Direct product of S3 and D10

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Definition

This group is the external direct product of symmetric group:S3 and dihedral group:D10. It is a group of order 60.

GAP implementation

Group ID

This finite group has order 60 and has ID 8 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(60,8)

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

gap> G := SmallGroup(60,8);

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

IdGroup(G) = [60,8]

or just do:

IdGroup(G)

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