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Determining conjugacy class of a subgroup from intersection of with conjugacy classes

Is a subgroup of a finite group uniquely determined, up to conjugation, by the set subset of conjugacy classes of the larger group that it intersects?

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Determining conjugacy class of a subgroup from intersection of conjugacy classes

Is a subgroup of a finite group uniquely determined, up to conjugation, by the set of conjugacy classes of the larger group that it intersects?