Non-solvable groups, whose character degrees are products of at most two prime numbers (Q1084174)

Let \(n\in {\mathbb{N}}\), \(n=p_ 1^{a_ 1}...p_ k^{a_ k}\) its prime decomposition, \(\omega (n)=a_ 1+...+a_ k\). If Irr(G) is the set of irreducible complex characters of the finite group G, then define \(\omega (G)=\max_{\chi \in Irr(G)}\omega (\chi (1)).\) In this paper a complete classification of the non-solvable groups G with \(\omega (G)=2\) is given.