Character degrees of 5-groups of maximal class

Let be a 5-group of maximal class with major centralizerG1=CG⁢(G2/G4)G_{1}=C_{G}({G_{2}}/{G_{4}}). In this paper, we prove that the irreducible character degrees of a 5-group of maximal class are almost determined by the irreducible character degrees of the major centralizerG1G_{1}and show that the set of irreducible character degrees of a 5-group of maximal class is either{1,5,53}\{1,5,5^{3}\}or{1,5,…,5k}\{1,5,\ldots,5^{k}\}withk≥1k\geq 1.