الخلاصة

The main purpose of this paper is to prove that the general form of a rational valued characters table of the group (Q2m C4)such that Q2m be the Quaternion group of order 4m when m is an even number and C4 be the cyclic group of order 4 and (Q2m×C4), be direct product of Q2m and C4 such that Q2m C4 = {(a,b):a Q2m ,b C4} and |Q2m×C4|=|Q2m|.|C4|=4m.4=16m. This table depends on a rational valued characters table of a quaternion groupof order 4m when m is an even number and is denoted by (Q2m C4 ).