Groups of order 108

Statistics at a glance
The number 108 has 2 and 3 as its only prime factors. It has prime factorization:

$$\! 108 = 2^2 \cdot 3^3 = 4 \cdot 27$$

GAP implementation
gap> SmallGroupsInformation(108);

There are 45 groups of order 108. 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 has Frattini factor [ 12, 4 ]. 5 has Frattini factor [ 12, 5 ]. 6 - 9 have Frattini factor [ 18, 3 ]. 10 - 11 have Frattini factor [ 18, 4 ]. 12 - 14 have Frattini factor [ 18, 5 ]. 15 has Frattini factor [ 36, 9 ]. 16 - 17 have Frattini factor [ 36, 10 ]. 18 - 22 have Frattini factor [ 36, 11 ]. 23 - 26 have Frattini factor [ 36, 12 ]. 27 - 28 have Frattini factor [ 36, 13 ]. 29 - 31 have Frattini factor [ 36, 14 ]. 32 has Frattini factor [ 54, 12 ]. 33 has Frattini factor [ 54, 13 ]. 34 has Frattini factor [ 54, 14 ]. 35 has Frattini factor [ 54, 15 ]. 36 - 45 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.