Dicyclic group:Dic12

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

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

A presentation for the group is given by:

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

GAP implementation

Group ID

The group has ID $1$ among the groups of order $12$. Hence, it can be defined using GAP's SmallGroup function:

SmallGroup(12,1)

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)];