Let \(n\geq 2\). The symmetric group \(S_n\) is the group with presentation \[ S_n \coloneqq \gens{ \sigma_1, \ldots, \sigma_{n-1} \st \sigma_i^2 \ (1\leq i\leq n-1),\ \sigma_i\sigma_j\sigma_i^{-1}\sigma_j^{-1} \ (\abs{i-j}\geq 2),\ \sigma_i \sigma_{i+1} \sigma_i \sigma_{i+1}^{-1} \sigma_i^{-1} \sigma_{i+1}^{-1} \ (1\leq i\leq n-2) }. \]
Sending \(\sigma_i\) to the transposition \((i, i+1)\) identifies this group with the group of bijections of \(\theset{1, \ldots, n}\).