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In a context, the author wrote that for a finite permutation group $G$ acting on a set $\Omega$ of degree $n$, the list of subdegrees is an invariant of the group. What could the meaning of "invariant of $G$" be? Does it mean invariant of group under the group action or I am wrong?

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    The lengths of the orbits of a point stabilizer are invariants of the *permutation group* $G$. So yes, it's an invariant of the group action. Different action have (generally) different subdegrees.2012-05-24

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