In this paper, we show that every conjugacy class of the imprimitive complex reflection group $G(m,1,n)$ can be represented by an admissible diagram. For this, we introduce a length function for elements of $G(m,1,n)$ and study its properties. This then allows us to establish the admissible diagram for each conjugacy class of $G(m,1,n)$. The corresponding results for Weyl groups and their conjugacy classes are well known.
Reflection groups, length function, admissible diagrams, conjugacy classes.
MSC 2000: 20F55, 20C30