frattini factor [ 100, 14 ]. 92 - 107 have Frattini factor [ 100, 15 ]. 108 - 115 have Frattini factor [ 100, 16 ]. 116 has Frattini factor [ 200, 40 ]. 117 - 123 have Frattini factor [ 200, 41 ]. 124 - 128 have Frattini factor [ 200, 42 ]. 129 - 133 have Frattini factor [ 200, 43 ]. 134 has Frattini factor [ 200, 44 ]. 135 - 141 have Frattini factor [ 200, 45 ]. 142 - 148 have Frattini factor [ 200, 46 ]. 149 - 155 have Frattini factor [ 200, 47 ]. 156 - 162 have Frattini factor [ 200, 48 ]. 163 - 180 have Frattini factor [ 200, 49 ]. 181 - 190 have Frattini factor [ 200, 50 ]. 191 - 200 have Frattini factor [ 200, 51 ]. 201 - 204 have Frattini factor [ 200, 52 ]. 205 - 221 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.