Gregor Kemper,
"Calculating Invariant Rings of Finite Groups over Arbitrary Fields",
to appear in the Journal of Symbolic Computation.

Abstract:
An algorithm is presented which calculates rings of polynomial
invariants of finite linear groups over an arbitrary field K. Up to
now, such algorithms have been available only for the case that the
characteristic of K does not divide the group order.
Some applications to the question whether a modular invariant ring is
Cohen-Macaulay or isomorphic to a polynomial ring are discussed.