Monster Group

The highest order Sporadic Group $M$. It has Order

$$2^{46}\cdot 3^{20}\cdot 5^9\cdot 7^6\cdot 11^2\cdot 13^3\cdo... ...ot 19\cdot 23\cdot 29\cdot 31\cdot 41\cdot 47\cdot 59\cdot 71,$$

and is also called the Friendly Giant Group. It was constructed in 1982 by Robert Griess as a Group of Rotations in 196,883-D space.

See also Baby Monster Group, Bimonster, Leech Lattice

References

Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; and Wilson, R. A. Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups. Oxford, England: Clarendon Press, p. viii, 1985.

Conway, J. H. and Norton, S. P. ``Monstrous Moonshine.'' Bull. London Math. Soc. 11, 308-339, 1979.

Conway, J. H. and Sloane, N. J. A. ``The Monster Group and its 196884-Dimensional Space'' and ``A Monster Lie Algebra?'' Chs. 29-30 in Sphere Packings, Lattices, and Groups, 2nd ed. New York: Springer-Verlag, pp. 554-571, 1993.

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