# Direct product of D8 and Z6

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

## Definition

This group is defined in the following equivalent ways:

1. It is the external direct product of the following two groups: dihedral group:D8 and cyclic group:Z6.
2. It is the external direct product of the following three groups: dihedral group:D8, cyclic group:Z2, and cyclic group:Z3.
3. It is the external direct product of the following two groups: direct product of D8 and Z2 and cyclic group:Z3.
4. It is the external direct product of the following two groups: direct product of D8 and Z3 and cyclic group:Z2.

## GAP implementation

### Group ID

This finite group has order 48 and has ID 45 among the groups of order 48 in GAP's SmallGroup library. For context, there are 52 groups of order 48. It can thus be defined using GAP's SmallGroup function as:

SmallGroup(48,45)

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

gap> G := SmallGroup(48,45);

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

IdGroup(G) = [48,45]

or just do:

IdGroup(G)

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

### Other descriptions

Description Functions used
DirectProduct(DihedralGroup(8),CyclicGroup(6)) DirectProduct, DihedralGroup, CyclicGroup
DirectProduct(DihedralGroup(8),CyclicGroup(2),CyclicGroup(3)) DirectProduct, DihedralGroup, CyclicGroup