Dicyclic group:Dic12

This group, sometimes denoted $$\operatorname{Dic}_{12}$$ and sometimes denoted $$\Gamma(3,2,2)$$, is defined in the following equivalent ways:


 * It is the member of family::dicyclic group (i.e., the binary dihedral group) of order $$12$$, and hence of degree $$3$$.
 * It is the member of family::binary von Dyck group with parameters $$(3,2,2)$$.

A presentation for the group is given by:

$$\langle a,b,c \mid a^3 = b^2 = c^2 = abc \rangle$$.

Other definitions
The group can also be defined using its presentation:

F := FreeGroup(3); G := F/[F.1^3 * F.2^(-2), F.2^2 * F.3^(-2), F.1 * F.2 * (F.3)^(-1)];