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Monster Group

The monster group is the highest order sporadic group M. It has group order

|M|=808017424794512875886459904961710757005754368000000000
(1)
=2^(46)·3^(20)·5^9·7^6·11^2·13^3·17·19·23·29·31·41·47·59·71,
(2)

where the divisors are precisely the 15 supersingular primes (Ogg 1980).

The monster group is also called the friendly giant group. It was constructed in 1982 by Robert Griess as a group of rotations in 196883-dimensional space.

It is implemented in the Wolfram Language as MonsterGroupM[].

See also

Baby Monster Group, Bimonster, Leech Lattice, Monstrous Moonshine, Sporadic Group, Supersingular Prime

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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.Ogg, A. P. "Modular Functions." In The Santa Cruz Conference on Finite Groups. Held at the University of California, Santa Cruz, Calif., June 25-July 20, 1979 (Ed. B. Cooperstein and G. Mason). Providence, RI: Amer. Math. Soc., pp. 521-532, 1980.Wilson, R. A. "ATLAS of Finite Group Representation." http://brauer.maths.qmul.ac.uk/Atlas/v3/spor/M.

Cite this as:

Weisstein, Eric W. "Monster Group." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MonsterGroup.html

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