Direct product of Z2 and Z14

This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this group
View a complete list of particular groups (this is a very huge list!)[SHOW MORE]

VIEW FACTS ABOUT THIS GROUP: All factsGroup property satisfactionsSubgroup property satisfactionsGroup property dissatisfactionsSubgroup property satisfactions
VIEW DEFINITIONS USING THIS AS EXAMPLE: All terms |Group properties |Subgroup properties|
VIEW FACTS USING THIS AS EXAMPLE: All facts |Group property non-implications |Subgroup property non-implications |Group metaproperty dissatisfactionsSubgroup metaproperty dissatisfactions

Definition

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

Properties

Property	Satisfied?	Explanation	Comment
Abelian group	Yes	Abelianness is direct product-closed
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.