Groups of order 300

Statistics at a glance
The number 300 has prime factors 2, 3, and 5. The prime factorization is:

$$\! 300 = 2^2 \cdot 3^1 \cdot 5^2 = 4 \cdot 3 \cdot 25$$

There are both solvable and non-solvable groups of this order. For the non-solvable groups, the only non-abelian composition factor is alternating group:A5 (order 60), hence the other composition factor must be cyclic group:Z5. In fact, the only non-solvable group is direct product of A5 and Z5.

GAP implementation
gap> SmallGroupsInformation(300);

There are 49 groups of order 300. They are sorted by their Frattini factors. 1 has Frattini factor [ 30, 1 ]. 2 has Frattini factor [ 30, 2 ]. 3 has Frattini factor [ 30, 3 ]. 4 has Frattini factor [ 30, 4 ]. 5 has Frattini factor [ 60, 6 ]. 6 has Frattini factor [ 60, 7 ]. 7 has Frattini factor [ 60, 8 ]. 8 has Frattini factor [ 60, 9 ]. 9 has Frattini factor [ 60, 10 ]. 10 has Frattini factor [ 60, 11 ]. 11 has Frattini factor [ 60, 12 ]. 12 has Frattini factor [ 60, 13 ]. 13 has Frattini factor [ 150, 5 ]. 14 has Frattini factor [ 150, 6 ]. 15 has Frattini factor [ 150, 7 ]. 16 has Frattini factor [ 150, 8 ]. 17 has Frattini factor [ 150, 9 ]. 18 has Frattini factor [ 150, 10 ]. 19 has Frattini factor [ 150, 11 ]. 20 has Frattini factor [ 150, 12 ]. 21 has Frattini factor [ 150, 13 ]. 22 - 49 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.