  Let $X$ be a \text{\rm{2}}-connected and \text{\rm{6}}-dimensional CW-complex
$X$ such that $H_{3}(X)\otimes\Z_2=0$. This paper aims to describe the group
$\E(X)$ of the self-homotopy equivalences of $X$ modulo its normal subgroup
$\E_{*}(X)$ of the elements that induce the identity on the homology groups.
Making use of the Whitehead exact sequence of $X$, denoted by WES$(X)$, we
define the group $\Gamma\mathcal{S}(X)$ of $\Gamma$-automorphisms of WES$(X)$
and we prove that $\E(X)/\E_*(X)\cong \Gamma\mathcal{S}(X).$
