(2,3,7)-triangle group

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Definition

The $(7,3,2)$-triangle group or $(2,3,7)$-triangle group is defined as the triangle group with parameters $(7,3,2)$. Equivalently, it is defined as:

$\langle s_{1},s_{2},s_{3}\mid s_{1}^{2}=s_{2}^{2}=s_{3}^{2}=(s_{1}s_{2})^{7}=(s_{2}s_{3})^{3}=(s_{3}s_{1})^{2}=e\rangle$.

Here, $e$ is the identity element.

The term $(7,3,2)$-triangle group or $(2,3,7)$-triangle group is also used for the subgroup of index two in this group, which we refer to (7,3,2)-von Dyck group.