Mathieu Group M11

The Mathieu group M11 is a finite simple group of order seven thousand nine hundred twenty, the smallest of the twenty-six sporadic simple groups, those finite simple groups that fall outside the standard infinite families in the classification of finite simple groups. It was discovered by the French mathematician Emile Mathieu in 1861, as the first of five related groups, M11, M12, M22, M23 and M24, that he found through his study of multiply transitive permutation groups acting on small sets of eleven to twenty-four points; M11 itself acts on eleven points. Because Mathieu found these groups more than a century before the sporadic groups were understood as a distinct class within the classification effort completed in the twentieth century, they are often called the earliest known sporadic groups. M11 is closely tied to the Steiner system on eleven points known as S(4,5,11), whose symmetries the group exactly captures.