Direct product of S3 and Z7

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Definition

This group is a direct product of symmetric group:S3 and cyclic group:Z7. It is a group of order 42.

GAP implementation

Group ID

This finite group has order 42 and has ID 3 among the groups of order 42 in GAP's SmallGroup library. For context, there are groups of order 42. It can thus be defined using GAP's SmallGroup function as:

SmallGroup(42,3)

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

gap> G := SmallGroup(42,3);

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

IdGroup(G) = [42,3]

or just do:

IdGroup(G)

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