Characters and Schur indices of the unitary reflection group [321]³

The group G considered in this paper is the finite irreducible unitary reflection group in 6 dimensions denoted by [3 21] 3 in the notation of H. S. M. Coxeter. A character table for G is constructed. There are 169 irreducible characters and it is shown that each character has Schur index 1 over Q. Furthermore, each character has values in the field Q(V^3) and this field is a splitting field for G.