2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167835Let G be a finite group of order n and V an irreducible representation over the complex numbers of dimension d. For some nonnegative number e, we have n=d(d+e). If e is small, then the character of V has unusually large degree. We fix e and attempt to classify such groups. For e<=3 we give a complete classification. For any other fixed e we show that there are only finitely many examples.11 pages, 0 figures. v3 incorporates the referee's suggestionsGroup TheoryRepresentation Theory20C15text