= Conjugacy classes of the symmetry group of a square
{title2=$\{e\},\ \{r^2\},\ \{r,r^3\},\ \{s,r^2s\},\ \{rs,r^3s\}$}
The displayed <conjugacy classes> have sizes one, one, two, two and two. The identity and half-turn are <central elements>. Reflection sends $r$ to $r^{-1}$, pairing the two quarter-turns. Conjugating a reflection by $r$ sends $r^ks$ to $r^{k+2}s$; conjugating by $s$ sends it to $r^{-k}s$. Thus the parity of $k$ is invariant under <conjugation>, separating the axis reflections from the diagonal reflections, and each displayed pair is one <conjugacy class>.
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