Recognizing the Automorphism Groups of Mathieu Groups

It is a well-known fact that characters of a finite group can giveimportant information about the structure of the group. It was alsoproved by the third author that a finite simple group can beuniquely determined by its character table. Here the authors attemptto investigate how to characterize a finite almost-simple group byusing less information of its character table, and successfullycharacterize the automorphism groups of Mathieu groups by theirorders and at most two irreducible character degrees of theircharacter tables.