Symmetric Group on 4 Letters

Group Example
Let $S_4$ denote the set of permutations on $4$ letters.

The symmetric group on $4$ letters is the algebraic structure:
 * $\struct {S_4, \circ}$

where $\circ$ denotes composition of mappings.

It is usually denoted, when the context is clear, without the operator: $S_4$.

Cycle Notation
It can be expressed in the form of permutations given in cycle notation as follows:

Cayley Table
The Cayley table of $S_4$ can be written:

Also see

 * Symmetric Group is Group, which demonstrates that this is a (finite) group.