Character degrees of 5-groups of maximal class

Abstract

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