The rational valued characters table of the group Q2p × D4 when p is a prime number

Abstract EN

The main purpose of this paper is to findthe rational valued characters table of the group Q2p × D4 when p is a prime number, which is denoted by ≡ * (Q2p × D4), where Q2p is denoted to quaternion group of order 4p, such that for each positive integer p, there are two generators x and y for Q2p satisfies Q2p = {xhyk, 0 , k=0,1}which has the properties x2p=y4=I,yxry-1=x-r and D4 is the dihedral group of order 8 is generate by a rotation r of order 4 and reflection s of order 2.

The eight elements of D4 can be written as: {I*,r,r2,r3,s,sr,sr2,sr3}with properties srks = r-k, k = 0,1,2,3.