# Category:Examples of Symmetric Groups

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This category contains examples of Symmetric Group.

Let $S$ be a set.

Let $\map \Gamma S$ denote the set of permutations on $S$.

Let $\struct {\map \Gamma S, \circ}$ be the algebraic structure such that $\circ$ denotes the composition of mappings.

Then $\struct {\map \Gamma S, \circ}$ is called the **symmetric group on $S$**.

If $S$ has $n$ elements, then $\struct {\map \Gamma S, \circ}$ is often denoted $S_n$.

## Subcategories

This category has the following 3 subcategories, out of 3 total.

### S

- Symmetric Group on 4 Letters (10 P)
- Symmetric Group on 5 Letters (1 P)