Groups of order 24

Factorization and useful forms
The number 24 has prime factors 2 and 3 and prime factorization:

$$24 = 2^3 \cdot 3^1 = 8 \cdot 3$$ Other expressions for this number are:

$$24 = 4! = 3^3 - 3 = 2^2(2^2 - 1)(2^2 - 2) = 2(2^2)(2^2 - 1) = 2^3 \cdot 3$$

The list
There are 15 groups of order 24.

Divisors of the order
More in-depth information can be found under subgroup structure of groups of order 24.

Multiples of the order
More in-depth information can be found under supergroups of groups of order 24.

GAP implementation
gap> SmallGroupsInformation(24);

There are 15 groups of order 24. 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 - 15 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.