The Cyclic Decomposition Of cf(Q_4q×C_5)/ R ̅(Q_4q×C_5)

. In this paper, we propose the cyclic decomposition of factor group , and  is Z-valued class functions direct product  under operation addition, is subgroup generalized characters .Then   an abelian denoted by  where quaternion order  and cyclic  Also, find the  rational  valued  characters  table  of   when prime numbers is  given  as  follows : (1)  in paper prove that (2)