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Groupprops β

(2,3,7)-triangle group

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.