The first Simple Sporadic Groups discovered. , , , , were discovered in 1861 and 1873 by Mathieu. Frobenius showed that all the Mathieu groups are Subgroups of .

The Mathieu groups are most simply defined as Automorphism groups of Steiner Systems. corresponds to and corresponds to . and are Transitive Permutation Groups of 11 and 23 elements.

The Orders of the Mathieu groups are

**References**

Conway, J. H. and Sloane, N. J. A. ``The Golay Codes and the Mathieu Groups.''
Ch. 11 in *Sphere Packings, Lattices, and Groups, 2nd ed.*
New York: Springer-Verlag, pp. 299-330, 1993.

Rotman, J. J. Ch. 9 in *An Introduction to the Theory of Groups, 4th ed.* New York: Springer-Verlag, 1995.

Wilson, R. A. ``ATLAS of Finite Group Representation.'' http://for.mat.bham.ac.uk/atlas/html/contents.html#spo.

© 1996-9

1999-05-26