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1 Introduction to the AtlasRep Package
 1.1 The ATLAS of Group Representations
 1.2 The GAP Interface to the ATLAS of Group Representations
 1.3 What's New in AtlasRep, Compared to Older Versions?
 1.4 Acknowledgements

1 Introduction to the AtlasRep Package

The aim of the GAP 4 package AtlasRep is to provide a link between GAP and databases such as the ATLAS of Group Representations [WWT+], which comprises generating permutations and matrices for many almost simple groups, and information about their maximal subgroups. This database is available independent of GAP at

The AtlasRep package consists of this database (see Section 1.1) and a GAP interface (see Section 1.2); the latter is extended by further information available via the internet (see Section 4.3).

This package manual has the following parts.

A tutorial

gives an overview how the functions of the package can be used, see Chapter 2.

User interface functions

are described in Chapter 3.

Customizations of the package

are described in Chapter 4.

Information how to extend the database

can be found in Chapter 5.

More technical information

can be found in the chapters 6 (concerning GAP objects that are introduced by the package) and 7 (concerning global variables and sanity checks).

1.1 The ATLAS of Group Representations

The ATLAS of Group Representations  [WWT+] consists of matrices over various rings, permutations, and shell scripts encoding so-called black box programs (see [Nic06] and Section 6.2). Many of these scripts are straight line programs (see [BSWW01], [SWW00], and Reference: Straight Line Programs) and straight line decisions (see Section 6.1). These programs can be used to compute certain elements in a group G from its standard generators (see [Wil96] and Section 3.3) for example generators of maximal subgroups of G or representatives of conjugacy classes of G.

The ATLAS of Group Representations has been prepared by Robert Wilson, Peter Walsh, Jonathan Tripp, Ibrahim Suleiman, Richard Parker, Simon Norton, Simon Nickerson, Steve Linton, John Bray, and Rachel Abbott (in reverse alphabetical order).

The information was computed and composed using computer algebra systems such as MeatAxe (see [Rin]), Magma (see [CP96]), and GAP (in reverse alphabetical order). Part of the constructions have been documented in the literature on almost simple groups, or the results have been used in such publications, see for example the bibliographies in [CCN+85] and [BN95] which are available online at

If you use the ATLAS of Group Representations to solve a problem then please send a short email to about it. The ATLAS of Group Representations database should be referenced with the entry [WWT+] in the bibliography of this manual.

If your work made use of functions of the GAP interface (see Section 1.2) then you should also reference this interface, using the information printed by the GAP function Cite (Reference: Cite).

For referencing the GAP system in general, use the entry [GAP19] in the bibliography of this manual, see also

1.2 The GAP Interface to the ATLAS of Group Representations

The GAP interface to the ATLAS of Group Representations consists of essentially two parts.

Information concerning the C-MeatAxe, including the manual [Rin], can be found at

The interface and this manual have been provided by Thomas Breuer, except for the interpreter for black box programs (see Section 6.2), which is due to Simon Nickerson. Comments, bug reports, and hints for improving the interface can be sent to

1.3 What's New in AtlasRep, Compared to Older Versions?

1.3-1 What's New in Version 2.1.8? (January 2024)

An example in Section 2.1-2 of the Tutorial had to be adjusted because the results of the function SmallerDegreePermutationRepresentation (Reference: SmallerDegreePermutationRepresentation) depend on random computations, in particular the implementation in GAP 4.13 may yield a nicer representation than had been shown before.

1.3-2 What's New in Version 2.1.7? (August 2023)

1.3-3 What's New in Version 2.1.6? (October 2022)

The package now requires the utils package [BGH+22], and uses its Download (Utils: Download) function for downloading remote files. The former user preference FileTransferTool of the AtlasRep package is no longer supported; it had been used in older versions to distinguish between different download tools.

A method for ConjugacyClasses (Reference: ConjugacyClasses attribute) has been added that uses a straight line program for computing class representatives of a group that has been created with AtlasGroup (3.5-8), provided such a program is available. Thanks to Frank Lübeck for suggesting this.

1.3-4 What's New in Version 2.1.5? (August 2022)

Two bugs concerning local file permissions and the handling of download failures were fixed. Thanks to Frank Lübeck and Fabian Zickgraf for reporting these problems.

1.3-5 What's New in Version 2.1.4? (August 2022)

A few changes in the code for downloading files were needed in order to make some CI tests happy.

1.3-6 What's New in Version 2.1.3? (August 2022)

The server address for the core part of the database has changed.

Additional table of contents files are now available, which contain checksums in SHA256 format instead of the checksums computed by CrcFile (Reference: CrcFile) and CrcString (Reference: CrcString). Note that the latter values can be interpreted only by GAP.

For 364 representations, the corresponding characters have been identified and can thus be used for accessing these representations with OneAtlasGeneratingSetInfo (3.5-6), see DisplayAtlasInfo (3.5-1).

1.3-7 What's New in Version 2.1.2? (March 2022)

Not much.

The release of Version 2.1.2 was necessary for technical reasons: Now the testfile mentioned in PackageInfo.g exits GAP in the end, and the external links in the package documentation were corrected (the links in version 2.1.1 pointed to a wrong directory).

1.3-8 What's New in Version 2.1.1? (February 2022)

1.3-9 What's New in Version 2.1.0? (May 2019)

The main differences to earlier versions concern extensions of the available data. Up to now, such extensions were possible only in the sense that one could notify certain locally available files to the package's functions. With this version, it becomes possible to notify also remote data files, i. e., data files which have to be downloaded before they can be read into GAP, in the same way as the data from the ATLAS of Group Representations. Two extensions of this kind become automatically available with this package version, see Section 5.1 for details.

Thus the focus of the package has changed. In earlier versions, it provided a GAP interface to the data in the ATLAS of Group Representations, whereas now this database is regarded as one collection (the "core part") among others. Where applicable, the package manual tries to distinguish between general data available to the AtlasRep functions and the data from the ATLAS of Group Representations.

In order to provide this new functionality, the following changes have been implemented. Note that some are incompatible changes, compared with earlier versions of the package.

The second major change concerns the handling of user parameters.

Finally, the following improvements have been added.

1.3-10 What's New in Version 1.5.1? (March 2016)

1.3-11 What's New in Version 1.5? (July 2011)

1.3-12 What's New in Version 1.4? (June 2008)

1.3-13 What's New in Version 1.3.1? (October 2007)

This version was mainly released in order to fix a few problems. Now one does not get warnings about unbound variables when the package is loaded and the GAP package IO [Neu14] is not available, and pathological situations in FFMatOrPermCMtxBinary (7.3-5) (concerning extremely short corrupted data files and different byte orderings in binary files) are handled more carefully.

Besides this, the two functions AtlasGroup (3.5-8) and AtlasSubgroup (3.5-9) were introduced, and the extended function QuaternionAlgebra (Reference: QuaternionAlgebra) of GAP 4.4.10 can now be used for describing base rings in OneAtlasGeneratingSetInfo (3.5-6) and AllAtlasGeneratingSetInfos (3.5-7). (This is the reason why this version of the package requires at least version 4.4.10 of GAP.)

1.3-14 What's New in Version 1.3? (June 2007)

1.3-15 What's New in Version 1.2? (November 2003)

Not much.

The release of Version 1.2 became necessary first of all in order to provide a package version that is compatible with GAP 4.4, since some cross-references into the GAP Reference Manual were broken due to changes of section names. Additionally, several web addresses concerning the package itself were changed and thus had to be adjusted.

This opportunity was used

For AtlasRep users, the new feature of GAP 4.4 is particularly interesting that due to better kernel support, reading large matrices over finite fields is now faster than it was in GAP 4.3.

1.3-16 What's New in Version 1.1? (October 2002)

The biggest change w. r. t. Version 1.1 is the addition of private extensions (see Chapter 5). It includes a new "free format" for straight line programs (see Section 5.2). Unfortunately, this feature requires the system program ls, so it may be not available for example under MS Windows operating systems. [But see Section 1.3-14.]

In order to admit the addition of other types of data, the implementation of several functions has been changed. Data types are described in Section 7.5. An example of a new data type are quaternionic representations (see Section 7.6). The user interface itself (see Chapter 3) remained the same.

As an alternative to perl, one can use wget now for transferring data files (see 4.2).

Data files can be read much more efficiently in GAP 4.3 than in GAP 4.2. In Version 1.1 of the AtlasRep package, this feature is used for reading matrices and permutations in MeatAxe text format with ScanMeatAxeFile (7.3-1). As a consequence, (at least) GAP 4.3 is required for AtlasRep Version 1.1.

The new compress component of the global variable AtlasOfGroupRepresentationsInfo (7.1-5) allows one to store data files automatically in gzipped form.

For matrix representations in characteristic zero, invariant forms and generators for the centralizer algebra are now accessible in GAP if they are contained in the source files –this information had been ignored in Version 1.0.

Additional information is now available via the internet (see 4.3).

The facilities for updating the table of contents have been extended.

The manual is now distributed also in PDF and HTML format; on the other hand, the PostScript format manual is no longer contained in the archives.

Apart from these changes, a few minor bugs in the handling of MeatAxe files have been fixed, typos in the documentation have been corrected, and the syntax checks for ATLAS straight line programs (see 7.4) have been improved.

1.4 Acknowledgements

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