Quasi-Coxeter Elements Of Primitive Complex Reflection Groups And Their Conjugacy Classes

The finite irreducible complex reflection groups were classified by Shephard and Todd in the middle of last century.Recently,Jianyi-shi defines quasi-Coxeter elements about complex reflection groups and reflection length.In this paper,we find all quasi-Coxeter elements of the primitive complex reflection groups G_i(i≤27) and partition them into conjugacy classes,then we calculate their orders and compute the length of these conjugacy classes.Last we find all the elements of the largest reflection length in certain primiteve complex reflection groups defined in a 2-dimensional space.