Hello,

in their book <a href="http://books.google.com/books?id=sKmshEctdw0C&dq=cohomology+of+finite+groups&printsec=frontcover&source=bn&hl=de&ei=vV3-S_3OFcSrsAb79c39CQ&sa=X&oi=book_result&ct=result&resnum=4&ved=0CDIQ6AEwAw#v=onepage&q&f=false"> Cohomology of Finite Groups</a> Adem and Milgram investigate the cohomology of the finite orthogonal and symplectic groups only in case $\mathbb{F}_2$. 


Let $p$ be a prime dividing the order of $\text{O}_n(q)$, $\text{Sp}_n(q)$ and $q$ a prime power. 

I am wondering if anything is known about $\text{H}^\ast(\text{O}_n(q),\mathbb{F}_p)$ or $\text{H}^\ast(\text{Sp}_n(q),\mathbb{F}_p)$.

I am also interested in the maximal elementary abelian $p$-subgroups of these groups.

In light of Quillen's stratification theorem these two questions are, of course, related to each other.


I would be grateful for any kind of information.