Finite solvable groups with exactly two nonlinear nonfaithful irreducible characters

Let [Formula: see text] be a solvable, nonnilpotent and directly indecomposable finite group. Suppose [Formula: see text] has exactly two nonlinear nonfaithful irreducible characters [Formula: see text]. In this paper, we classify the finite groups that satisfy these properties with [Formula: see text].