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  "body": "\n## Example\n\nLet $G$ be a [[group|G5S1M9]] and let $H$ be a [[subgroup|0X1JXT47GA]] of $G$.\nLet $G/H$ be the set of the [[left cosets|03DEH43F4H]] of $H$ in $G$.\nThe map $G \\times G/H \\to G/H$, $(g, aH) \\mapsto gaH$, is an [[action|0WCY42EV9V]] of $G$ on $G/H$.\nThe map is well defined, because $aH = bH$ implies $gaH = gbH$.\nThe action is [[transitive|02GK6HZYBT]], because $(ba^{-1}) \\cdot aH = bH$.\nThe [[stabiliser|0AYMP41THN]] of the coset $aH$ is the conjugate subgroup $aHa^{-1}$.\nThe kernel of the associated homomorphism $G \\to \\operatorname{Sym}(G/H)$ is the [[normal core|0GETX79CJN]] of $H$, the intersection of all conjugates of $H$.\nFor $H = \\{e\\}$, this is the [[action by left multiplication|0K5TWJAGPD]].\n",
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