Groups of order 224

Statistics at a glance
The number 224 has prime factors 2 and 7. The prime factorization is

$$\! 224 = 2^5 \cdot 7 = 32 \cdot 7$$

GAP implementation
gap> SmallGroupsInformation(224);

There are 197 groups of order 224. They are sorted by their Frattini factors. 1 has Frattini factor [ 14, 1 ]. 2 has Frattini factor [ 14, 2 ]. 3 - 43 have Frattini factor [ 28, 3 ]. 44 - 62 have Frattini factor [ 28, 4 ]. 63 - 148 have Frattini factor [ 56, 12 ]. 149 - 172 have Frattini factor [ 56, 13 ]. 173 has Frattini factor [ 112, 41 ]. 174 - 188 have Frattini factor [ 112, 42 ]. 189 - 194 have Frattini factor [ 112, 43 ]. 195 - 197 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.