Groups of order 48

Factorization and useful forms
The number 48 has prime factors 2 and 3, and factorization:

$$48 = 2^4 \cdot 3^1 = 16 \cdot 3$$

Other expressions for this number are:

$$48 = (3^2 - 1)(3^2 - 3) = 2(4!) = \frac{4}{\frac{1}{2} + \frac{1}{3} + \frac{1}{4} - 1}$$

2-Sylow subgroups
Here is the occurrence summary:

GAP implementation
gap> SmallGroupsInformation(48);

There are 52 groups of order 48. 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 - 19 have Frattini factor [ 12, 4 ]. 20 - 27 have Frattini factor [ 12, 5 ]. 28 - 30 have Frattini factor [ 24, 12 ]. 31 - 33 have Frattini factor [ 24, 13 ]. 34 - 43 have Frattini factor [ 24, 14 ]. 44 - 47 have Frattini factor [ 24, 15 ]. 48 - 52 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.