quasi-permutation representations of metacyclic 2-groups

by a quasi-permutation matrix we mean a square matrix over the complex field c with non-negative integral trace. thus, every permutation matrix over c is a quasipermutation matrix. for a given finite group g, let p(g) denote the minimal degree of a faithful permutation representation of g (or of a faithful representation of g by permutation matrices), let q(g) denote the minimal degree of a faithful representation of g by quasi-permutation matrices over the rational field q, and let c(g) be the minimal degree of a faithful representation of g by complex quasi-permutation matrices. in this paper, we will calculate the irreducible modules and characters of metacyclic 2-groups and we also find c(g), q(g) and p(g) for these groups.