  Given a spherical fibration $\xi$ over the classifying space $BG$ of a finite
group we define a dimension function for the $m-$fold fiber join of $\xi$ where
$m$ is some large positive integer. We show that the dimension functions
satisfy the Borel-Smith conditions when $m$ is large enough. As an application
we prove that there exists no spherical fibration over the classifying space of
$\text{Qd}(p)= (\mathbb{Z}/p)^2\rtimes\text{SL}_2(\mathbb{Z}/p)$ with
$p-$effective Euler class, generalizing the result of \"Ozg\"un \"Unl\"u about
group actions on finite complexes homotopy equivalent to a sphere. We have been
informed that this result will also appear in a future paper as a corollary of
a previously announced program on homotopy group actions due to Jesper Grodal.
