Two remarks on Wall's D2 problem

If a finite group $G$ is isomorphic to a subgroup of $SO(3)$, then $G$ has the D2-property. Let $X$ be a finite complex satisfying Wall’s D2-conditions. If ${\pi }_1(X)=G$ is finite, and $\chi (X)\ge 1-Def(G)$, then $X\vee S^2$ is simple homotopy equivalent to a finite $2$-complex, whose simple homotopy type depends only on $G$ and $\chi (X)$.