  We compute the total Stiefel Whitney class for a real representation $\pi$ of
$\mathrm{GL}_n(\mathbb{F}_q)$, where $q$ is odd in terms of character values of
$\pi$ on order $2$ diagonal elements. We also compute the total Stiefel Whitney
class of real representations of $\mathrm{GL}_n(\mathbb{R})$ and
$\mathrm{GL}_n(\mathbb{C})$.
