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<h3>References</h3>

<a id="biBABCImp" name="biBABCImp"></a>

[ABC]
Improvements to the ATLAS of Brauer Characters,
The MOC Group,
<a href="https://www.math.rwth-aachen.de/homes/MOC/ABCerr.html">https://www.math.rwth-aachen.de/homes/MOC/ABCerr.html</a>.


<a id="biBGMN" name="biBGMN"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2669683">BGL+10</a>] Breuer, T., Guralnick, R. M., Lucchini, A., Maróti, A. and Nagy, G. P.,
<a href="http://dx.doi.org/10.1112/blms/bdq017">Hamiltonian cycles in the generating graphs of finite groups</a>,
Bull. London Math. Soc.,
42 (4)
(2010),
621–633.


<a id="biBBrowse" name="biBBrowse"></a>

[BL23] Breuer, T. and Lübeck, F.,
Browse, ncurses interface and browsing applications,
 Version 1.8.21
(2023) 
(GAP package),
<a href="https://www.math.rwth-aachen.de/~Browse">https://www.math.rwth-aachen.de/~Browse</a>.


<a id="biBBMO17" name="biBBMO17"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=3682588">BMO17</a>] Breuer, T., Malle, G. and O'Brien, E. A.,
Reliability and reproducibility of Atlas information,
 in Finite simple groups: thirty years of the atlas and beyond,
Amer. Math. Soc.,
Contemp. Math.,
694,
Providence, RI
(2017),
21–31.


<a id="biBBMverify" name="biBBMverify"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=4135540">BMW20</a>] Breuer, T., Magaard, K. and Wilson, R. A.,
<a href="https://doi.org/10.1016/j.jalgebra.2019.06.047">Verification of the ordinary character table
 of the Baby Monster</a>,
J. Algebra,
561
(2020),
111–130.


<a id="biBMverify" name="biBMverify"></a>

[BMW24] Breuer, T., Magaard, K. and Wilson, R. A.,
Verification of the conjugacy classes and ordinary character table
 of the Monster
(2024),
submitted.


<a id="biBBN95" name="biBBN95"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1367961">BN95</a>] Breuer, T. and Norton, S. P.,
Improvements to the Atlas,
The Clarendon Press Oxford University Press,
London Mathematical Society Monographs. New Series,
11,
New York
(1995),
297–327 
(Appendix 2 by T. Breuer and S. Norton,
 Oxford Science Publications).


<a id="biBBos90" name="biBBos90"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1325517">Bos90</a>] Bosma, W.,
<a href="http://dx.doi.org/10.1007/BF01810296">Canonical bases for cyclotomic fields</a>,
Appl. Algebra Engrg. Comm. Comput.,
1 (2)
(1990),
125–134.


<a id="biBAmbigFus" name="biBAmbigFus"></a>

[Brea] Breuer, T.,
Ambiguous Class Fusions in the GAP
 Character Table Library,
<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>.


<a id="biBCCE" name="biBCCE"></a>

[Breb] Breuer, T.,
Constructing Character Tables of Central Extensions
 in GAP,
<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>.


<a id="biBAtlasVerifyLargeArxiv" name="biBAtlasVerifyLargeArxiv"></a>

[Brec] Breuer, T.,
Constructing the ordinary character tables of some Atlas
 groups using character theoretic methods.,
<a href="https://export.arxiv.org/abs/1604.00754">arXiv:1604.00754</a>.


<a id="biBctblpope" name="biBctblpope"></a>

[Bred] Breuer, T.,
Permutation Characters in GAP,
<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>.


<a id="biBProbGenArxiv" name="biBProbGenArxiv"></a>

[Bree] Breuer, T.,
GAP computations concerning
 probabilistic generation of finite simple groups,
<a href="https://export.arxiv.org/abs/0710.3267">arXiv:0710.3267</a>.


<a id="biBAuto" name="biBAuto"></a>

[Bref] Breuer, T.,
Using Table Automorphisms for Constructing Character Tables
 in GAP,
<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>.


<a id="biBBre11" name="biBBre11"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2831228">Bre11</a>] Breuer, T.,
<a href="http://dx.doi.org/10.1112/S1461157010000318">Computing character tables of groups of type
 M.G.A</a>,
LMS J. Comput. Math.,
14
(2011),
173–178.


<a id="biBCCN85" name="biBCCN85"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=827219">CCN+85</a>] Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A.,
Atlas of finite groups,
Oxford University Press,
Eynsham
(1985),
xxxiv+252 pages 
(Maximal subgroups and ordinary characters for simple groups,
 With computational assistance from J. G. Thackray).


<a id="biBCla05" name="biBCla05"></a>

[Cla05] Claßen-Houben, M.,
Jordan-Zerlegung der Charaktere für
 die
 GAP-Charaktertafeln der endlichen Gruppen
 vom Lie-Typ,
Diplomarbeit,
Lehrstuhl D für Mathematik,
 Rheinisch Westfälische Technische Hochschule,
Aachen, Germany
(2005).


<a id="biBCP96" name="biBCP96"></a>

[CP96] Cannon, J. J. and Playoust, C.,
An introduction to algebraic programming in Magma,
School of Mathematics and Statistics,
 University of Sydney,
Sydney, Australia
(1996),
<a href="http://www.math.usyd.edu.au:8000/u/magma">http://www.math.usyd.edu.au:8000/u/magma</a>.


<a id="biBDan06" name="biBDan06"></a>

[Dan06] Dany, S.,
Berechnung von Charaktertafeln zentraler Erweiterungen
 ausgewählter Gruppen,
Diplomarbeit,
Lehrstuhl D für Mathematik,
 Rheinisch Westfälische Technische Hochschule,
Aachen, Germany
(2006).


<a id="biBDLP25" name="biBDLP25"></a>

[DLP25] Dietrich, H., Lee, M. and Popiel, T.,
The maximal subgroups of the Monster
(2025),
<a href="https://doi.org/10.1016/j.aim.2025.110214">Advances in Mathematics 469 (2025), article 110214</a>.


<a id="biBDLPP24" name="biBDLPP24"></a>

[DLPP24] Dietrich, H., Lee, M., Pisani, A. and Popiel, T.,
Explicit construction of the maximal subgroups of the Monster
(2024),
<a href="https://arxiv.org/abs/2411.12230">arXiv:2411.12230</a>.


<a id="biBGAP" name="biBGAP"></a>

[GAP24]
GAP –
 Groups, Algorithms, and Programming,
 Version 4.13.1,
The GAP Group
(2024),
<a href="https://www.gap-system.org">https://www.gap-system.org</a>.


<a id="biBGR20" name="biBGR20"></a>

[GR] Guralnick, R. M. and Robinson, G. R.,
Commuting involutions and elementary abelian subgroups
 of simple groups,
<a href="http://export.arxiv.org/abs/2012.08693">arXiv:2012.08693</a>.


<a id="biBHan88" name="biBHan88"></a>

[Han88] Hanrath, W.,
Irreduzible Darstellungen von Raumgruppen,
Dissertation,
Rheinisch Westfälische
 Technische Hochschule,
Aachen, Germany
(1988).


<a id="biBHJLP92" name="biBHJLP92"></a>

[HJLP] Hiss, G., Jansen, C., Lux, K. and Parker, R. A.,
Computational Modular Character Theory,
<a href="http://www.math.rwth-aachen.de/~MOC/CoMoChaT/">http://www.math.rwth-aachen.de/~MOC/CoMoChaT/</a>.


<a id="biBHP89" name="biBHP89"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1025760">HP89</a>] Holt, D. F. and Plesken, W.,
Perfect groups,
The Clarendon Press Oxford University Press,
Oxford Mathematical Monographs,
New York
(1989),
xii+364 pages 
(With an appendix by W. Hanrath,
 Oxford Science Publications).


<a id="biBJLPW95" name="biBJLPW95"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1367961">JLPW95</a>] Jansen, C., Lux, K., Parker, R. and Wilson, R.,
An atlas of Brauer characters,
The Clarendon Press Oxford University Press,
London Mathematical Society Monographs. New Series,
11,
New York
(1995),
xviii+327 pages 
(Appendix 2 by T. Breuer and S. Norton,
 Oxford Science Publications).


<a id="biBGAPDoc" name="biBGAPDoc"></a>

[LN18] Lübeck, F. and Neunhöffer, M.,
GAPDoc,
 A Meta Package for GAP
 Documentation,
 Version 1.6.2
(2018) 
(GAP package),
<a href="https://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc">https://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc</a>.


<a id="biBLOST2010" name="biBLOST2010"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2654085">LOST10</a>] Liebeck, M. W., O'Brien, E. A., Shalev, A. and Tiep, P. H.,
<a href="http://dx.doi.org/10.4171/JEMS/220">The Ore conjecture</a>,
J. Eur. Math. Soc. (JEMS),
12 (4)
(2010),
939–1008.


<a id="biBLP91" name="biBLP91"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1112157">LP91</a>] Lux, K. and Pahlings, H. (Michler, G. O. and Ringel, C. M., Eds.),
Computational aspects of representation theory of finite
 groups,
 in Representation theory of finite groups and finite-dimensional
 algebras (Bielefeld, 1991),
Birkhäuser,
Progr. Math.,
95,
Basel
(1991),
37–64.


<a id="biBLP10" name="biBLP10"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2680716">LP10</a>] Lux, K. and Pahlings, H.,
Representations of groups,
Cambridge University Press,
Cambridge Studies in Advanced Mathematics,
124,
Cambridge
(2010),
x+460 pages 
(A computational approach).


<a id="biBTomLib" name="biBTomLib"></a>

[MNP19] Merkwitz, T., Naughton, L. and Pfeiffer, G.,
TomLib, The GAP Library of Tables of Marks,
 Version 1.2.9
(2019) 
(GAP package),
<a href="https://gap-packages.github.io/tomlib">https://gap-packages.github.io/tomlib</a>.


<a id="biBNav98" name="biBNav98"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1632299">Nav98</a>] Navarro, G.,
<a href="http://dx.doi.org/10.1017/CBO9780511526015">Characters and blocks of finite groups</a>,
Cambridge University Press,
London Mathematical Society Lecture Note Series,
250,
Cambridge
(1998),
x+287 pages.


<a id="biBNoe02" name="biBNoe02"></a>

[Noe02] Noeske, F.,
Zur Darstellungstheorie der Schurschen Erweiterungen
 symmetrischer Gruppen,
Diplomarbeit,
Lehrstuhl D für Mathematik,
 Rheinisch Westfälische
 Technische Hochschule
(2002).


<a id="biBAtlasImpII" name="biBAtlasImpII"></a>

[Nor] Norton, S. P.,
Improvements to the ATLAS–II,
<a href="http://brauer.maths.qmul.ac.uk/Atlas/info/fullatlasmods.html">http://brauer.maths.qmul.ac.uk/Atlas/info/fullatlasmods.html</a>.


<a id="biBNPP84" name="biBNPP84"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=760658">NPP84</a>] Neubüser, J., Pahlings, H. and Plesken, W. (Atkinson, M. D., Ed.),
CAS; design and use of a system for the handling of
 characters of finite groups,
 in Computational group theory (Durham, 1982),
Academic Press,
London
(1984),
195–247.


<a id="biBOst86" name="biBOst86"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=872094">Ost86</a>] Ostermann, T.,
Charaktertafeln von Sylownormalisatoren sporadischer
 einfacher Gruppen,
Universität Essen,
Universität Essen Fachbereich Mathematik,
Vorlesungen aus dem Fachbereich Mathematik der
 Universität
 GH Essen [Lecture Notes in Mathematics at the University of
 Essen],
14,
Essen
(1986),
x+187 pages.


<a id="biBPis25" name="biBPis25"></a>

[Pis25] Pisani, A.,
Computing the Character Table of a 2-local Maximal Subgroup of the Monster
(2025),
<a href="https://arxiv.org/abs/2503.15857">arXiv:2503.15857</a>.


<a id="biBPP24" name="biBPP24"></a>

[PP24] Pisani, A. and Popiel, T.,
Conjugacy class fusion from four maximal subgroups of the Monste
(2024),
<a href="https://arxiv.org/abs/2404.05194">arXiv:2404.05194</a>.


<a id="biBAtlasRep" name="biBAtlasRep"></a>

[WPN+22] Wilson, R. A., Parker, R. A., Nickerson, S., Bray, J. N. and Breuer, T.,
AtlasRep, A GAP Interface
 to the Atlas of Group Representations,
 Version 2.1.6
(2022) 
(GAP package),
<a href="https://www.math.rwth-aachen.de/~Thomas.Breuer/atlasrep">https://www.math.rwth-aachen.de/~Thomas.Breuer/atlasrep</a>.


 

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