A new characterization of L 2(r) by their Sylow numbers

Let G be a finite centerless group, let .(G) be the set of prime divisors of the order of G, and let n p (G) be the number of Sylow p-subgroups of G, that is, n p (G) = |Sylp(G)|. Set NS(G):= {n p (G)| p . .(G)}. In this paper, we are investigating whether L 2(r) is determined up to isomorphism by NS(L 2(r)) when r is prime.