  Suzuki (1998) showed that an imprimitive Q-polynomial association scheme with
first multiplicity at least three is either Q-bipartite, Q-antipodal, or with
four or six classes. The exceptional case with four classes has recently been
ruled out by Cerzo and Suzuki (2009). In this paper, we show the nonexistence
of the last case with six classes. Hence Suzuki's theorem now exactly mirrors
its well-known counterpart for imprimitive distance-regular graphs.
