(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:

$\langle s_1, s_2, s_3 \mid s_1^2 = s_2^2 = s_3^2 = (s_1s_2)^7 = (s_2s_3)^3 = (s_3s_1)^2 = e \rangle$.

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.