  For a simply connected CW-complex $X$, let $\mathcal{E}(X)$ denote the group
of homotopy classes of self-homotopy equivalence of $X$ and let
$\mathcal{E}_{\sharp}(X)$ be its subgroup of homotopy classes which induce the
identity on homotopy groups. As we know, the quotient group
$\frac{\mathcal{E}(X)}{\mathcal{E}_{\sharp}(X)}$ can be identified with a
subgroup of $Aut(\pi_{*}(X))$. The aim of this work is to determine this
subgroup for rational spaces. We construct the Whitehead exact sequence
associated with the minimal Sullivan model of $X$ which allows us to define the
subgroup $\mathrm{Coh.Aut}(\mathrm{Hom}\big(\pi_{*}(X),\Bbb Q)\big)$ of
self-coherent automorphisms of the graded vector space
$\mathrm{Hom}(\pi_*(X),\Bbb Q)$. As a consequence we establish that
$\mathcal{E}(X) / \mathcal{E}_{\sharp}(X) \cong \mathrm{Coh.Aut}
(\mathrm{Hom}(\pi_*(X),\Bbb Q))$. In addition, by computing the group
$\mathrm{Coh.Aut}\big(\mathrm{Hom}(\pi_{*}(X),\Bbb Q)\big)$, we give examples
of rational spaces that have few self-homotopy equivalences.
