The generalized Taft Hopf algebra Hn,d is an Hn,d -module under the ad- joint actions. In this paper all submodules of such a module are presented, and a decomposition of such a module into indecomposable direct summands is given. Al- so, the adjoint actions of Hn,d on itself are used to present the Killing matrix and the Killing radical of Hn,d .
