# Symmetric Group on 3 Letters/Cycle Notation

## Cycle Notation for Symmetric Group on $3$ Letters
The symmetric group on $3$ letters can be given in cycle notation as follows:
 $\displaystyle e$ $:=$ $\displaystyle \text { the identity mapping}$ $\displaystyle p$ $:=$ $\displaystyle \tuple {1 2 3}$ $\displaystyle q$ $:=$ $\displaystyle \tuple {1 3 2}$
 $\displaystyle r$ $:=$ $\displaystyle \tuple {2 3}$ $\displaystyle s$ $:=$ $\displaystyle \tuple {1 3}$ $\displaystyle t$ $:=$ $\displaystyle \tuple {1 2}$