Schur indices of characters of groups related to finite sporadic simple groups (Q1912788)

The Schur index measures the extend to which a representation cannot be written over the field of its character. The most common examples are real characters of non-real representations. This paper is concerned with the more subtle cases which occasionally arise. Specifically, the Schur indices of all characters of the groups \(M.G.A\) are calculated, where \(G\) is a sporadic simple group, \(M\) is its Schur multiplier, and \(A\) is its outer automorphism group. In all cases, \(A\) is 1 or 2, and the corresponding calculations for the groups \(M.G\) were described in an earlier paper [Isr. J. Math. 46, 274-300 (1983; Zbl 0528.20009)]. Section 2 contains a useful discussion of isoclinism and its effect on character tables -- in the examples, if \(M\) is even, then there are two groups \(M.G.2\), whose character tables differ simply by multiplying certain entries by \(\sqrt{-1}\). Sections 3 and 4 contain the important lemmas and an outline of the method, while the case-by-case analysis is presented in Section 5, and the tables of results in Section 6.