We show that the character table of a finite group G determines whether a Sylow 2-subgroup of G is generated by 2 elements, in terms of the Galois action on characters. Our proof of this result requires the use of the Classification of Finite Simple Groups and provides new evidence for the so-far elusive Alperin–McKay–Navarro conjecture.
Classification
subjects
Mathematics
keywords
sylow 2-subgroups; charactertables; principal blocks;alperin–galois-mckay conjecture