Groups of order 96

Factorization and useful forms
The number 96 has prime factors 2 and 3, and factorization:

$$96 = 2^5 \cdot 3^1 = 32 \cdot 3$$

Other expressions for this number are:

$$96 = 2(3^2 - 1)(3^2 - 3)$$

GAP implementation
gap> SmallGroupsInformation(96);

There are 231 groups of order 96. 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 - 44 have Frattini factor [ 12, 4 ]. 45 - 63 have Frattini factor [ 12, 5 ]. 64 - 67 have Frattini factor [ 24, 12 ]. 68 - 74 have Frattini factor [ 24, 13 ]. 75 - 160 have Frattini factor [ 24, 14 ]. 161 - 184 have Frattini factor [ 24, 15 ]. 185 - 195 have Frattini factor [ 48, 48 ]. 196 - 202 have Frattini factor [ 48, 49 ]. 203 - 204 have Frattini factor [ 48, 50 ]. 205 - 219 have Frattini factor [ 48, 51 ]. 220 - 225 have Frattini factor [ 48, 52 ]. 226 - 231 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.