الخلاصة

The main purpose of this paper is to find The Cyclic decomposition of the group (Q2m C4) when m= ,h,r ∈ Z+ and p is prime number, which is denoted by AC (Q2m ×C4) where Q2m is the Quaternion group and C4 is the cyclic group of order 4 . We have also found the general form of Artin's characters table of Ar(Q2m×C4) when m= , h,r ∈ Z+ and p is prime number.