Direct product of Z3 and the Frobenius group of order 21

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This group is the direct product of the cyclic group cyclic group:Z3 and the Frobenius group of order 21. It is a group of order 63.

GAP implementation

Group ID

This finite group has order 63 and has ID 3 among the groups of order 63 in GAP's SmallGroup library. For context, there are groups of order 63. It can thus be defined using GAP's SmallGroup function as:

SmallGroup(63,3)

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

gap> G := SmallGroup(63,3);

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

IdGroup(G) = [63,3]

or just do:

IdGroup(G)

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