(2,3,7)-triangle group

Definition
The $$(7,3,2)$$-triangle group or $$(2,3,7)$$-triangle group is defined as the member of family::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.