Direct product of Z2 and Z14

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Definition

This group is the external direct product of cyclic group:Z2 and cyclic group:Z14.

Properties

Property	Satisfied?	Explanation	Comment
Abelian group	Yes	Direct product of abelian groups is abelian
Nilpotent group	Yes	Abelian implies nilpotent

GAP implementation

Group ID

This finite group has order 28 and has ID 4 among the groups of order 28 in GAP's SmallGroup library. For context, there are groups of order 28. It can thus be defined using GAP's SmallGroup function as:

SmallGroup(28,4)

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

gap> G := SmallGroup(28,4);

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

IdGroup(G) = [28,4]

or just do:

IdGroup(G)

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