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My professor mentioned how it is a way to get from one subgroup to other subgroups. I see this with some of our book's examples (Contemporary Abstract Algebra, Gallian) but I feel like I am still missing the big picture, point, purpose, whatever you may call it. Any explanations appreciated

goosechild
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    See here https://math.stackexchange.com/questions/11971/intuition-behind-conjugation-in-group-theory – Snaw Feb 22 '22 at 19:39
  • (Edit: this is greatly expanded by Qiaochu's answer from the question that Snaw linked.) Note that if the group is a matrix group, then $A\mapsto PAP^{-1}$ is a "change of basis" operation. That is, the element and its image under conjugation describe "the same essential object, but viewed through a different lens" (formally: the same linear transformation, written in different bases) – Eric Nathan Stucky Feb 22 '22 at 19:40

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