Stiefel-Whitney Classes of Representations of Some Finite Groups of Lie Type

Abstract: In this note we present the Stiefel-Whitney classes (SWCs) for orthogonal representations of several finite groups of Lie type, namely for $G=\text{SL}(2,q),$ $\text{SL}(3,q),$ $\text{Sp}(4,q)$, and $\text{Sp}(6,q)$, with $q$ odd. We also describe the SWCs for $G=\text{SL}(2,q)$ when $q$ is even.