Groups of order 112

Statistics at a glance
The number 112 has prime factors 2 and 7. The prime factorization is as follows:

$$\! 112 = 2^4 \cdot 7^1 = 16 \cdot 7$$

GAP implementation
gap> SmallGroupsInformation(112);

There are 43 groups of order 112. They are sorted by their Frattini factors. 1 has Frattini factor [ 14, 1 ]. 2 has Frattini factor [ 14, 2 ]. 3 - 18 have Frattini factor [ 28, 3 ]. 19 - 26 have Frattini factor [ 28, 4 ]. 27 - 36 have Frattini factor [ 56, 12 ]. 37 - 40 have Frattini factor [ 56, 13 ]. 41 - 43 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.