1.I.1B

(a) State the Orbit-Stabilizer Theorem for a finite group $G$ acting on a set $X$.

(b) Suppose that $G$ is the group of rotational symmetries of a cube $C$. Two regular tetrahedra $T$ and $T^{\prime}$ are inscribed in $C$, each using half the vertices of $C$. What is the order of the stabilizer in $G$ of $T$ ?

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