Primitive groups of degree 4096 to 8191 for PrimGrp in GAP

This database contains the primitive groups of degree 4096 to 8191. It is intended to be used in GAP via the PrimGrp library (https://gap-packages.github.io/primgrp/).

The groups were originally computed by Benjamin Mark Stratford and reported in Chapter 3 of the following PhD thesis:

Benjamin Mark Stratford,Topics in computational group theory relating to classifications of permutation groups. PhD thesis, University of Warwick, 2022.(http://webcat.warwick.ac.uk/record=b3821786)

Additional information such as the order, simplicity, solubility, O'Nan-Scott type, collected suborbits, transitivity, and socle type have also been computed for the convenience of the user, and to facilitate identification of an arbitrary primitive group. The primitive identification number of each group has been assigned according to the ordering in which the data was originally provided. Along with the generators of the group, this information is stored as a GAP record object.

In order to use this data, download the file "ExtendedPrimitiveGroupsData.tar" into the "data" directory of the PrimGrp library. Untar the file in this directory. This should result in a subdirectory called "ExtendedPrimitiveGroupsData" which contains files of the format "PrimitiveGroups_N_ID.g.gz" where N is the degree of the permutation group and ID is its primitive identification.  Do not decompress the files of the format "PrimitiveGroups_N_ID.g.gz". Do not move them into the "data" directory, but rather leave them in the "ExtendedPrimitiveGroupsData" subdirectory.

Note that the extended primitive groups data is reasonably large (~1GB) and ensure you have sufficient space available on your computer.

PrimGrp version 4.0.0 or later is required. For more information about how to use the primitive groups library in GAP see the PrimGrp documentation (https://gap-packages.github.io/primgrp/)