Groups of order 210

Statistics at a glance
The number 210 has prime factors 2, 3, 5, and 7. The prime factorization is:

$$\ 210 = 2^1 \cdot 3^1 \cdot 5^1 \cdot 7^1 = 2 \cdot 3 \cdot 5 \cdot 7$$

Square-free implies solvability-forcing, so all groups of this order are finite solvable groups. In fact, every Sylow subgroup is cyclic implies metacyclic, so all groups of this order are metacyclic groups.

GAP implementation
gap> SmallGroupsInformation(210);

There are 12 groups of order 210. They are sorted by their Frattini factors. 1 - 12 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.