On Artin's characters table of the group (Q2m Cp) when m is an odd number and p is prime number

Abstract

In this paper, we prove that the general form of Artin's characters table of the group (Q2m Cp ) such that Q2m be the Quaternion group of order 4m when m is an odd number and Cp be the cyclic group of order p when p is prime number and (Q2m×Cp) be direct product of Q2m and Cp such that (Q2m Cp ) = {(q,c):q Q2m ,c Cp} and |Q2m×Cp|=|Q2m|.|Cp|=4m.p=4pm. This table which depends on Artin's characters table of a quaternion group of order 4m when m is an odd number. which is denoted by Ar(Q2m Cp ).