Direct product of D8 and Q8

View a complete list of particular groups (this is a very huge list!)[SHOW MORE]

Definition

This group is defined as the external direct product of dihedral group:D8 (the dihedral group of degree four and order eight) and quaternion group (the quaternion group of order eight).

GAP implementation

Group ID

This finite group has order 64 and has ID 230 among the groups of order 64 in GAP's SmallGroup library. For context, there are groups of order 64. It can thus be defined using GAP's SmallGroup function as:

SmallGroup(64,230)

For instance, we can use the following assignment in GAP to create the group and name it $G$:

gap> G := SmallGroup(64,230);

Conversely, to check whether a given group $G$ is in fact the group we want, we can use GAP's IdGroup function:

IdGroup(G) = [64,230]

or just do:

IdGroup(G)

to have GAP output the group ID, that we can then compare to what we want.

Other descriptions

The group can be constructed using GAP's SmallGroup and DirectProduct functions as:

DirectProduct(SmallGroup(8,3),SmallGroup(8,4))