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We describe an algorithm for splitting permutation representations of finitegroup over fields of characteristic zero into irreducible components. Thealgorithm is based on the fact that the components of the invariant innerproduct in invariant subspaces are operators of projection into thesesubspaces. An important element of the algorithm is the calculation ofGr\"obner bases of polynomial ideals. A preliminary implementation of thealgorithm splits representations up to dimensions of tens of thousands. Someexamples of computations are given in appendix.

An Algorithm to Decompose Permutation Representations of Finite Groups: Polynomial Algebra Approach