10.50 (1986)

Complex characters of a finite group $G$ induced by linear characters of cyclic subgroups are called induced cyclic characters of $G$. Computer-aided computations (A. V. Rukolaine, Abstracts of the 10th All–Union Sympos. on Group Theory, Gomel’, 1986, p. 199 (Russian)) show that there exist groups (for example, $\mathbb{S}_5$, $SL_2(13)$, $M_{11}$) all of whose irreducible complex characters are integral linear combinations of induced cyclic characters and the principal character of the group. Describe all finite groups with this property.