Template:HallSenior

Hall-Senior number

This group of prime power order has [[groups of order {{{1}}}|order {{{1}}}]] and has Hall-Senior number {{{2}}} among the groups of order {{{1}}}. This information can be used to construct the group in GAP using the Gap3CatalogueGroup function as follows:

Gap3CatalogueGroup({{{1}}},{{{2}}})

WARNING: There is some disagreement between the GAP 3 catalogue numbers and the Hall-Senior numbers for some abelian groups, but it does not affect this group.

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

gap> G := Gap3CatalogueGroup({{{1}}},{{{2}}});

Conversely, to check whether a given group $G$ is in fact the group we want, we can use GAP's Gap3CatalogueIdGroup function:

Gap3CatalogueIdGroup(G) = [{{{1}}},{{{2}}}]

or just do:

Gap3CatalogueIdGroup(G)

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