  Let g be a random element of a finite classical group G, and let
\lambda_{z-1}(g) denote the partition corresponding to the polynomial z-1 in
the rational canonical form of g. As the rank of G tends to infinity,
\lambda_{z-1}(g) tends to a partition distributed according to a Cohen-Lenstra
type measure on partitions. We give sharp upper and lower bounds on the total
variation distance between the random partition \lambda_{z-1}(g) and the
Cohen-Lenstra type measure.
