(2,3,7)-von Dyck group

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Definition

The $(7,3,2)$-von Dyck group, also sometimes termed the $(2,3,7)$-von Dyck group, is defined as the von Dyck group with parameters $(7,3,2)$. In other words, it has the presentation:

$\langle a,b,c\mid a^{7}=b^{3}=c^{2}=abc=e\rangle$

where $e$ denotes the identity element.

This group is also sometimes termed the $(7,3,2)$-triangle group, though that name is also used for the (7,3,2)-triangle group, in which this is a subgroup of index two.