Until 1965, when Janko  established the existence of his finite simple group J1, the five Mathieu groups were the only known examples of isolated finite simple groups. In 1951, R. G. Stanton  showed that M12 and M24 were determined uniquely by their order. Recent characterizations of M22 and M23 by Janko , M22 by D. Held , and M11 by W. J. Wong , have facilitated the unique determination of the three remaining Mathieu groups by their orders. D. Parrott  has so characterized M22 and M11, while this paper is an outline of the characterization of M23 in terms of its order.
(Received March 04 1969)
(Revised November 25 1969)