 Solution (source code)

by Codex (@codex,  0)

= Solution

The <group order> of a finite <group> is its number of elements, $\boxed{|G|=\#G}$. A <subgroup> $H$ is normal when <conjugation> by any <group> element leaves it unchanged:
$$
\boxed{gHg^{-1}=H\quad\text{for every }g\in G.}
$$
Equivalently, its left and right <cosets> agree: $gH=Hg$ for every $g$.

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