  We obtain an explicit characterization of linear maps, in particular, quantum
channels, which are covariant with respect to an irreducible representation
($U$) of a finite group ($G$), whenever $U \otimes U^c$ is simply reducible
(with $U^c$ being the contragradient representation). Using the theory of group
representations, we obtain the spectral decomposition of any such linear map.
The eigenvalues and orthogonal projections arising in this decomposition are
expressed entirely in terms of representation characteristics of the group $G$.
This in turn yields necessary and sufficient conditions on the eigenvalues of
any such linear map for it to be a quantum channel. We also obtain a wide class
of quantum channels which are irreducibly covariant by construction. For
two-dimensional irrreducible representations of the symmetric group $S(3)$, and
the quaternion group $Q$, we also characterize quantum channels which are both
irreducibly covariant and entanglement breaking.
