Solution (source code)

= Solution
{c}

For a <group action>, the <orbit> and <stabilizer> are
$$
Gx=\{gx:g\in G\},\qquad G_x=\{g\in G:gx=x\}.
$$
The <orbit-stabilizer theorem> for a <finite group> states
$$
\boxed{|G|=|Gx|\,|G_x|.}
$$