The GAP library of finite perfect groups provides, up to isomorphism, a list of all perfect groups whose sizes are less than 2 000 000. The groups of orders up to 10^6 have been enumerated by Derek F. Holt and Wilhelm Plesken and published in their book "Perfect Groups" (Oxford University Press, 1989). The remaining groups were enumerated by Alexander Hulpke, The perfect groups of order up to two million, Math. Comp. 91 (2022), no. 334, 1007-1017, https://doi.org/10.1090/mcom/3684.
In addition, this package provides methods for computing the perfect and
simple subgroups of a finite group, via the attributes
RepresentativesPerfectSubgroups, RepresentativesSimpleSubgroups and
ConjugacyClassesPerfectSubgroups.
This code used to be part of the GAP core system, and was moved into a separate package to reduce the size of the GAP distribution and to allow independent updates of the data.
Full information and documentation can be found in the manual, available as
PDF doc/manual.pdf or as HTML doc/chap0_mj.html, or on the package
homepage at
https://gap-packages.github.io/perfgrp/
PerfGrp is a needed package of GAP, so it is contained in every GAP distribution and no separate installation is required.
To install a development version, place the contents of this repository into
the pkg directory of your GAP installation, in a subdirectory named
perfgrp.
GAP 4.16 and earlier contain the perfect groups library themselves. This package can be loaded into such a version of GAP, but is then a no-op: GAP already provides everything it contains, so nothing is read.
For reasons of size, the data for the orders 1376256 and 1966080 is not
shipped with this package. If you need those groups, fetch perf27.grp
respectively perf33.grp from https://github.com/hulpke/extraperfect and
put them into the data subdirectory. GAP tells you which file it wants if
you ask for a group it does not have; see the section "Data Not Distributed
with the Package" in the manual.
Please report any issues you encounter at
https://github.com/gap-packages/perfgrp/issues
PerfGrp is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.
For details, see the file LICENSE distributed with this package or the FSF's
own site https://www.gnu.org/licenses/old-licenses/gpl-2.0.html.