I quite often use the SmallGroups library in GAP while collating lists
of graphs with various properties.
The questions are:
- is the order in which the groups appear arbitrary or are
there some principles underlying it? I notice that the
abelian groups don't seem to appear as the first few groups
of each order; this is mildly surprising for lists of groups,
but maybe there is a deeper underlying principle of which I
am not aware.
- is this order guaranteed to remain unchanged (so that if I
refer in a paper to "the 5044th group of order 512" then this
can definitely be recovered by the future reader)
Dr. Gordon F Royle, http://www.cs.uwa.edu.au/~gordon, email@example.com