I would welcome information on methods which have been found efficient
for recognising groups of small order.

I am assuming that some construction has produced a finitely presented
group G of order at most 100 (say). The question to be answered is:
"which group" is it?

It appears that the GAP group libraries do not include a library of
groups of small order. If there were such a library, then a selection
function of the type
OneLibraryGroup(isIsomorphic,G)
would do. Is this possible for the 2-Groups library?

A permutation representation of minimal degree would be helpful,
but this appears to require computation of the subgroup lattice,
which may be time-consuming.

A list of the normal subgroups is available speedily, so an
IsDirectSummand(G,N)
function would be helpful.

Chris Wensley (UWB, Bangor)