Free product of class two of two Klein four-groups

Definition
This group is defined in the following equivalent ways:


 * 1) It is the quotient of the free product of two Klein four-groups by the third member of its lower central series. In other words, it is the free product of two Klein four-groups within the variety of groups of nilpotency class at most two.
 * 2) It is the maximal unipotent subgroup of symplectic group of degree four over field:F4. Equivalently, it is the 2-Sylow subgroup of symplectic group:Sp(4,4).

Other descriptions
The group can be constructed as follows:

gap> F := FreeProduct(ElementaryAbelianGroup(4),ElementaryAbelianGroup(4));  gap> G := F/CommutatorSubgroup(F,DerivedSubgroup(F)); Group([ f1, f2, f3, f4 ])