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This group is the dihedral group of order .
This finite group has order 24 and has ID 6 among the groups of order 24 in GAP's SmallGroup library. For context, there are 15 groups of order 24. It can thus be defined using GAP's SmallGroup function as:
For instance, we can use the following assignment in GAP to create the group and name it :
gap> G := SmallGroup(24,6);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [24,6]
or just do:
to have GAP output the group ID, that we can then compare to what we want.
The group can be defined using GAP's DihedralGroup function: