Template:GAP ID

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

SmallGroup

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

gap> G := SmallGroup;

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

IdGroup(G) = [,]

or just do:

IdGroup(G)

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