On quadratic conjecture

Quadratic conjecture is a strengthening of oliver’s [Formula: see text]-group conjecture. Let [Formula: see text] be a [Formula: see text]-group of maximal class of order [Formula: see text]. We prove that if [Formula: see text] or [Formula: see text] then [Formula: see text] satisfies Quadratic Conjecture. Hence, the quadratic conjecture holds if [Formula: see text] is a [Formula: see text]-group of maximal class where [Formula: see text].