Template:GAP ID

Group ID

This finite group has [[groups of order {{{1}}}|order {{{1}}}]] and has ID {{{2}}} among the groups of order {{{1}}} in GAP's SmallGroup library. For context, there are groups of order {{{1}}}. It can thus be defined using GAP's SmallGroup function as:

SmallGroup({{{1}}},{{{2}}})

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

gap> G := SmallGroup({{{1}}},{{{2}}});

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

IdGroup(G) = [{{{1}}},{{{2}}}]

or just do:

IdGroup(G)

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