In this paper we present an algorithm for e ciently counting xed points in a nite monoid M under a conjugacy-like action. We then prove a formula for the character table of M in terms of xed points and radical, which allows for the e ective computation of the character table of M over a eld of null characteristic, as well as its Cartan matrix, using a formula from [Thiéry '12], again in terms of xed points. We discuss the implementation details of the resulting algorithms and provide benchmarks of their performances.