On the Wedderburn decomposition of the total ring of quotients of certain Iwasawa algebras

Let G HΓ be the semidirect product of a finite group H and Γ Zₚ. Let F/ Qₚ be a finite extension with ring of integers OF. Then the total ring of quotients QF( G) of the completed group ring OF[[ G]] is a semisimple ring. We determine its Wedderburn decomposition by relating it to the Wedderburn decomposition of the group ring $F[H]$.