# What could the meaning of “invariant of $G$” be?

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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What context? What is a subdegree? –  Qiaochu Yuan May 23 '12 at 15:53
@QiaochuYuan: Permutaion Groups by J.D.Dixon. It is a lenght of the orbit of one of the point stablizres. Thanks –  Babak S. May 23 '12 at 16:04
I don't have this book and cannot understand what is meant here. Can you quote a longer passage? –  Qiaochu Yuan May 23 '12 at 16:25
@QiaochuYuan: Thanks for the time Prof.,in a Theorem 3.2B., he took somewhere a $\Sigma$ subset of $\Omega$ x $\Omega$ an $G$-invarant when for all $x\in G$, $\Sigma(\alpha)^x=\Sigma(\alpha^x)$ wherein a group $G$ acts transitively on the set $\Omega$. Is this the same he quoted above? –  Babak S. May 23 '12 at 16:45
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. –  j.p. May 24 '12 at 7:11