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  "body": "\n## Example\n\nThe [[symmetric group|0515A6D2Y1]] $S_3$ has order $6$.\nThe identity has [[order|0JPYSD5E0B]] $1$.\nEach transposition $(1\\,2)$, $(1\\,3)$ and $(2\\,3)$ has order $2$.\nEach $3$-cycle $(1\\,2\\,3)$ and $(1\\,3\\,2)$ has order $3$.\nEach of the orders $1$, $2$ and $3$ divides $6$, as the [[result on element orders|08V7JHS3QZ]] states.\n\n## Remarks\n\nNo element has order $6$, so $S_3$ is not cyclic.\n",
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