  We describe a basis of the centre of the Schur algebra which comes from
conjugacy classes in the symmetric group via Schur-Weyl duality. We give a
combinatorial description of expansions of these basis elements in terms of the
basis originally used by Schur. The primitive central idempotents of the Schur
algebra can be written down using this basis and the character table of the
symmetric group. Along the way we prove a result on the non-singularity of the
submatrix of the character table matrix of a symmetric group obtained by taking
rows and columns indexed by partitions with at most n parts for any n.
