An algorithm for computing Schur indices of characters

We describe an algorithm for computing Schur indices of irreducible characters of a finite group $G$, based on computations within $G$ and its subgroups and with their character tables. The algorithm has been implemented within \Magma\ and examples of its use are given. We also compare the output of the algorithm on groups associated with sporadic simple groups with the results of W. Feit. The differences are considered.