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<h3>References</h3>
<p><a id="biBABCImp" name="biBABCImp"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>ABC</span>]
<i class='BibTitle'>Improvements to the ATLAS of Brauer Characters</i>,
<span class='BibOrganization'>The MOC Group</span>,
<span class='BibHowpublished'><a href="https://www.math.rwth-aachen.de/homes/MOC/ABCerr.html">https://www.math.rwth-aachen.de/homes/MOC/ABCerr.html</a></span>.
</p>
<p><a id="biBGMN" name="biBGMN"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=2669683">BGL+10</a></span>] <b class='BibAuthor'>Breuer, T., Guralnick, R. M., Lucchini, A., Maróti, A. and Nagy, G. P.</b>,
<a href="http://dx.doi.org/10.1112/blms/bdq017"><i class='BibTitle'>Hamiltonian cycles in the generating graphs of finite groups</i></a>,
<span class='BibJournal'>Bull. London Math. Soc.</span>,
<em class='BibVolume'>42</em> (<span class='BibNumber'>4</span>)
(<span class='BibYear'>2010</span>),
<span class='BibPages'>621–633</span>.
</p>
<p><a id="biBBrowse" name="biBBrowse"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BL23</span>] <b class='BibAuthor'>Breuer, T. and Lübeck, F.</b>,
<i class='BibTitle'>Browse, ncurses interface and browsing applications,
Version 1.8.21</i>
(<span class='BibYear'>2023</span>)<br />
(<span class='BibNote'><strong class='pkg'>GAP</strong> package</span>),
<span class='BibHowpublished'><a href="https://www.math.rwth-aachen.de/~Browse">https://www.math.rwth-aachen.de/~Browse</a></span>.
</p>
<p><a id="biBBMO17" name="biBBMO17"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3682588">BMO17</a></span>] <b class='BibAuthor'>Breuer, T., Malle, G. and O'Brien, E. A.</b>,
<i class='BibTitle'>Reliability and reproducibility of Atlas information</i>,
in <i class='BibBooktitle'>Finite simple groups: thirty years of the atlas and beyond</i>,
<span class='BibPublisher'>Amer. Math. Soc.</span>,
<span class='BibSeries'>Contemp. Math.</span>,
<em class='BibVolume'>694</em>,
<span class='BibAddress'>Providence, RI</span>
(<span class='BibYear'>2017</span>),
<span class='BibPages'>21–31</span>.
</p>
<p><a id="biBBMverify" name="biBBMverify"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=4135540">BMW20</a></span>] <b class='BibAuthor'>Breuer, T., Magaard, K. and Wilson, R. A.</b>,
<a href="https://doi.org/10.1016/j.jalgebra.2019.06.047"><i class='BibTitle'>Verification of the ordinary character table
of the Baby Monster</i></a>,
<span class='BibJournal'>J. Algebra</span>,
<em class='BibVolume'>561</em>
(<span class='BibYear'>2020</span>),
<span class='BibPages'>111–130</span>.
</p>
<p><a id="biBMverify" name="biBMverify"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BMW24</span>] <b class='BibAuthor'>Breuer, T., Magaard, K. and Wilson, R. A.</b>,
<i class='BibTitle'>Verification of the conjugacy classes and ordinary character table
of the Monster</i>
(<span class='BibYear'>2024</span>),
<span class='BibHowpublished'>submitted</span>.
</p>
<p><a id="biBBN95" name="biBBN95"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=1367961">BN95</a></span>] <b class='BibAuthor'>Breuer, T. and Norton, S. P.</b>,
<i class='BibTitle'>Improvements to the Atlas</i>,
<span class='BibPublisher'>The Clarendon Press Oxford University Press</span>,
<span class='BibSeries'>London Mathematical Society Monographs. New Series</span>,
<em class='BibVolume'>11</em>,
<span class='BibAddress'>New York</span>
(<span class='BibYear'>1995</span>),
<span class='BibPages'>297–327</span><br />
(<span class='BibNote'>Appendix 2 by T. Breuer and S. Norton,
Oxford Science Publications</span>).
</p>
<p><a id="biBBos90" name="biBBos90"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=1325517">Bos90</a></span>] <b class='BibAuthor'>Bosma, W.</b>,
<a href="http://dx.doi.org/10.1007/BF01810296"><i class='BibTitle'>Canonical bases for cyclotomic fields</i></a>,
<span class='BibJournal'>Appl. Algebra Engrg. Comm. Comput.</span>,
<em class='BibVolume'>1</em> (<span class='BibNumber'>2</span>)
(<span class='BibYear'>1990</span>),
<span class='BibPages'>125–134</span>.
</p>
<p><a id="biBAmbigFus" name="biBAmbigFus"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Brea</span>] <b class='BibAuthor'>Breuer, T.</b>,
<i class='BibTitle'>Ambiguous Class Fusions in the <strong class='pkg'>GAP</strong>
Character Table Library</i>,
<span class='BibHowpublished'><a href="https://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc2/manual.pdf">https://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc2/manual.pdf</a></span>.
</p>
<p><a id="biBCCE" name="biBCCE"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Breb</span>] <b class='BibAuthor'>Breuer, T.</b>,
<i class='BibTitle'>Constructing Character Tables of Central Extensions
in <strong class='pkg'>GAP</strong></i>,
<span class='BibHowpublished'><a href="https://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc2/manual.pdf">https://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc2/manual.pdf</a></span>.
</p>
<p><a id="biBAtlasVerifyLargeArxiv" name="biBAtlasVerifyLargeArxiv"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Brec</span>] <b class='BibAuthor'>Breuer, T.</b>,
<i class='BibTitle'>Constructing the ordinary character tables of some Atlas
groups using character theoretic methods.</i>,
<span class='BibHowpublished'><a href="https://export.arxiv.org/abs/1604.00754">arXiv:1604.00754</a></span>.
</p>
<p><a id="biBctblpope" name="biBctblpope"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Bred</span>] <b class='BibAuthor'>Breuer, T.</b>,
<i class='BibTitle'>Permutation Characters in <strong class='pkg'>GAP</strong></i>,
<span class='BibHowpublished'><a href="https://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc2/manual.pdf">https://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc2/manual.pdf</a></span>.
</p>
<p><a id="biBProbGenArxiv" name="biBProbGenArxiv"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Bree</span>] <b class='BibAuthor'>Breuer, T.</b>,
<i class='BibTitle'><strong class='pkg'>GAP</strong> computations concerning
probabilistic generation of finite simple groups</i>,
<span class='BibHowpublished'><a href="https://export.arxiv.org/abs/0710.3267">arXiv:0710.3267</a></span>.
</p>
<p><a id="biBAuto" name="biBAuto"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Bref</span>] <b class='BibAuthor'>Breuer, T.</b>,
<i class='BibTitle'>Using Table Automorphisms for Constructing Character Tables
in <strong class='pkg'>GAP</strong></i>,
<span class='BibHowpublished'><a href="https://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc2/manual.pdf">https://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc2/manual.pdf</a></span>.
</p>
<p><a id="biBBre11" name="biBBre11"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=2831228">Bre11</a></span>] <b class='BibAuthor'>Breuer, T.</b>,
<a href="http://dx.doi.org/10.1112/S1461157010000318"><i class='BibTitle'>Computing character tables of groups of type
M.G.A</i></a>,
<span class='BibJournal'>LMS J. Comput. Math.</span>,
<em class='BibVolume'>14</em>
(<span class='BibYear'>2011</span>),
<span class='BibPages'>173–178</span>.
</p>
<p><a id="biBCCN85" name="biBCCN85"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=827219">CCN+85</a></span>] <b class='BibAuthor'>Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A.</b>,
<i class='BibTitle'>Atlas of finite groups</i>,
<span class='BibPublisher'>Oxford University Press</span>,
<span class='BibAddress'>Eynsham</span>
(<span class='BibYear'>1985</span>),
<span class='BibPages'>xxxiv+252 pages</span><br />
(<span class='BibNote'>Maximal subgroups and ordinary characters for simple groups,
With computational assistance from J. G. Thackray</span>).
</p>
<p><a id="biBCla05" name="biBCla05"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Cla05</span>] <b class='BibAuthor'>Claßen-Houben, M.</b>,
<i class='BibTitle'>Jordan-Zerlegung der Charaktere für
die
<strong class='pkg'>GAP</strong>-Charaktertafeln der endlichen Gruppen
vom Lie-Typ</i>,
<span class='BibType'>Diplomarbeit</span>,
<span class='BibSchool'>Lehrstuhl D für Mathematik,
Rheinisch Westfälische Technische Hochschule</span>,
<span class='BibAddress'>Aachen, Germany</span>
(<span class='BibYear'>2005</span>).
</p>
<p><a id="biBCP96" name="biBCP96"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>CP96</span>] <b class='BibAuthor'>Cannon, J. J. and Playoust, C.</b>,
<i class='BibTitle'>An introduction to algebraic programming in Magma</i>,
<span class='BibOrganization'>School of Mathematics and Statistics,
University of Sydney</span>,
<span class='BibAddress'>Sydney, Australia</span>
(<span class='BibYear'>1996</span>),
<span class='BibHowpublished'><a href="http://www.math.usyd.edu.au:8000/u/magma">http://www.math.usyd.edu.au:8000/u/magma</a></span>.
</p>
<p><a id="biBDan06" name="biBDan06"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Dan06</span>] <b class='BibAuthor'>Dany, S.</b>,
<i class='BibTitle'>Berechnung von Charaktertafeln zentraler Erweiterungen
ausgewählter Gruppen</i>,
<span class='BibType'>Diplomarbeit</span>,
<span class='BibSchool'>Lehrstuhl D für Mathematik,
Rheinisch Westfälische Technische Hochschule</span>,
<span class='BibAddress'>Aachen, Germany</span>
(<span class='BibYear'>2006</span>).
</p>
<p><a id="biBDLP25" name="biBDLP25"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>DLP25</span>] <b class='BibAuthor'>Dietrich, H., Lee, M. and Popiel, T.</b>,
<i class='BibTitle'>The maximal subgroups of the Monster</i>
(<span class='BibYear'>2025</span>),
<span class='BibHowpublished'><a href="https://doi.org/10.1016/j.aim.2025.110214">Advances in Mathematics 469 (2025), article 110214</a></span>.
</p>
<p><a id="biBDLPP24" name="biBDLPP24"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>DLPP24</span>] <b class='BibAuthor'>Dietrich, H., Lee, M., Pisani, A. and Popiel, T.</b>,
<i class='BibTitle'>Explicit construction of the maximal subgroups of the Monster</i>
(<span class='BibYear'>2024</span>),
<span class='BibHowpublished'><a href="https://arxiv.org/abs/2411.12230">arXiv:2411.12230</a></span>.
</p>
<p><a id="biBGAP" name="biBGAP"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>GAP24</span>]
<i class='BibTitle'><strong class='pkg'>GAP</strong> –
Groups, Algorithms, and Programming,
Version 4.13.1</i>,
<span class='BibOrganization'>The GAP Group</span>
(<span class='BibYear'>2024</span>),
<span class='BibHowpublished'><a href="https://www.gap-system.org">https://www.gap-system.org</a></span>.
</p>
<p><a id="biBGR20" name="biBGR20"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>GR</span>] <b class='BibAuthor'>Guralnick, R. M. and Robinson, G. R.</b>,
<i class='BibTitle'>Commuting involutions and elementary abelian subgroups
of simple groups</i>,
<span class='BibHowpublished'><a href="http://export.arxiv.org/abs/2012.08693">arXiv:2012.08693</a></span>.
</p>
<p><a id="biBHan88" name="biBHan88"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Han88</span>] <b class='BibAuthor'>Hanrath, W.</b>,
<i class='BibTitle'>Irreduzible Darstellungen von Raumgruppen</i>,
<span class='BibType'>Dissertation</span>,
<span class='BibSchool'>Rheinisch Westfälische
Technische Hochschule</span>,
<span class='BibAddress'>Aachen, Germany</span>
(<span class='BibYear'>1988</span>).
</p>
<p><a id="biBHJLP92" name="biBHJLP92"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>HJLP</span>] <b class='BibAuthor'>Hiss, G., Jansen, C., Lux, K. and Parker, R. A.</b>,
<i class='BibTitle'>Computational Modular Character Theory</i>,
<span class='BibHowpublished'><a href="http://www.math.rwth-aachen.de/~MOC/CoMoChaT/">http://www.math.rwth-aachen.de/~MOC/CoMoChaT/</a></span>.
</p>
<p><a id="biBHP89" name="biBHP89"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=1025760">HP89</a></span>] <b class='BibAuthor'>Holt, D. F. and Plesken, W.</b>,
<i class='BibTitle'>Perfect groups</i>,
<span class='BibPublisher'>The Clarendon Press Oxford University Press</span>,
<span class='BibSeries'>Oxford Mathematical Monographs</span>,
<span class='BibAddress'>New York</span>
(<span class='BibYear'>1989</span>),
<span class='BibPages'>xii+364 pages</span><br />
(<span class='BibNote'>With an appendix by W. Hanrath,
Oxford Science Publications</span>).
</p>
<p><a id="biBJLPW95" name="biBJLPW95"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=1367961">JLPW95</a></span>] <b class='BibAuthor'>Jansen, C., Lux, K., Parker, R. and Wilson, R.</b>,
<i class='BibTitle'>An atlas of Brauer characters</i>,
<span class='BibPublisher'>The Clarendon Press Oxford University Press</span>,
<span class='BibSeries'>London Mathematical Society Monographs. New Series</span>,
<em class='BibVolume'>11</em>,
<span class='BibAddress'>New York</span>
(<span class='BibYear'>1995</span>),
<span class='BibPages'>xviii+327 pages</span><br />
(<span class='BibNote'>Appendix 2 by T. Breuer and S. Norton,
Oxford Science Publications</span>).
</p>
<p><a id="biBGAPDoc" name="biBGAPDoc"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>LN18</span>] <b class='BibAuthor'>Lübeck, F. and Neunhöffer, M.</b>,
<i class='BibTitle'><strong class='pkg'>GAPDoc</strong>,
A Meta Package for <strong class='pkg'>GAP</strong>
Documentation,
Version 1.6.2</i>
(<span class='BibYear'>2018</span>)<br />
(<span class='BibNote'><strong class='pkg'>GAP</strong> package</span>),
<span class='BibHowpublished'><a href="https://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc">https://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc</a></span>.
</p>
<p><a id="biBLOST2010" name="biBLOST2010"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=2654085">LOST10</a></span>] <b class='BibAuthor'>Liebeck, M. W., O'Brien, E. A., Shalev, A. and Tiep, P. H.</b>,
<a href="http://dx.doi.org/10.4171/JEMS/220"><i class='BibTitle'>The Ore conjecture</i></a>,
<span class='BibJournal'>J. Eur. Math. Soc. (JEMS)</span>,
<em class='BibVolume'>12</em> (<span class='BibNumber'>4</span>)
(<span class='BibYear'>2010</span>),
<span class='BibPages'>939–1008</span>.
</p>
<p><a id="biBLP91" name="biBLP91"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=1112157">LP91</a></span>] <b class='BibAuthor'>Lux, K. and Pahlings, H.</b> (<span class='BibEditor'>Michler, G. O. and Ringel, C. M.</span>, Eds.),
<i class='BibTitle'>Computational aspects of representation theory of finite
groups</i>,
in <i class='BibBooktitle'>Representation theory of finite groups and finite-dimensional
algebras (Bielefeld, 1991)</i>,
<span class='BibPublisher'>Birkhäuser</span>,
<span class='BibSeries'>Progr. Math.</span>,
<em class='BibVolume'>95</em>,
<span class='BibAddress'>Basel</span>
(<span class='BibYear'>1991</span>),
<span class='BibPages'>37–64</span>.
</p>
<p><a id="biBLP10" name="biBLP10"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=2680716">LP10</a></span>] <b class='BibAuthor'>Lux, K. and Pahlings, H.</b>,
<i class='BibTitle'>Representations of groups</i>,
<span class='BibPublisher'>Cambridge University Press</span>,
<span class='BibSeries'>Cambridge Studies in Advanced Mathematics</span>,
<em class='BibVolume'>124</em>,
<span class='BibAddress'>Cambridge</span>
(<span class='BibYear'>2010</span>),
<span class='BibPages'>x+460 pages</span><br />
(<span class='BibNote'>A computational approach</span>).
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[<span class='BibKey'>MNP19</span>] <b class='BibAuthor'>Merkwitz, T., Naughton, L. and Pfeiffer, G.</b>,
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(<span class='BibYear'>2019</span>)<br />
(<span class='BibNote'>GAP package</span>),
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[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=1632299">Nav98</a></span>] <b class='BibAuthor'>Navarro, G.</b>,
<a href="http://dx.doi.org/10.1017/CBO9780511526015"><i class='BibTitle'>Characters and blocks of finite groups</i></a>,
<span class='BibPublisher'>Cambridge University Press</span>,
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[<span class='BibKey'>Noe02</span>] <b class='BibAuthor'>Noeske, F.</b>,
<i class='BibTitle'>Zur Darstellungstheorie der Schurschen Erweiterungen
symmetrischer Gruppen</i>,
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[<span class='BibKey'>Nor</span>] <b class='BibAuthor'>Norton, S. P.</b>,
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[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=760658">NPP84</a></span>] <b class='BibAuthor'>Neubüser, J., Pahlings, H. and Plesken, W.</b> (<span class='BibEditor'>Atkinson, M. D.</span>, Ed.),
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<i class='BibTitle'>Charaktertafeln von Sylownormalisatoren sporadischer
einfacher Gruppen</i>,
<span class='BibOrganization'>Universität Essen</span>,
<span class='BibPublisher'>Universität Essen Fachbereich Mathematik</span>,
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[<span class='BibKey'>PP24</span>] <b class='BibAuthor'>Pisani, A. and Popiel, T.</b>,
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[<span class='BibKey'>WPN+22</span>] <b class='BibAuthor'>Wilson, R. A., Parker, R. A., Nickerson, S., Bray, J. N. and Breuer, T.</b>,
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<p> </p>
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