Groups of order 56

This article gives basic information comparing and contrasting groups of order 56. The prime factorization of 56 is $$56 = 2^3 \cdot 7$$.

GAP implementation
gap> SmallGroupsInformation(56);

There are 13 groups of order 56. They are sorted by their Frattini factors. 1 has Frattini factor [ 14, 1 ]. 2 has Frattini factor [ 14, 2 ]. 3 - 7 have Frattini factor [ 28, 3 ]. 8 - 10 have Frattini factor [ 28, 4 ]. 11 - 13 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.