Let $G$ be a finite group and $k$ be a finite field of characteristic $p>0$ such that $p\mid |G|$.
Is there a computer algebra system which can compute a direct product decomposition of such group algebras $kG$?
If yes, I'd be interested in getting the idempotents for the decomposition as output, too.
Remark: We can assume that $G$ is given as a permutation group.
Thanks for the help.