Direct product of Z6 and D10

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Definition

This group is the external direct product of cyclic group:Z6 and dihedral group:D10. It is a group of order 60.

GAP implementation

Group ID

This finite group has order 60 and has ID 10 among the groups of order 60 in GAP's SmallGroup library. For context, there are groups of order 60. It can thus be defined using GAP's SmallGroup function as:

SmallGroup(60,10)

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

gap> G := SmallGroup(60,10);

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

IdGroup(G) = [60,10]

or just do:

IdGroup(G)

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