Direct product of Z7 and D8

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Definition

This group is the external direct product of cyclic group:Z7 and dihedral group:D8. It is a group of order 56.

Arithmetic functions

Function	Value	Explanation
order	56
nilpotency class	2

GAP implementation

Group ID

This finite group has order 56 and has ID 9 among the groups of order 56 in GAP's SmallGroup library. For context, there are groups of order 56. It can thus be defined using GAP's SmallGroup function as:

SmallGroup(56,9)

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

gap> G := SmallGroup(56,9);

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

IdGroup(G) = [56,9]

or just do:

IdGroup(G)

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