Cayley's Group Theorem

Every Finite Group of order $n$ can be represented as a Permutation Group on $n$ letters, as first proved by Cayley in 1878 (Rotman 1995).

See also Finite Group, Permutation Group

References

Rotman, J. J. An Introduction to the Theory of Groups, 4th ed. New York: Springer-Verlag, p. 52, 1995.