Groups of order 84

Statistics at a glance
The number 84 has the prime factorization:

$$\! 84 = 2^2 \cdot 3^1 \cdot 7^1 = 4 \cdot 3 \cdot 7$$

All groups of this order are solvable groups.

GAP implementation
gap> SmallGroupsInformation(84);

There are 15 groups of order 84. They are sorted by their Frattini factors. 1 has Frattini factor [ 42, 1 ]. 2 has Frattini factor [ 42, 2 ]. 3 has Frattini factor [ 42, 3 ]. 4 has Frattini factor [ 42, 4 ]. 5 has Frattini factor [ 42, 5 ]. 6 has Frattini factor [ 42, 6 ]. 7 - 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.