Every finite group of order 
can be represented as a
permutation group on 
letters, as first proved by Cayley in 1878 (Rotman 1995).
Cayley's Group Theorem
See also
Finite Group, Permutation Group, Symmetric GroupExplore with Wolfram|Alpha
References
Rotman, J. J. An Introduction to the Theory of Groups, 4th ed. New York: Springer-Verlag, p. 52, 1995.Referenced on Wolfram|Alpha
Cayley's Group TheoremCite this as:
Weisstein, Eric W. "Cayley's Group Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CayleysGroupTheorem.html