Groups of order 180

Statistics at a glance
The number 180 has prime factorization $$180 = 2^2 \cdot 3^2 \cdot 5$$. There are both solvable and non-solvable groups of this order. The only possible non-abelian composition factor for this order is alternating group:A5.

GAP implementation
gap> SmallGroupsInformation(180);

There are 37 groups of order 180. They are sorted by their Frattini factors. 1 has Frattini factor [ 30, 1 ]. 2 has Frattini factor [ 30, 2 ]. 3 has Frattini factor [ 30, 3 ]. 4 has Frattini factor [ 30, 4 ]. 5 has Frattini factor [ 60, 6 ]. 6 has Frattini factor [ 60, 7 ]. 7 has Frattini factor [ 60, 8 ]. 8 has Frattini factor [ 60, 9 ]. 9 has Frattini factor [ 60, 10 ]. 10 has Frattini factor [ 60, 11 ]. 11 has Frattini factor [ 60, 12 ]. 12 has Frattini factor [ 60, 13 ]. 13 has Frattini factor [ 90, 5 ]. 14 has Frattini factor [ 90, 6 ]. 15 has Frattini factor [ 90, 7 ]. 16 has Frattini factor [ 90, 8 ]. 17 has Frattini factor [ 90, 9 ]. 18 has Frattini factor [ 90, 10 ]. 19 - 37 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.