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  "body": "\n## Summary\n\nIn mathematics, especially in the area of algebra known as group theory, the **holomorph** of a group $G$, denoted $\\operatorname{Hol}(G)$, is a group that simultaneously contains (copies of) $G$ and its [[automorphism group|0CWXCWP0Y0]] $\\operatorname{Aut}(G)$. It provides interesting examples of groups, and allows one to treat group elements and group automorphisms in a uniform context. The holomorph can be described as a [[semidirect product|014E1DZQE8]] or as a permutation group.\n",
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