= Minimal faithful permutation degree of the quaternion group
{title2=$\mu(Q_8)=8$}
The least size of a finite set on which the <quaternion group> acts faithfully is eight. Every nontrivial <subgroup> of $Q_8$ contains its central involution $-1$. In an action on fewer than eight points, the <orbit-stabilizer theorem> makes every <stabilizer subgroup> nontrivial, so $-1$ fixes every point. This rules out a <faithful group action>, even with several <group orbits>. The regular action on eight points is faithful by <Cayley theorem>.
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