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<h1>The <strong class="pkg">GAP</strong> Character Table Library</h1>
<p>(Version 1.3.11)</p>
</div>
<p><b>Thomas Breuer
</b>
<br />Email: <span class="URL"><a href="mailto:sam@math.rwth-aachen.de">sam@math.rwth-aachen.de</a></span>
<br />Homepage: <span class="URL"><a href="https://www.math.rwth-aachen.de/~Thomas.Breuer">https://www.math.rwth-aachen.de/~Thomas.Breuer</a></span>
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<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 2003–2025 by Thomas Breuer</p>
<p>This package may be distributed under the terms and conditions of the GNU Public License Version 3 or later, see <span class="URL"><a href="http://www.gnu.org/licenses">http://www.gnu.org/licenses</a></span>.</p>
<p><a id="X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8"></a></p>
<div class="contents">
<h3>Contents<a id="contents" name="contents"></a></h3>
<div class="ContChap"><a href="chap1.html#X86DEA3CF7802FFF7">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#X7ED5D4B77E9F2A4C">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#X7DFD446B7840A6E0">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#X84BDBA6B7F5900CC">1.2-1 <span class="Heading">What's New in Version 1.3.11?
(May 2025)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap1.html#X85710FDF79D428D2">1.2-2 <span class="Heading">What's New in Version 1.3.9? (March 2024)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap1.html#X78A8624787A5F2BB">1.2-3 <span class="Heading">What's New in Version 1.3.8? (March 2024)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap1.html#X87C0A6BA86AF8C25">1.2-4 <span class="Heading">What's New in Version 1.3.7? (January 2024)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap1.html#X788E2D9E8715CEBF">1.2-5 <span class="Heading">What's New in Version 1.3.6? (May 2023)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap1.html#X853CED1A7F4A7CB6">1.2-6 <span class="Heading">What's New in Version 1.3.5? (March 2023)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap1.html#X8673993582B1792E">1.2-7 <span class="Heading">What's New in Version 1.3.4? (April 2022)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap1.html#X81F15ABF81515359">1.2-8 <span class="Heading">What's New in Version 1.3.3? (January 2022)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap1.html#X7C0B3B6D7EC044DC">1.2-9 <span class="Heading">What's New in Version 1.3.2? (March 2021)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap1.html#X79418416826FE5F2">1.2-10 <span class="Heading">What's New in Version 1.3.1? (April 2020)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap1.html#X83D8236D7E750DFE">1.2-11 <span class="Heading">What's New in Version 1.3.0? (December 2019)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap1.html#X7BC6B5FD7F720EA0">1.2-12 <span class="Heading">What's New in Version 1.2.2? (March 2013)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap1.html#X7E26A5FD7EBB4FA1">1.2-13 <span class="Heading">What's New in Version 1.2.0 and 1.2.1? (May 2012)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap1.html#X79402202865D152A">1.2-14 <span class="Heading">What's New in Version 1.1? (November 2003)</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>
<div class="ContChap"><a href="chap2.html#X7C4E7E1181E82D8E">2 <span class="Heading">Tutorial for the <strong class="pkg">GAP</strong> Character Table Library</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X86B34875862028E8">2.1 <span class="Heading">Concepts used in 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="chap2.html#X84930B2D7849E019">2.2 <span class="Heading">Accessing a Character Table from the Library</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X8658DC3A83B5A98B">2.2-1 <span class="Heading">Accessing a Character Table via a name</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7AA474817D17BF49">2.2-2 <span class="Heading">Accessing a Character Table via properties</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7C6BFB4384CAFFC8">2.2-3 <span class="Heading">Accessing a Character Table via a Table of Marks</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7E6AF18C7F139F54">2.2-4 <span class="Heading">Accessing a Character Table relative to another Character Table
</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7CD1E9AA871848EC">2.2-5 <span class="Heading">Different character tables for the same group</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X83B721F3801ED6D1">2.3 <span class="Heading">Examples of Using the <strong class="pkg">GAP</strong> Character Table Library</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X87AC9A4181AC369C">2.3-1 <span class="Heading">Example: Ambivalent Simple Groups</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7AD705F685FBF179">2.3-2 <span class="Heading">Example: Simple <span class="SimpleMath">p</span>-pure Groups</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7C2C7B138646D0C5">2.3-3 <span class="Heading">Example: Simple Groups with only one <span class="SimpleMath">p</span>-Block</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7FA308D585DC1B40">2.3-4 <span class="Heading">Example:The Sylow <span class="SimpleMath">3</span> subgroup of <span class="SimpleMath">3.O'N</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X83BF83D87BC1B123">2.3-5 <span class="Heading">Example: Primitive Permutation Characters of <span class="SimpleMath">2.A_6</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X808DD8997F10D429">2.3-6 <span class="Heading">Example: A Permutation Character of <span class="SimpleMath">Fi_23</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7A23CB7D8267FE55">2.3-7 <span class="Heading">Example: Non-commutators in the commutator group</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X79CDDEE67A41EAB8">2.3-8 <span class="Heading">Example: An irreducible <span class="SimpleMath">11</span>-modular character of <span class="SimpleMath">J_4</span>
(December 2018)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X8135F74080E50B14">2.3-9 <span class="Heading">Example: Tensor Products that are Generalized Projectives
(October 2019)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7AD5E36B7D44C507">2.3-10 <span class="Heading">Example: Certain elementary abelian subgroups in quasisimple groups
(November 2020)</span></a>
</span>
</div></div>
</div>
<div class="ContChap"><a href="chap3.html#X7EB517EB7A50A58F">3 <span class="Heading">The User Interface to the <strong class="pkg">GAP</strong> Character Table Library</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7A5EECF8853A05A0">3.1 <span class="Heading">Accessing Data of the <strong class="pkg">CTblLib</strong> Package</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X818A9DE5799A4809">3.1-1 <span class="Heading">Admissible Names for Character Tables in <strong class="pkg">CTblLib</strong>
</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X86C06F408706F27A">3.1-2 CharacterTable</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7E42C22278DA4048">3.1-3 BrauerTable</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7C091641852BB6FE">3.1-4 AllCharacterTableNames</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7EC4A57E8393D75C">3.1-5 OneCharacterTableName</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X845DEEE282D4F1EB">3.1-6 NameOfEquivalentLibraryCharacterTable</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7EED71B4827BEBFA">3.2 <span class="Heading">The Interface to the <strong class="pkg">TomLib</strong> Package</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X8400C0397CA2FA3C">3.2-1 TableOfMarks</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X87110C1584D09BE4">3.2-2 CharacterTable</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7A82CB487DBDDC53">3.2-3 FusionCharTableTom</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7B1AAED68753B1BE">3.2-4 FusionToTom</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X8435BFE878FFFDAB">3.2-5 NameOfLibraryCharacterTable</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X83D85EB2792D9D22">3.3 <span class="Heading">The Interface to <strong class="pkg">GAP</strong>'s Group Libraries</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X78DCD38B7D96D8A4">3.3-1 GroupInfoForCharacterTable</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X87CFDC8081767CA4">3.3-2 KnowsSomeGroupInfo</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X78B7A5DB87B5285C">3.3-3 CharacterTableForGroupInfo</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X804D2AC37E0D4755">3.3-4 GroupForGroupInfo</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X83B9EFB47CE0A617">3.3-5 GroupForTom</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X8032EF83823B1D88">3.3-6 AtlasStabilizer</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7AADD757809DFDD5">3.3-7 IsNontrivialDirectProduct</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7C1F6C01852D7933">3.4 <span class="Heading">Unipotent Characters of Finite Groups of Lie Type</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X79F645F278C27F23">3.4-1 UnipotentCharacter</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X803FD7F87AFBBDE4">3.4-2 DeligneLusztigNames</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X84B9D8EF84EB4145">3.4-3 DeligneLusztigName</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X78A05C0A82E23048">3.4-4 KnowsDeligneLusztigNames</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7900893987A89915">3.5 <span class="Heading"><strong class="pkg">Browse</strong> Applications Provided by
<strong class="pkg">CTblLib</strong></span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X8684C73E844E7033">3.5-1 DisplayCTblLibInfo</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7A038A267CD17032">3.5-2 BrowseCTblLibInfo</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X83FDD44E7E0AE885">3.5-3 BrowseCommonIrrationalities</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X87CA74CF7B533CC6">3.5-4 BrowseCTblLibDifferences</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X8135745381E1C0E2">3.5-5 BrowseAtlasContents</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X810789F77F20C839">3.5-6 DisplayAtlasContents</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X86AC6408815EF122">3.5-7 BrowseAtlasMap</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X875A6BB485A49976">3.5-8 DisplayAtlasMap</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X79DC72707B08A701">3.5-9 BrowseAtlasTable</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X79E3F783818FE75A">3.5-10 BrowseAtlasImprovements</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7E5CFB187E313B11">3.6 <span class="Heading">Duplicates of Library Character Tables</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7FD4A9DF7CBAA418">3.6-1 IsDuplicateTable</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X860F49407882658F">3.6-2 IdentifierOfMainTable</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7C83435B78DE62F6">3.6-3 IdentifiersOfDuplicateTables</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7CCFEC998135F6FA">3.7 <span class="Heading">Attributes for Library Character Tables</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X8150E63F7DBDF252">3.7-1 Maxes</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X82DC2E7779322DA8">3.7-2 ProjectivesInfo</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X82A008987DB887C2">3.7-3 ExtensionInfoCharacterTable</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X851118377D1D6EC9">3.7-4 ConstructionInfoCharacterTable</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X871562FD7F982C12">3.7-5 InfoText</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X867813EB79DC6953">3.7-6 IsAtlasCharacterTable</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap4.html#X85854AF07F2F8745">4 <span class="Heading">Contents of the <strong class="pkg">GAP</strong> Character Table Library</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X80EEFF8B79856A75">4.1 <span class="Heading">Ordinary and Brauer Tables in the <strong class="pkg">GAP</strong> Character Table Library
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X8569BC8E7A9D4BCE">4.1-1 <span class="Heading">Ordinary Character Tables</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X7AD048607A08C6FF">4.1-2 <span class="Heading">Brauer Tables</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X81E3F9A384365282">4.2 <span class="Heading">Generic Character Tables</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X78CD9A2D8680506B">4.2-1 <span class="Heading">Available generic character tables</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X78DA225F78F381C9">4.2-2 CharacterTableSpecialized</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X7C2CB9E07990B63D">4.2-3 <span class="Heading">Components of generic character tables</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X7D693E9787073E30">4.2-4 <span class="Heading">Example: The generic table of cyclic groups</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X81231BCE79486FA3">4.2-5 <span class="Heading">Example: The generic table of the general linear group GL<span class="SimpleMath">(2,q)</span>
</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X7F44BD4B79473085">4.3 <span class="Heading"><strong class="pkg">Atlas</strong> Tables</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X7CC608CD8690F9B1">4.3-1 <span class="Heading">Improvements to the <strong class="pkg">Atlas</strong></span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X7FED949A86575949">4.3-2 <span class="Heading">Power Maps</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X824823F47BB6AD6C">4.3-3 <span class="Heading">Projective Characters and Projections</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X78732CDF85FB6774">4.3-4 <span class="Heading">Tables of Isoclinic Groups</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X7C4B91CD84D5CDCC">4.3-5 <span class="Heading">Ordering of Characters and Classes</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X7ADC9DC980CF0685">4.3-6 AtlasLabelsOfIrreducibles</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X827044A37C04C0D1">4.3-7 <span class="Heading">Examples of the <strong class="pkg">Atlas</strong> Format for <strong class="pkg">GAP</strong> Tables</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X7BC3F0B0814D5B67">4.4 <span class="Heading"><strong class="pkg">CAS</strong> Tables</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X786A80A279674E91">4.4-1 CASInfo</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X835811C279FB1E56">4.5 <span class="Heading">Customizations of the <strong class="pkg">GAP</strong> Character Table Library</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X8202ACD57ACD5CAC">4.5-1 <span class="Heading">Installing the <strong class="pkg">GAP</strong> Character Table Library</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X83FA9D6B86150501">4.5-2 <span class="Heading">Unloading Character Table Data</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X7E859C3482F27089">4.5-3 <span class="Heading">Changing the display format of several functions</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X7DFAD31F84F55870">4.5-4 <span class="Heading">User preference <code class="code">MagmaPath</code></span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X8782716579A1B993">4.6 <span class="Heading">Technicalities of the Access to Character Tables from the Library
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X84E18B0B84F50B1E">4.6-1 <span class="Heading">Data Files of the <strong class="pkg">GAP</strong> Character Table Library</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X84E728FD860CAC0F">4.6-2 LIBLIST</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X80B7DF9C83A0F3F1">4.6-3 LibInfoCharacterTable</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X78FFDF0F83E7EB0D">4.7 <span class="Heading">How to Extend the <strong class="pkg">GAP</strong> Character Table Library</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X7A3B010A8790DD6E">4.7-1 NotifyNameOfCharacterTable</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X8160EA7C85DCB485">4.7-2 LibraryFusion</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X79E06BD67F6BC3A5">4.7-3 LibraryFusionTblToTom</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X780CBC347876A54B">4.7-4 PrintToLib</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X79366F797CD02DAF">4.7-5 NotifyCharacterTable</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X8374B5D081F85DBC">4.7-6 NotifyCharacterTables</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X7E3235FD7864A672">4.8 <span class="Heading">Sanity Checks for 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="chap4.html#X7D24C9D17DAB50D0">4.9 <span class="Heading">Maintenance of the <strong class="pkg">GAP</strong> Character Table Library</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap5.html#X7B915AD178236991">5 <span class="Heading">Functions for Character Table Constructions</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X7C32AA0784A79D53">5.1 <span class="Heading">Character Tables of Groups of Structure <span class="SimpleMath">M.G.A</span></span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X78F82DD67E083B88">5.1-1 PossibleCharacterTablesOfTypeMGA</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X83BE977185ADC24B">5.1-2 BrauerTableOfTypeMGA</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7899AA12836EEF8F">5.1-3 PossibleActionsForTypeMGA</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X821F4CB186913250">5.2 <span class="Heading">Character Tables of Groups of Structure <span class="SimpleMath">G.S_3</span></span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7E06095E7CB3316D">5.2-1 <span class="Heading">CharacterTableOfTypeGS3</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X82FC6C377BEF0139">5.2-2 PossibleActionsForTypeGS3</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X83EB02D38624821C">5.3 <span class="Heading">Character Tables of Groups of Structure <span class="SimpleMath">G.2^2</span></span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7CACDDED7A8C1CF9">5.3-1 <span class="Heading">PossibleCharacterTablesOfTypeGV4</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7CCD5A2979883144">5.3-2 PossibleActionsForTypeGV4</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X79142119791673EF">5.4 <span class="Heading">Character Tables of Groups of Structure <span class="SimpleMath">2^2.G</span></span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7E7043A5857B9240">5.4-1 <span class="Heading">PossibleCharacterTablesOfTypeV4G</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X8536F9027F097C79">5.4-2 <span class="Heading">BrauerTableOfTypeV4G</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X7B7282A37F293B36">5.5 <span class="Heading">Character Tables of Subdirect Products of Index Two</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7D0207B07B48FD06">5.5-1 CharacterTableOfIndexTwoSubdirectProduct</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X8714D24B802DA949">5.5-2 ConstructIndexTwoSubdirectProduct</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X8254CA95814DF613">5.5-3 ConstructIndexTwoSubdirectProductInfo</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X81255DAA7AB13278">5.6 <span class="Heading">Brauer Tables of Extensions by <span class="SimpleMath">p</span>-regular Automorphisms
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7AF3EA6C783FCFF9">5.6-1 IBrOfExtensionBySingularAutomorphism</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X844C69217B80537A">5.7 <span class="Heading">Character Tables of Coprime Central Extensions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X82CEF31D7815C53D">5.7-1 CharacterTableOfCommonCentralExtension</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X874C19D079CE0BE0">5.8 <span class="Heading">Construction Functions used in the Character Table Library</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7A948B397B5BC0AD">5.8-1 ConstructMGA</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X84DE92E579BA7171">5.8-2 ConstructMGAInfo</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X80F14D1C86CF1E9C">5.8-3 ConstructGS3</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7C1CE54A864936E0">5.8-4 ConstructV4G</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X8726ADCC7BCEA96F">5.8-5 ConstructProj</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7EF9996082140544">5.8-6 ConstructDirectProduct</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X781EAFEB80EC1ED8">5.8-7 ConstructCentralProduct</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X84F6BB30845D75E1">5.8-8 ConstructSubdirect</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7F26BEC67B744999">5.8-9 ConstructWreathSymmetric</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7F6A9FE57C77D778">5.8-10 ConstructIsoclinic</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7D3F0AC2825C8CA1">5.8-11 ConstructPermuted</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X85FE8954830F85A0">5.8-12 ConstructAdjusted</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X803FE1FF82790290">5.8-13 ConstructFactor</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap6.html#X81C250407B91443F">6 <span class="Heading">Interfaces to Other Data Formats for Character Tables</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X79F5E5A283E0D190">6.1 <span class="Heading">Interface to the <strong class="pkg">CAS</strong> System</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X841537DA7E495B73">6.1-1 CASString</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X835EE8028539BB63">6.2 <span class="Heading">Interface to the <strong class="pkg">MOC</strong> System</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X842957217E3697A1">6.2-1 MAKElb11</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X832005B37F0A2872">6.2-2 MOCTable</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7FBC528C7818814C">6.2-3 MOCString</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7F17B82879C8F953">6.2-4 ScanMOC</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7FBA67C585BEBFE5">6.2-5 GAPChars</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7BF1B6BF83BDD27E">6.2-6 MOCChars</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X80E1850F7DCED030">6.3 <span class="Heading">Interface to <strong class="pkg">GAP</strong> 3</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7DB321DE80046931">6.3-1 GAP3CharacterTableScan</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7B2C53137D1227FE">6.3-2 GAP3CharacterTableString</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7B2725D2789A9D85">6.3-3 GAP3CharacterTableData</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X7806073380076800">6.4 <span class="Heading">Interface to the Cambridge Format</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X78A84889878D98BB">6.4-1 CambridgeMaps</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X8209063C813240E5">6.4-2 StringOfCambridgeFormat</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X8676916F81F40A0F">6.5 <span class="Heading">Interface to the <strong class="pkg">MAGMA</strong> System</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X79D160BD7ECA6D2F">6.5-1 BosmaBase</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7B1FAE1A7FD5D5A1">6.5-2 GAPTableOfMagmaFile</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X824D2B4A79A9E5AE">6.5-3 CharacterTableComputedByMagma</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap7.html#X797E1693780F1093">7 <span class="Heading">Utility Functions Provided by the <strong class="pkg">CTblLib</strong>
Package</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X7BC89F7C8460E979">7.1 <span class="Heading">Write Character Values in Terms of Atomic <strong class="pkg">Atlas</strong>
Irrationalities</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X874167957FD2B7EA">7.1-1 CTblLib.StringOfAtlasIrrationality</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X7D867FE08240B83B">7.2 <span class="Heading">Create a String that Describes the Group Structure</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X816807E4874585FD">7.2-1 StructureDescriptionCharacterTableName</a></span>
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<div class="ContChap"><a href="chapBib.html"><span class="Heading">References</span></a></div>
<div class="ContChap"><a href="chapInd.html"><span class="Heading">Index</span></a></div>
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