  An approach to representations of finite groups is presented without recourse
to character theory. Considering the group algebra C[G] as an algebra of linear
maps on C[G] (by left multiplication), we derive the primitive central
idempotents as a simultaneous eigenbasis of the centre, Z(C[G]). We apply this
framework to obtain the irreducible representations of a class of finite
meta-abelian groups. In particular, we give a general construction of the
isomorphism between simple blocks of C[G] and the corresponding matrix algebra
where G can be any finite group.
