  For a 1-connected CW-complex $X$, let $\mathcal{E}(X)$ denote the group of
homotopy classes of self-homotopy equivalences of $X$. The aim of this paper is
to prove that, for every $n\in\Bbb N$, there exists a 1-connected rational
CW-complex $X_{n}$ such that $\mathcal{E}(X_{n})\cong
\underset{2^{n+1}\mathrm{. times}}{\underbrace{\Bbb Z_{2}\oplus... \Bbb \oplus
\Bbb Z_{2}}}$.
