Hypoabelian not implies imperfect

Statement
It is possible for a group to be a hypoabelian group but not be an imperfect group.

Facts used

 * 1) uses::Every group is a quotient of a hypoabelian group (this in turn follows from uses::every group is a quotient of a free group and uses::free implies hypoabelian)

Explicit proof
The proof is pretty direct from Step (1), but it is spelled out explicitly below.