Groups of order 72

Statistics at a glance
The number 72 has prime factorization $$72 = 2^3 \cdot 3^2$$.

GAP implementation
gap> SmallGroupsInformation(72);

There are 50 groups of order 72. They are sorted by their Frattini factors. 1 has Frattini factor [ 6, 1 ]. 2 has Frattini factor [ 6, 2 ]. 3 has Frattini factor [ 12, 3 ]. 4 - 8 have Frattini factor [ 12, 4 ]. 9 - 11 have Frattini factor [ 12, 5 ]. 12 has Frattini factor [ 18, 3 ]. 13 has Frattini factor [ 18, 4 ]. 14 has Frattini factor [ 18, 5 ]. 15 has Frattini factor [ 24, 12 ]. 16 has Frattini factor [ 24, 13 ]. 17 has Frattini factor [ 24, 14 ]. 18 has Frattini factor [ 24, 15 ]. 19 has Frattini factor [ 36, 9 ]. 20 - 24 have Frattini factor [ 36, 10 ]. 25 has Frattini factor [ 36, 11 ]. 26 - 30 have Frattini factor [ 36, 12 ]. 31 - 35 have Frattini factor [ 36, 13 ]. 36 - 38 have Frattini factor [ 36, 14 ]. 39 - 50 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.