2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/103671We prove that a knowledge of the character degrees of a finite group G and of their multiplicities determines whether G has a Sylow p-subgroup as a direct factor. An analogous result based on a knowledge of the conjugacy class sizes was known. We prove variations of both results and discuss their similarities.9 pages, to be published in Proc. Amer. Math. SocGroup Theory20C05; 20C15; 20E45text