 Seitz notation

Write a Euclidean isometry as $\{R\mid t\}$, acting by $x\mapsto Rx+t$. Composition is $\{R\mid t\}\{R^{\prime }\mid t^{\prime }\}=\{R{R}^{\prime }\mid R{t}^{\prime }+t\}$. The translation subgroup is normal; the quotient is the crystallographic point group.