provenance.txt

Provenance of small group data set

Michael Torpey

This data set was created using GAP 4.10.0 and SmallGrp 1.3, called using the
script hosted at https://github.com/mtorpey/smallgrp-to-csv, which uses GAP's
"IO_Fork" to split into parallel threads to compute information for different
groups.

The data set contains an entry for each of the 11,759,892 groups of size up to
1023, up to isomorphism (most of these are of size 512).  In each entry are
several pieces of information about the group:

* the group's size (int),
* the group's ID in the small groups library (int),
* whether the group is abelian (bool),
* whether the group is nilpotent (bool),
* whether the group is supersolvable (bool),
* whether the group is solvable (bool),
* the length of the group's LG-series if solvable (int or "fail")
* the isomorphism class of the group's Frattini factor (a pair of ints
  describing the factor's ID in the small groups library)
* a structure description of the group (an string roughly describing its
  isomorphism class)

Of these pieces of information, all but the last are already known by the small
groups library, and GAP simply extracted the information from that library.  The
structure description was computed fresh for each group, and accounted for the
vast majority of processor time.

The computation took approximately 44 days to complete, from 25 May to 3 July
2019.  This was a parallel computation using 32 parallel threads on the "cormac"
machine in St Andrews.  Since the computation was very parallelisable (11
million small independent tasks) we can assume that the computation time was
around 32*44 = 1408 processor days, or about 4 processor years.

[SmallGrp]
B. Eick, H. U. Besche, and E. O'Brien.
SmallGrp (GAP package),
Version 1.3 (2018),
https://gap-packages.github.io/smallgrp

[GAP2019]
The GAP Group,
GAP - Groups, Algorithms, and Programming,
Version 4.10.2 (2019),
https://www.gap-system.org