Let F be a free group of rank d >= 2. Consider the quotient F/[gamma(4)(F'), F]F"'. A peculiar feature of this group is the occurence of torsion in its centre. In this article, we describe an elementary abelian 2-group of rank ((d)(7)) in F/[gamma(4)(F'), F]F''' in terms of generators of F. We solve this purely, group theoretic problem using homological methods namely, computing certain connecting homomorphisms.