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<h3>References</h3>

<a id="biBBe00" name="biBBe00"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1799483">Ber00</a>] Bereczky, Á.,
<a href="http://dx.doi.org/10.1006/jabr.2000.8458">Maximal overgroups of Singer elements in classical
 groups</a>,
J. Algebra,
234 (1)
(2000),
187–206.


<a id="biBBG21" name="biBBG21"></a>

[BG] Breuer, T. and Guralnick, R. M.,
Finite groups can be generated by a pi-subgroup and a pi'-subgroup,
<a href="https://arxiv.org/abs/2103.17216">arXiv:2103.17216</a>.


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[<a href="https://www.ams.org/mathscinet-getitem?mr=2422303">BGK08</a>] Breuer, T., Guralnick, R. M. and Kantor, W. M.,
<a href="http://dx.doi.org/10.1016/j.jalgebra.2007.10.028">Probabilistic generation of finite simple groups, II</a>,
J. Algebra,
320 (2)
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443–494.


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[<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="biBBGS11" name="biBBGS11"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2781219">BGS11</a>] Burness, T. C., Guralnick, R. M. and Saxl, J.,
<a href="http://dx.doi.org/10.1112/blms/bdq123">On base sizes for symmetric groups</a>,
Bull. Lond. Math. Soc.,
43 (2)
(2011),
386–391.


<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
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21–31.


<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="biBBP98copy" name="biBBP98copy"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1633876">BP98</a>] Breuer, T. and Pfeiffer, G.,
<a href="http://dx.doi.org/10.1006/jsco.1998.0217">Finding possible permutation characters</a>,
J. Symbolic Comput.,
26 (3)
(1998),
343–354.


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

[Breb] 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>

[Brec] 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="biBBre91" name="biBBre91"></a>

[Bre91] Breuer, T.,
Potenzabbildungen, Untergruppenfusionen,
 Tafel-Automorphismen,
Diplomarbeit,
Lehrstuhl D für Mathematik, Rheinisch Westfälische
 Technische Hochschule,
Aachen, Germany
(1991).


<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="biBCTblLib" name="biBCTblLib"></a>

[Bre25] Breuer, T.,
The GAP Character Table
 Library, Version 1.3.11
(2025) 
(GAP package),
<a href="https://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib">https://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib</a>.


<a id="biBBW1" name="biBBW1"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=0372033">BW75</a>] Brenner, J. L. and Wiegold, J.,
Two-generator groups. I,
Michigan Math. J.,
22
(1975),
53–64.


<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="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="biBDad66" name="biBDad66"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=0200355">Dad66</a>] Dade, E. C.,
<a href="http://dx.doi.org/10.2307/1970529">Blocks with cyclic defect groups</a>,
Ann. of Math. (2),
84
(1966),
20–48.


<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="biBDNT" name="biBDNT"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=096641">DNT13</a>] Dolfi, S., Navarro, G. and Tiep, P. H.,
Finite groups whose same degree characters are Galois
 conjugate,
Israel J. Math.,
198 (1)
(2013),
283–331.


<a id="biBFeit82" name="biBFeit82"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=661045">Fei82</a>] Feit, W.,
The representation theory of finite groups,
North-Holland Publishing Co.,
North-Holland Mathematical Library,
25
(1982) 
(xiv+502 pp., ISBN 0-444-86155-6).


<a id="biBGag86" name="biBGag86"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=817904">Gag86</a>] Gagola, Jr., S. M.,
<a href="http://dx.doi.org/10.1307/mmj/1029003285">Formal character tables</a>,
Michigan Math. J.,
33 (1)
(1986),
3–10.


<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="biBGMS89" name="biBGMS89"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1025167">GJMS89</a>] Griess Jr., R. L., Meierfrankenfeld, U. and Segev, Y.,
<a href="https://doi.org/10.2307/1971455">A uniqueness proof for the Monster</a>,
Ann. of Math. (2),
130 (3)
(1989),
567–602.


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

[<a href="https://www.ams.org/mathscinet-getitem?mr=1800754">GK00</a>] Guralnick, R. M. and Kantor, W. M.,
<a href="http://dx.doi.org/10.1006/jabr.2000.8357">Probabilistic generation of finite simple groups</a>,
J. Algebra,
234 (2)
(2000),
743–792 
(Special issue in honor of Helmut Wielandt).


<a id="biBGM01" name="biBGM01"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1849484">GM01</a>] Ganief, S. and Moori, J.,
<a href="http://dx.doi.org/10.1081/AGB-100105019">On the spread of the sporadic simple groups</a>,
Comm. Algebra,
29 (8)
(2001),
3239–3255.


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

[<a href="https://www.ams.org/mathscinet-getitem?mr=1658168">GPPS99</a>] Guralnick, R., Penttila, T., Praeger, C. E. and Saxl, J.,
<a href="http://dx.doi.org/10.1112/S0024611599001616">Linear groups with orders having certain large prime divisors</a>,
Proc. London Math. Soc.,
78 (1)
(1999),
167–214.


<a id="biBHL89" name="biBHL89"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1033265">HL89</a>] Hiss, G. and Lux, K.,
Brauer trees of sporadic groups,
The Clarendon Press, Oxford University Press,
Oxford Science Publications,
New York
(1989),
x+526 pages.


<a id="biBHL94" name="biBHL94"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1278806">HL94</a>] Hiss, G. and Lux, K.,
<a href="http://dx.doi.org/10.1080/00927879408825042">The 5-modular characters of the sporadic simple
 Fischer
 groups Fi_{22} and Fi_{23}</a>,
Comm. Algebra,
22 (9)
(1994),
3563–3590 
(With an appendix by Thomas Breuer).


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

[Hol08] Holt, D.,
cohomolo,
 computing cohomology groups and Schur multipliers,
 Version 1.6
(2008) 
(GAP package),
<a href="http://www.maths.warwick.ac.uk/~dfh/cohomolo">http://www.maths.warwick.ac.uk/~dfh/cohomolo</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="biBHulpkeTG" name="biBHulpkeTG"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2168238">Hul05</a>] Hulpke, A.,
Constructing transitive permutation groups,
J. Symbolic Comput.,
39 (1)
(2005),
1–30.


<a id="biBHup67" name="biBHup67"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=0224703">Hup67</a>] Huppert, B.,
Endliche Gruppen. I,
Springer-Verlag,
Die Grundlehren der Mathematischen Wissenschaften, Band 134,
Berlin
(1967),
xii+793 pages.


<a id="biBHW04" name="biBHW04"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2025332">HW04</a>] Holmes, P. E. and Wilson, R. A.,
<a href="http://dx.doi.org/10.1112/S0024610703004915">PSL_2(59) is a subgroup of the Monster</a>,
J. London Math. Soc.,
69 (1)
(2004),
141–152.


<a id="biBHW08" name="biBHW08"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2397402">HW08</a>] Holmes, P. E. and Wilson, R. A.,
<a href="http://dx.doi.org/10.1016/j.jalgebra.2003.11.014">On subgroups of the Monster containing A_5's,
J. Algebra,
319 (7)
(2008),
2653–2667.


<a id="biBIsa76" name="biBIsa76"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=0460423">Isa76</a>] Isaacs, I. M.,
Character theory of finite groups,
Academic Press [Harcourt Brace Jovanovich Publishers],
New York
(1976),
xii+303 pages 
(Pure and Applied Mathematics, No. 69).


<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="biBKlL90" name="biBKlL90"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1057341">KL90</a>] Kleidman, P. and Liebeck, M.,
<a href="http://dx.doi.org/10.1017/CBO9780511629235">The subgroup structure of the finite classical groups</a>,
Cambridge University Press,
London Mathematical Society Lecture Note Series,
129,
Cambridge
(1990),
x+303 pages.


<a id="biBKle87" name="biBKle87"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=904187">Kle87</a>] Kleidman, P. B.,
<a href="http://dx.doi.org/10.1016/0021-8693(87)90042-1">The maximal subgroups of the finite 8-dimensional
 orthogonal groups PΩ^+_8(q) and of their
 automorphism groups</a>,
J. Algebra,
110 (1)
(1987),
173–242.


<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="biBLW91" name="biBLW91"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1105720">LW91</a>] Linton, S. A. and Wilson, R. A.,
<a href="http://dx.doi.org/10.1112/plms/s3-63.1.113">The maximal subgroups of the Fischer groups Fi_{24} and Fi'_{24},
Proc. London Math. Soc. (3),
63 (1)
(1991),
113–164.


<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="biBMSW94" name="biBMSW94"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1261575">MSW94</a>] Malle, G., Saxl, J. and Weigel, T.,
<a href="http://dx.doi.org/10.1007/BF01263536">Generation of classical groups</a>,
Geom. Dedicata,
49 (1)
(1994),
85–116.


<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="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="biBNR14" name="biBNR14"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=3225128">NR14</a>] Navarro, G. and Rizo, N.,
<a href="http://dx.doi.org/10.1142/S0219498814500613">Nilpotent and perfect groups with the same set of character
 degrees</a>,
J. Algebra Appl.,
13 (8)
(2014),
1450061, 3.


<a id="biBNW02" name="biBNW02"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1888424">NW02</a>] Norton, S. P. and Wilson, R. A.,
<a href="http://dx.doi.org/10.1112/S0024611502013357">Anatomy of the Monster. II</a>,
Proc. London Math. Soc. (3),
84 (3)
(2002),
581–598.


<a id="biBNW12" name="biBNW12"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=3073684">NW13</a>] Norton, S. P. and Wilson, R. A.,
<a href="https://doi.org/10.1112/jlms/jds078">A correction to the 41-structure of the Monster,
 a construction of a new maximal subgroup L_2(41)
 and a new Moonshine phenomenon</a>,
J. Lond. Math. Soc. (2),
87 (3)
(2013),
943–962.


<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="biBVdo00" name="biBVdo00"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1805754">Vdo00</a>] Vdovin, E. P.,
<a href="http://dx.doi.org/10.1007/BF02681614">Large nilpotent subgroups of finite simple groups</a>,
Algebra Log.,
39 (5)
(2000),
526–546, 630.


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

[Wil] Wilson, R. A.,
ATLAS: Monster group M,
<a href="http://brauer.maths.qmul.ac.uk/Atlas/spor/M">http://brauer.maths.qmul.ac.uk/Atlas/spor/M</a>.


<a id="biBWil93a" name="biBWil93a"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1254061">Wil93a</a>] Wilson, R. A.,
More on maximal subgroups of the Baby Monster,
Arch. Math. (Basel),
61 (6)
(1993),
497–507.


<a id="biBWilson93" name="biBWilson93"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1190359">Wil93b</a>] Wilson, R. A.,
<a href="http://dx.doi.org/10.1112/blms/25.1.23">Some new subgroups of the Baby Monster</a>,
Bull. London Math. Soc.,
25 (1)
(1993),
23–28.


<a id="biBWil98" name="biBWil98"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1643110">Wil98</a>] Wilson, R. A.,
<a href="http://dx.doi.org/10.1006/jabr.1998.7450">The McKay conjecture is true for the sporadic simple
 groups</a>,
J. Algebra,
207 (1)
(1998),
294–305.


<a id="biBWil99" name="biBWil99"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1656568">Wil99</a>] Wilson, R. A.,
<a href="http://dx.doi.org/10.1006/jabr.1998.7601">The maximal subgroups of the Baby Monster.
 I</a>,
J. Algebra,
211 (1)
(1999),
1–14.


<a id="biBWil10" name="biBWil10"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2681789">Wil10</a>] Wilson, R. A.,
New computations in the Monster,
 in Moonshine: the first quarter century and beyond,
Cambridge Univ. Press,
London Math. Soc. Lecture Note Ser.,
372,
Cambridge
(2010),
393–403.


<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>.


<a id="biBAGRv3" name="biBAGRv3"></a>

[WWT+] Wilson, R. A., Walsh, P., Tripp, J., Suleiman, I., Parker, R. A., Norton, S. P., Nickerson, S., Linton, S., Bray, J. and Abbott, R.,
ATLAS of Finite Group Representations,
<a href="http://brauer.maths.qmul.ac.uk/Atlas/v3">http://brauer.maths.qmul.ac.uk/Atlas/v3</a>.


 

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