An interesting class of problems in character theory arises from considering how the structure of a group G and the set {(1) |  2 Irr(G)} are related. It is proved that some nite groups are uniquely determined by their character tables. Recently Xu, Chen and Yan proved that if G is a simple K3-group, then G is uniquely determined by its order and one or both of its largest irreducible character degrees. In this paper, we determine groups with the same order and the same largest and second largest irreducible character degrees as PGL(2, 9) and as a consequence of our result it follows that PGL(2, 9) is characterizable by the structure of its complex group algebra.