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<p><a id="X7D6FF2107D7F1D4E" name="X7D6FF2107D7F1D4E"></a></p>
<div class="ChapSects"><a href="chap1.html#X7D6FF2107D7F1D4E">1 <span class="Heading">Introduction to the <strong class="pkg">GAP</strong> Character Table Library</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X7EBC45767BEB936B">1.1 <span class="Heading">History of the <strong class="pkg">GAP</strong> Character Table Library</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X78D24D397B2E9813">1.2 <span class="Heading">What's New in <strong class="pkg">CTblLib</strong>,
Compared to Older Versions?</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap1.html#X839B2C7A7B592F20">1.2-1 <span class="Heading">What's New in Version 1.2?</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap1.html#X8129F9467ED8C5B2">1.2-2 <span class="Heading">What's New in Version 1.1?</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X82A988D47DFAFCFA">1.3 <span class="Heading">Acknowledgements</span></a>
</span>
</div>
</div>
<h3>1 <span class="Heading">Introduction to the <strong class="pkg">GAP</strong> Character Table Library</span></h3>
<p>The usefulness of <strong class="pkg">GAP</strong> for character theoretic tasks depends on the availability of many known character tables, and there are a lot of character tables in the <strong class="pkg">GAP</strong> table library. Of course, this library is "open" in the sense that it shall be extended. So we would be grateful for any further tables of interest sent to us for inclusion into our library. Please offer interesting new character tables via e-mail to <span class="URL"><a href="mailto:sam@math.rwth-aachen.de">sam@math.rwth-aachen.de</a></span>.</p>
<p>It depends on your <strong class="pkg">GAP</strong> installation whether the character table library is available. You can check this as follows.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">InstalledPackageVersion( "ctbllib" ) <> fail;</span>
true
</pre></div>
<p>If the result is <code class="keyw">false</code> then the library is not installed, and you may ask your system administrator for installing it, or install the library in your home directory, see Section <a href="chap4.html#X780747027FB9E58B"><span class="RefLink">4.5-1</span></a>.</p>
<p>For general information about character tables in <strong class="pkg">GAP</strong>, see Chapter <span class="RefLink">Reference: Character Tables</span>.</p>
<p>The <code class="file">doc</code> and <code class="file">htm</code> directories of the <strong class="pkg">GAP</strong> Character Table Library contain several files with examples of character theoretic computations, in PDF and HTML format. <a name="application_files">Currently these are</a></p>
<ul>
<li><p>Ambiguous class fusions, see <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ambigfus.pdf"><code class="file">doc/ambigfus.pdf</code></a></span> and <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ambigfus.htm"><code class="file">htm/ambigfus.htm</code></a></span>.</p>
</li>
<li><p>Constructions of character tables using table automorphisms, see <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctblcons.pdf"><code class="file">doc/ctblcons.pdf</code></a></span> and <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ctblcons.htm"><code class="file">htm/ctblcons.htm</code></a></span>.</p>
</li>
<li><p>Ordinary character tables, Brauer tables, and decomposition matrices, see <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctbldeco.pdf"><code class="file">doc/ctbldeco.pdf</code></a></span> and <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ctbldeco.htm"><code class="file">htm/ctbldeco.htm</code></a></span>.</p>
</li>
<li><p>Constructing the irreducible characters of <span class="SimpleMath">J_4</span> from one faithful character, see <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctblj4.pdf"><code class="file">doc/ctblj4.pdf</code></a></span> and <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ctblj4.htm"><code class="file">htm/ctblj4.htm</code></a></span>.</p>
</li>
<li><p>Computations of possible permutation characters, see <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctblpope.pdf"><code class="file">doc/ctblpope.pdf</code></a></span> and <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ctblpope.htm"><code class="file">htm/ctblpope.htm</code></a></span>.</p>
</li>
<li><p>Computations of common central extensions, see <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctocenex.pdf"><code class="file">doc/ctocenex.pdf</code></a></span> and <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ctocenex.htm"><code class="file">htm/ctocenex.htm</code></a></span>.</p>
</li>
<li><p>Some computations concerning the classification of groups with the property that all complex irreducible characters of the same degree are Galois conjugate (together with Klaus Lux), see <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/dntgap.pdf"><code class="file">doc/dntgap.pdf</code></a></span> and <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/dntgap.htm"><code class="file">htm/dntgap.htm</code></a></span>.</p>
</li>
<li><p>Hamiltonian cycles in the generating graphs of finite groups, see <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/hamilcyc.pdf"><code class="file">doc/hamilcyc.pdf</code></a></span> and <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/hamilcyc.htm"><code class="file">htm/hamilcyc.htm</code></a></span>.</p>
</li>
<li><p>Multiplicity-free permutation characters of the sporadic simple groups and their automorphism groups, see <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/multfree.pdf"><code class="file">doc/multfree.pdf</code></a></span> and <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/multfree.htm"><code class="file">htm/multfree.htm</code></a></span>.</p>
</li>
<li><p>Multiplicity-free permutation characters of central extensions of the sporadic simple groups, and their automorphic extensions (together with Jürgen Müller), see <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/multfre2.pdf"><code class="file">doc/multfre2.pdf</code></a></span> and <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/multfre2.htm"><code class="file">htm/multfre2.htm</code></a></span>.</p>
</li>
<li><p>A question about the group PSO<span class="SimpleMath">^+(8,5).S_3</span>, see <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/o8p2s3_o8p5s3.pdf"><code class="file">doc/o8p2s3_o8p5s3.pdf</code></a></span> and <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/o8p2s3_o8p5s3.htm"><code class="file">htm/o8p2s3_o8p5s3.htm</code></a></span>.</p>
</li>
<li><p>Probabilistic generation of finite simple groups, see <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/probgen.pdf"><code class="file">doc/probgen.pdf</code></a></span> and <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/probgen.htm"><code class="file">htm/probgen.htm</code></a></span>.</p>
</li>
<li><p>Solvable subgroups of maximal order in sporadic simple groups <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/sporsolv.pdf"><code class="file">doc/sporsolv.pdf</code></a></span> and <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/sporsolv.htm"><code class="file">htm/sporsolv.htm</code></a></span>.</p>
</li>
<li><p>Maintenance issues concerning the <strong class="pkg">GAP</strong> Character Table Library <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/maintain.pdf"><code class="file">doc/maintain.pdf</code></a></span> and <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/maintain.htm"><code class="file">htm/maintain.htm</code></a></span>.</p>
</li>
</ul>
<p>If you use the <strong class="pkg">GAP</strong> Character Table Library to solve a problem then please send a short e-mail to <span class="URL"><a href="mailto:sam@math.rwth-aachen.de">sam@math.rwth-aachen.de</a></span> about it. The <strong class="pkg">GAP</strong> Character Table Library database should be referenced as follows.</p>
<div class="example"><pre>
@misc{ CTblLib1.2.1,
author = {Breuer, T.},
title = {The \textsf{GAP} {C}haracter {T}able {L}ibrary,
{V}ersion 1.2.1},
month = {May},
year = {2012},
note = {\textsf{GAP} package},
howpublished = {http://www.math.rwth-aachen.de/\~{}Thomas.Breuer/ctbllib}
}
</pre></div>
<p>For referencing the <strong class="pkg">GAP</strong> system in general, use the entry <a href="chapBib.html#biBGAP">[GAP]</a> in the bibliography of this manual, see also</p>
<p><span class="URL"><a href="http://www.gap-system.org">http://www.gap-system.org</a></span>.</p>
<p><a id="X7EBC45767BEB936B" name="X7EBC45767BEB936B"></a></p>
<h4>1.1 <span class="Heading">History of the <strong class="pkg">GAP</strong> Character Table Library</span></h4>
<p>The first version of the <strong class="pkg">GAP</strong> Character Table Library was released with <strong class="pkg">GAP</strong> 3.1 in March 1992.</p>
<p>It was the first aim of this library to continue the character table library of the <strong class="pkg">CAS</strong> system (see <a href="chapBib.html#biBNPP84">[NPP84]</a>) in <strong class="pkg">GAP</strong>, as a part of the process of reimplementing the algorithms of <strong class="pkg">CAS</strong> in <strong class="pkg">GAP</strong>, see <span class="RefLink">Reference: History of Character Theory Stuff in GAP</span>. <strong class="pkg">GAP</strong> 3.1 provided only very restricted methods for computing character tables from groups, so its character theory part was concerned mainly with library tables.</p>
<p>A second aspect of the character table library was to make all character tables shown in the <strong class="pkg">Atlas</strong> of Finite Groups <a href="chapBib.html#biBCCN85">[CCNPW85]</a> available in <strong class="pkg">GAP</strong>. In fact <strong class="pkg">GAP</strong> turned out to provide a very good environment for systematic checks of these character tables.</p>
<p>To some extent, the access to the (ordinary) character tables in <a href="chapBib.html#biBCCN85">[CCNPW85]</a> was a prerequisite for storing also the corresponding Brauer character tables in the <strong class="pkg">GAP</strong> Character Table Library. Already <strong class="pkg">GAP</strong> 3.1 contained many of these tables. They have been computed mainly "outside of <strong class="pkg">GAP</strong>", using the methods described in <a href="chapBib.html#biBHJLP92">[HJLP]</a>, and part of the library has been published in the <strong class="pkg">Atlas</strong> of Brauer Characters <a href="chapBib.html#biBJLPW95">[JLPW95]</a>. One of the roles of <strong class="pkg">GAP</strong> was again to perform systematic checks.</p>
<p>Besides these projects, many individual character tables have been added to the <strong class="pkg">GAP</strong> Character Table Library since the times of <strong class="pkg">GAP</strong> 3.1. They were computed from groups or with character theoretic methods or using a combination of these two possibilities (see, e. g., <a href="chapBib.html#biBNPP84">[NPP84]</a> and <a href="chapBib.html#biBLP91">[LP91]</a>).</p>
<p>Section <a href="chap4.html#X7F5CE9D67B1498B0"><span class="RefLink">4.1</span></a> lists some of the sources. The changes in the <strong class="pkg">GAP</strong> Character Table Library since the release of <strong class="pkg">GAP</strong> 4.1 (in July 1999) are individually documented in the file <span class="URL"><a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctbldiff.pdf"><code class="file">doc/ctbldiff.pdf</code></a></span> of the package.</p>
<p>Currently the main focus in the development of the <strong class="pkg">GAP</strong> Character Table Library is –besides the addition of tables that appear to be interesting– the better interaction with other databases, such as the <strong class="pkg">Atlas</strong> of Group Representations and the <strong class="pkg">GAP</strong> Library of Tables of Marks (see the <strong class="pkg">GAP</strong> packages <strong class="pkg">AtlasRep</strong> and <strong class="pkg">TomLib</strong>) and <strong class="pkg">GAP</strong>'s group libraries, and an improvement of the "database" aspect of the character table library itself, see the sections <a href="chap3.html#X8784D56585604FD2"><span class="RefLink">3.1</span></a> and <a href="chap3.html#X791FFEA17DD18034"><span class="RefLink">3.5</span></a>.</p>
<p>Until the release of <strong class="pkg">GAP</strong> 4.3 in spring 2002, the <strong class="pkg">GAP</strong> Character Table Library had been a part of the main <strong class="pkg">GAP</strong> library. With <strong class="pkg">GAP</strong> 4.3, it was "split off" as a <strong class="pkg">GAP</strong> package.</p>
<p><a id="X78D24D397B2E9813" name="X78D24D397B2E9813"></a></p>
<h4>1.2 <span class="Heading">What's New in <strong class="pkg">CTblLib</strong>,
Compared to Older Versions?</span></h4>
<p><a id="sect:news"/></p>
<p><a id="X839B2C7A7B592F20" name="X839B2C7A7B592F20"></a></p>
<h5>1.2-1 <span class="Heading">What's New in Version 1.2?</span></h5>
<p>The following bugs were fixed in version 1.2.2.</p>
<ul>
<li><p>The functions <code class="func">AllCharacterTableNames</code> (<a href="chap3.html#X7C091641852BB6FE"><span class="RefLink">3.1-3</span></a>) and <code class="func">OneCharacterTableName</code> (<a href="chap3.html#X7EC4A57E8393D75C"><span class="RefLink">3.1-4</span></a>) ran into an error in certain situations, if the library had been extended by private tables, see Section <a href="chap4.html#X7F18333C7C6E5F9E"><span class="RefLink">4.7</span></a>. (As a consequence, the description of <code class="func">IsDuplicateTable</code> (<a href="chap3.html#X7FD4A9DF7CBAA418"><span class="RefLink">3.6-1</span></a>) has been extended.) Thanks to Alexander Konovalov and Lukas Maas for pointing out this error.</p>
</li>
<li><p>The function <code class="func">CharacterTableOfIndexTwoSubdirectProduct</code> (<a href="chap5.html#X7D0207B07B48FD06"><span class="RefLink">5.5-1</span></a>) returned a wrong result if the two factors were given by the same character table, for example in the case of <span class="SimpleMath">(A_5 × A_5).2</span> created as a subdirect product of two copies of <span class="SimpleMath">S_5</span>.</p>
</li>
</ul>
<p>Concerning character table data, we have the following.</p>
<ul>
<li><p>A few bugs in character tables have been fixed.</p>
</li>
<li><p>Several class fusions stored in character tables have been changed, in order to be more consistent with related data, see Section <a href="chap4.html#X8304BCF786C2BBB7"><span class="RefLink">4.9</span></a> for reasons of such changes.</p>
</li>
<li><p>Many new character tables have been added. For example, a character table is available for each table of marks in the <strong class="pkg">TomLib</strong> package.</p>
</li>
</ul>
<p>Like in earlier versions, the PDF file <code class="file">doc/ctbldiff.pdf</code> of the package lists the important changes, mainly related to the relevant simple groups. However, a probably more suitable overview is given by the <strong class="pkg">GAP</strong> readable file <code class="file">data/ctbldiff.dat</code>, which contains a complete overview of all changes, including the additions of class fusions. (Note that each added or changed fusion is mentioned twice in this list, once for the "from" table and once for the "to" table.) This list of changes can be shown using <code class="func">BrowseCTblLibDifferences</code> (<a href="chap3.html#X87CA74CF7B533CC6"><span class="RefLink">3.5-4</span></a>) if the <strong class="pkg">Browse</strong> package (see <a href="chapBib.html#biBBrowse">[BL14]</a>) is available.</p>
<p>Besides these changes of the data, the following features are new.</p>
<ul>
<li><p>A tutorial for beginners was added to the package manual, see Chapter <a href="chap2.html#X80D9421C7E7658E3"><span class="RefLink">2</span></a>, and the package manual was restructured. The manual is now based on the <strong class="pkg">GAPDoc</strong> package.</p>
</li>
<li><p>Generic constructions of Brauer tables are now available if the underlying ordinary table is encoded via <code class="func">ConstructMGA</code> (<a href="chap5.html#X7A948B397B5BC0AD"><span class="RefLink">5.8-1</span></a>), <code class="func">ConstructIndexTwoSubdirectProduct</code> (<a href="chap5.html#X8714D24B802DA949"><span class="RefLink">5.5-2</span></a>), or <code class="func">ConstructV4G</code> (<a href="chap5.html#X7C1CE54A864936E0"><span class="RefLink">5.8-4</span></a>), and if the Brauer tables of the compound tables are known.</p>
</li>
<li><p>The attributes <code class="func">FusionToTom</code> (<a href="chap3.html#X7B1AAED68753B1BE"><span class="RefLink">3.2-4</span></a>) and <code class="func">Maxes</code> (<a href="chap3.html#X8150E63F7DBDF252"><span class="RefLink">3.7-1</span></a>) are no longer set in duplicate tables. This can be regarded as a bugfix, in the following sense. For the sake of consistency, it would in general be necessary to apply a permutation to the fusion into the table of marks, and to add the class fusions from the tables of the maximal subgroups to the duplicate table.</p>
</li>
<li><p>The consistency checks for character tables have been improved and are now documented, see Section <a href="chap4.html#X7C19A1C08709A106"><span class="RefLink">4.8</span></a>. Due to these checks, several class fusions had to be replaced.</p>
</li>
<li><p>The concept of duplicate character tables is now explicit, see Section <a href="chap3.html#X7E5CFB187E313B11"><span class="RefLink">3.6</span></a>. As a consequence, the behaviour of <code class="func">AllCharacterTableNames</code> (<a href="chap3.html#X7C091641852BB6FE"><span class="RefLink">3.1-3</span></a>) has changed in situations where <code class="code">IsSimple</code> and <code class="code">IsSporadicSimple</code> (see <span class="RefLink">Reference: Group Operations Applicable to Character Tables</span>) occur, as follows. In earlier versions of the package, duplicate tables had automatically been excluded. From now on, duplicates can be excluded if one wants so, but they are not automatically excluded. This change may be regarded as a bugfix.</p>
</li>
<li><p>Several attribute values for character tables, such as <code class="func">Size</code> (<span class="RefLink">Reference: Size</span>) and <code class="func">NrConjugacyClasses</code> (<span class="RefLink">Reference: NrConjugacyClasses</span>) are now available without reading the character table data files, provided that the <strong class="pkg">Browse</strong> package (see <a href="chapBib.html#biBBrowse">[BL14]</a>) has been loaded. See the documentation of <code class="func">AllCharacterTableNames</code> (<a href="chap3.html#X7C091641852BB6FE"><span class="RefLink">3.1-3</span></a>) for details; this function is much faster if only these attributes appear in the conditions given. Thus it is now more reasonable to use this function for searches in the table library.</p>
</li>
<li><p><strong class="pkg">GAP</strong>'s group libraries provide many groups for which the Character Table Library contains the character tables. Given a character table from the library, one can list and access available groups with the functions described in Section <a href="chap3.html#X80C2448B7FC619B9"><span class="RefLink">3.3</span></a>, provided that the <strong class="pkg">Browse</strong> package (see <a href="chapBib.html#biBBrowse">[BL14]</a>) has been loaded.</p>
</li>
<li><p>An interactive overview of the contents is now available that is based on the <strong class="pkg">Browse</strong> package <a href="chapBib.html#biBBrowse">[BL14]</a>, see Section <a href="chap3.html#X791FFEA17DD18034"><span class="RefLink">3.5</span></a>.</p>
</li>
<li><p>Information about Deligne-Lusztig names of unipotent characters of finite groups of Lie type is now available, see Section <a href="chap3.html#X7C1F6C01852D7933"><span class="RefLink">3.4</span></a>.</p>
</li>
<li><p>An interface for reading <strong class="pkg">Magma</strong> tables was added, see Section <a href="chap6.html#X863CB6737FF9B740"><span class="RefLink">6.5</span></a>.</p>
</li>
</ul>
<p><a id="X8129F9467ED8C5B2" name="X8129F9467ED8C5B2"></a></p>
<h5>1.2-2 <span class="Heading">What's New in Version 1.1?</span></h5>
<p>First of all, of course several character tables were added; for an overview, see the file <code class="file">doc/ctbldiff.pdf</code> in the home directory of the package. Also lots of class fusions were added. This includes factor fusions onto the tables of the factor groups modulo the largest normal <span class="SimpleMath">p</span>-subgroups whenever the tables of the factors are available; these maps admit the automatic construction of the <span class="SimpleMath">p</span>-modular Brauer tables if the corresponding tables of the factors are available. For example, the <span class="SimpleMath">2</span>-modular Brauer table of the maximal subgroup of the type <span class="SimpleMath">2^10:M_22</span> in the group <span class="SimpleMath">Fi_22</span> is available because of the known <span class="SimpleMath">2</span>-modular table of <span class="SimpleMath">M_22</span> and the stored factor fusion onto the table of <span class="SimpleMath">M_22</span>.</p>
<p>Second, more information has been made more explicit, in the following sense.</p>
<ul>
<li><p><code class="func">Identifier</code> (<span class="RefLink">Reference: Identifier (for character tables)</span>) values of tables that are constructed from generic tables are now valid arguments of <code class="func">CharacterTable</code> (<span class="RefLink">Reference: CharacterTable</span>), for example <code class="code">CharacterTable( "C10" )</code> and <code class="code">CharacterTable( "Sym(5)" )</code> can be used to create the character table of the cyclic group of order <span class="SimpleMath">10</span> and of the symmetric group of degree <span class="SimpleMath">5</span>, respectively.</p>
</li>
<li><p>Attributes have been introduced that replace more or less hidden components (see Section <a href="chap3.html#X7CCFEC998135F6FA"><span class="RefLink">3.7</span></a>); in particular, the way how many ordinary tables are encoded via the construction from other tables is no longer encapsulated in a function call but instead the name of the function and the arguments are stored as an attribute value (see <code class="func">ConstructionInfoCharacterTable</code> (<a href="chap3.html#X851118377D1D6EC9"><span class="RefLink">3.7-4</span></a>)).</p>
</li>
<li><p>The functions that are used for the table constructions have been documented (see Chapter <a href="chap5.html#X7B915AD178236991"><span class="RefLink">5</span></a>).</p>
</li>
<li><p>Several consistency checks are now part of the package distribution, in the files <code class="file">gap4/test.gd</code> and <code class="file">gap4/test.gi</code>. However, currently they are not documented. The new file <code class="file">tst/testall.g</code> lists the files that belong to the "standard test suite". Further checks involving the <strong class="pkg">GAP</strong> Character Table Library are parts of the <strong class="pkg">GAP</strong> packages AtlasRep (see <a href="chapBib.html#biBAtlasRep">[WPNBB07]</a>) and TomLib.</p>
</li>
<li><p>As a part of the consistency checks, class fusions between character tables and from character tables into corresponding tables of marks have been recomputed, and the <code class="code">text</code> components have been standardized; this means that the texts express whether the maps are unique, unique up to table automorphisms, or ambiguous. However, currently this is not documented.</p>
</li>
<li><p>One can now avoid unloading the contents of data files, which can speed up computations involving many library tables. (In version 1.1, the function <code class="code">CTblLibSetUnload</code> had been provided for that. Since version 1.2, a <strong class="pkg">GAP</strong> 4.5 user preference replaces this function.)</p>
</li>
</ul>
<p>Third, several errors have been corrected (again see <code class="file">doc/ctbldiff.pdf</code>). Most of them affect class fusions, and for most of those, the term "error" could be regarded as not really appropriate. See <a href="chap4.html#X8304BCF786C2BBB7"><span class="RefLink">4.9</span></a> for details.</p>
<p>Finally, the <strong class="pkg">GAP</strong> functions for reading and writing other formats of character tables have been moved from the main <strong class="pkg">GAP</strong> library to this package (see Chapter <a href="chap6.html#X81C250407B91443F"><span class="RefLink">6</span></a>), because they are useful only for library tables. The <strong class="pkg">GAP</strong> 3 format is now also supported, mainly for documentation purposes (see Section <a href="chap6.html#X85BBAB537B4B72F5"><span class="RefLink">6.3</span></a>).</p>
<p><a id="X82A988D47DFAFCFA" name="X82A988D47DFAFCFA"></a></p>
<h4>1.3 <span class="Heading">Acknowledgements</span></h4>
<p>The development of the <strong class="pkg">GAP</strong> Character Table Library has been supported by several DFG grants, in particular the project "Representation Theory of Finite Groups and Finite Dimensional Algebras" (until 1991), and the Schwerpunkt "Algorithmische Zahlentheorie und Algebra" (from 1991 until 1997).</p>
<p>The functions for the conversion of <strong class="pkg">CAS</strong> tables to <strong class="pkg">GAP</strong> format have been written by Götz Pfeiffer. The functions for converting the so-called "Cambridge format" (in which the original data of the <strong class="pkg">Atlas</strong> of Finite Groups had been stored) to <strong class="pkg">GAP</strong> format have been written by Christoph Jansen.</p>
<p>The generic character tables of double covers of alternating and symmetric groups were contributed by Felix Noeske, see <a href="chapBib.html#biBNoe02">[Noe02]</a>.</p>
<p>The functions in Section <a href="chap3.html#X7C1F6C01852D7933"><span class="RefLink">3.4</span></a> (<code class="func">DeligneLusztigName</code> (<a href="chap3.html#X84B9D8EF84EB4145"><span class="RefLink">3.4-3</span></a>), <code class="func">DeligneLusztigNames</code> (<a href="chap3.html#X803FD7F87AFBBDE4"><span class="RefLink">3.4-2</span></a>), and <code class="func">UnipotentCharacter</code> (<a href="chap3.html#X79F645F278C27F23"><span class="RefLink">3.4-1</span></a>)) as well as the corresponding data for the finite groups of Lie type in the <strong class="pkg">GAP</strong> Character Table Library have been contributed by Michael Claßen-Houben, see <a href="chapBib.html#biBCla05">[Cla05]</a>.</p>
<p>Several character tables of maximal subgroups of covering groups of simple groups have been computed by Sebastian Dany, see <a href="chapBib.html#biBDan06">[Dan06]</a>.</p>
<p>Thanks to Frank Lübeck and Max Neunhöffer for their help with solving technical problems concerning the HMTL part of the example files that belong to the package documentation, and to Ian Hutchinson whose TeX to HTML translator <code class="code">TtH</code> was used to provide these HTML files.</p>
<p>Thanks to Frank Lübeck and Max Neunhöffer also for developing the <strong class="pkg">GAPDoc</strong> package, on which the manual of the <strong class="pkg">CTblLib</strong> package is based. The previously available documentation format had been completely inappropriate.</p>
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