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Let G be a finite group and n_{p}(G) be the number of Sylow <sub>p- subgroup of G. In this work it is proved if G is a centerless group and n_{p}(G)=n_{p}(L_{2}(r)), for every prime p in pi (G), where r is prime number, r^2 does not divide |G| and r is not Mersenne prime, then L_{2}(r)<=G<=Aut(L_{2}(r)

<b>On recognition of simple group <i>L<sub>2</sub></i>(<i>r</i>) by the number of Sylow subgroups