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  "body": "\n## Example\n\nIn the [[symmetric group|0515A6D2Y1]] $S_3$, let $H = \\{e, (1\\,2)\\}$. Compose permutations from right to left.\n$H$ is a subgroup, because $(1\\,2)(1\\,2) = e$.\nThe [[left coset|05FD317V2W]] of $(1\\,2\\,3)$ is $(1\\,2\\,3)H = \\{(1\\,2\\,3), (1\\,3)\\}$.\nThe right coset of $(1\\,2\\,3)$ is $H(1\\,2\\,3) = \\{(1\\,2\\,3), (2\\,3)\\}$.\nThese cosets are different. Thus $H$ is not [[normal|0W77CVBCHQ]] in $S_3$.\n\n## Remarks\n\n$H$ has index $3$. Thus the result for index two does not apply to $H$.\n",
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