# $g$$H_{x}$$g^{-1}$=$H_{y}$, the orbits of action H on X have the same size?

G is a finite group that acts transitively on $X$. And H is a normal subgroup of G. The question asks about the size of orbit under the induced action of $H$ on $X$. I pick up $x$, $y$ from set $X$ and write it as $gx=y$.

Then I established the following: $g$$H_{x}$$g^{-1}$=$H_{y}$

($x$ and $y$ may not on the same orbit of action $H$, but I still prove that they have conjugate stabilizers)

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