  In 1997 Clarke et al. studied a $q$-analogue of Euler's difference table for
$n!$ using a key bijection $\Psi$ on symmetric groups. In this paper we extend
their results to the wreath product of a cyclic group with the symmetric group.
In particular we obtain a new mahonian statistic \emph{fmaf} on wreath
products. We also show that Foata and Han's two recent transformations on the
symmetric groups provide indeed a factorization of $\Psi$.
