How is s decomposed into h-orbits

Reference no: EM13193781

Let n=pm such that p is the largest prime factor and n is divisible by p only once. Let G be of order n. Let H be a Sylow p-subgroup of G, and S is the set of all Sylow p-subgroups. How is S decomposed into H-orbits?

First of all, I can't tell whether this means we're looking for the orbits of H under the actions of G (in which case there is only one, as all Sylow p-subgroups are conjugate.) So I assume that's not what it's saying, and rather it means, "how is S partitioned when we have S acting on H?" Or does H-orbits mean something else? Regardless, I'm not sure how to go about the problem.

Reference no: EM13193781

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