/usr/share/gap/pkg/CtblLib/doc/chap1.txt

  
  1 Introduction to the GAP Character Table Library
  
  The  usefulness  of  GAP  for  character  theoretic  tasks  depends  on  the
  availability  of  many  known  character  tables,  and  there  are  a lot of
  character  tables  in the GAP 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
  mailto:sam@math.rwth-aachen.de.
  
  It  depends  on your GAP installation whether the character table library is
  available. You can check this as follows.
  
    Example  
    gap> InstalledPackageVersion( "ctbllib" ) <> fail;
    true
  
  
  If  the  result  is false 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[14 X4.5-1.
  
  For    general    information   about   character   tables   in   GAP,   see
  Chapter[14 X'Reference: Character Tables'.
  
  Examples  of  character  theoretic  computations involving the GAP Character
  Table  Library  are part of the package. They are dealing with the following
  aspects.
  
      Maintenance   issues   concerning  the  GAP  Character  Table  Library
        'CTblLibXpls: Maintenance Issues for the GAP Character Table Library'.
  
      Constructions  of  character  tables  using  table  automorphisms, see
        'CTblLibXpls:  Using  Table  Automorphisms  for Constructing Character
        Tables in GAP'.
  
      Computations   of   common   central   extensions,  see  'CTblLibXpls:
        Constructing Character Tables of Central Extensions in GAP'.
  
      Hamiltonian  cycles  in  the  generating  graphs of finite groups, see
        'CTblLibXpls:  GAP  Computations  Concerning Hamiltonian Cycles in the
        Generating Graphs of Finite Groups'.
  
      A  question  about  the  group  PSO^+(8,5).S_3,  see 'CTblLibXpls: GAP
        Computations with O_8^+(5).S_3 and O_8^+(2).S_3'.
  
      Solvable   subgroups  of  maximal  order  in  sporadic  simple  groups
        'CTblLibXpls:  Solvable  Subgroups of Maximal Order in Sporadic Simple
        Groups'.
  
      Large  Nilpotent  Subgroups  of  sporadic  simple groups 'CTblLibXpls:
        Large Nilpotent Subgroups of Sporadic Simple Groups'.
  
      Computations  of  possible  permutation  characters, see 'CTblLibXpls:
        Permutation Characters in GAP'.
  
      Ambiguous  class fusions, see 'CTblLibXpls: Ambiguous Class Fusions in
        the GAP Character Table Library'.
  
      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 'CTblLibXpls: GAP
        computations needed in the proof of [DNT13, Theorem 6.1 (ii)]'.
  
      Probabilistic  generation  of  finite  simple groups, see [Bree] or an
        updated   version   at   'CTblLibXpls:   GAP  Computations  Concerning
        Probabilistic Generation of Finite Simple Groups'.
  
      Ordinary  character tables, Brauer tables, and decomposition matrices,
        see                                                   doc/ctbldeco.pdf
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctbldeco.pdf
        )                         and                         htm/ctbldeco.htm
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ctbldeco.htm
        ).
  
      Multiplicity-free permutation characters of the sporadic simple groups
        and     their     automorphism     groups,     see    doc/multfree.pdf
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/multfree.pdf
        )                         and                         htm/multfree.htm
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/multfree.htm
        ).
  
      Multiplicity-free  permutation characters of central extensions of the
        sporadic  simple  groups,  and  their automorphic extensions (together
        with         Jürgen        Müller),        see        doc/multfre2.pdf
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/multfre2.pdf
        )                         and                         htm/multfre2.htm
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/multfre2.htm
        ).
  
      The  construction  of  some  character  tables  of Atlas groups, using
        character  theoretic  methods,  see  [Brec]  or  an updated version at
        doc/ctblatlas.pdf
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctblatlas.pdf
        )                         and                        htm/ctblatlas.htm
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ctblatlas.htm
        ).
  
      The verification of the character table of the Baby Monster group, see
        [BMW20]     or     an     updated     version     at    doc/ctblbm.pdf
        (http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctblbm.pdf)
        and                                                     htm/ctblbm.htm
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ctblbm.htm).
  
  If  you  use  the GAP Character Table Library to solve a problem then please
  send  a  short  e-mail  to  mailto:sam@math.rwth-aachen.de about it. The GAP
  Character Table Library database should be referenced as follows.
  
  
    @misc{ CTblLib1.3.4,
      author =       {Breuer, T.},
      title =        {The \textsf{GAP} {C}haracter {T}able {L}ibrary,
                      {V}ersion 1.3.4},
      month =        {April},
      year =         {2022},
      note =         {\textsf{GAP} package},
      howpublished = {http://www.math.rwth-aachen.de/\~{}Thomas.Breuer/ctbllib}
    }
  
  
  For  referencing  the  GAP  system  in general, use the entry [GAP21] in the
  bibliography of this manual, see also
  
  http://www.gap-system.org.
  
  
  1.1 History of the GAP Character Table Library
  
  The  first  version  of  the  GAP  Character Table Library was released with
  GAP 3.1 in March 1992.
  
  It was the first aim of this library to continue the character table library
  of  the  CAS  system  (see  [NPP84])  in  GAP,  as  a part of the process of
  reimplementing  the  algorithms  of  CAS  in GAP, see[14 X'Reference: History of
  Character  Theory  Stuff  in  GAP'.  GAP 3.1  provided  only very restricted
  methods  for computing character tables from groups, so its character theory
  part was concerned mainly with library tables.
  
  A  second  aspect  of  the character table library was to make all character
  tables  shown  in  the  Atlas of Finite Groups [CCN+85] available in GAP. In
  fact GAP turned out to provide a very good environment for systematic checks
  of these character tables.
  
  To  some  extent,  the access to the (ordinary) character tables in [CCN+85]
  was  a  prerequisite  for  storing  also  the corresponding Brauer character
  tables in the GAP Character Table Library. Already GAP 3.1 contained many of
  these  tables.  They  have  been  computed  mainly outside of GAP, using the
  methods  described  in [HJLP], and part of the library has been published in
  the  Atlas  of Brauer Characters [JLPW95]. One of the roles of GAP was again
  to perform systematic checks.
  
  Besides  these projects, many individual character tables have been added to
  the  GAP  Character  Table  Library  since  the  times of GAP 3.1. They were
  computed  from  groups  or  with  character  theoretic  methods  or  using a
  combination of these two possibilities (see, e. g., [NPP84] and [LP91]).
  
  Section[14 X4.1  lists  some  of  the  sources. The changes in the GAP Character
  Table  Library  since the release of GAP 4.1 (in July 1999) are individually
  documented           in          the          file          doc/ctbldiff.pdf
  (http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctbldiff.pdf)  of
  the package.
  
  Currently  the  main  focus  in  the  development of the GAP Character Table
  Library  is  –besides  the addition of tables that appear to be interesting–
  the  better  interaction  with  other  databases, such as the Atlas of Group
  Representations and the GAP Library of Tables of Marks (see the GAP packages
  AtlasRep  and  TomLib)  and GAP's group libraries, and an improvement of the
  database  aspect of the character table library itself, see the sections 3.1
  and 3.5.
  
  Until the release of GAP 4.3 in spring 2002, the GAP Character Table Library
  had been a part of the main GAP library. With GAP 4.3, it was split off as a
  GAP package.
  
  
  1.2 What's New in CTblLib, Compared to Older Versions?
  
  The  PDF file doc/ctbldiff.pdf of the package lists the important changes to
  the data since October 1996, mainly related to the relevant simple groups.
  
  A  perhaps  more  suitable  overview  of  these  changes is given by the GAP
  readable  file data/ctbldiff.json, 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 and evaluated
  using BrowseCTblLibDifferences (3.5-4) if the Browse package (see [BL18]) is
  available.
  
  
  1.2-1 What's New in Version 1.3.4? (April 2022)
  
  The  release  of  Version 1.3.4 was necessary for technical reasons: Now the
  testfile mentioned in PackageInfo.g exits GAP in the end.
  
  
  1.2-2 What's New in Version 1.3.3? (January 2022)
  
  The  reason  for  this  release  was the addition of the new example section
  'CTblLibXpls:  Generation  of  sporadic simple groups by π- and π'-subgroups
  (December 2021)',  which  requires  the new data file data/prim_perm_M.json.
  (The  data had already been used before in the example section 'CTblLibXpls:
  The Monster', which has now been changed accordingly.)
  
  The database attribute IsQuasisimple has been added, which describes perfect
  central  extensions  of nonabelian simple groups. It can be used for example
  to    select    the    character   tables   of   quasisimple   groups   with
  AllCharacterTableNames  (3.1-4).  Thanks to Gunter Malle for suggesting this
  addition.
  
  No  new character tables have been added, and there are only a few new class
  fusions, admissible names, and group constructions.
  
  
  1.2-3 What's New in Version 1.3.2? (March 2021)
  
  The main new features of this release are technical.
  
      The  initialization of the database (at the time when the package gets
        loaded)  has  been  changed.  Instead  of  executing  GAP  code in the
        formerly  available (huge) file data/ctprimar.tbl, now one calls a few
        short  GAP  functions, in the new file gap4/ctprimar.g, which evaluate
        JSON  format  files.  This  was  one  more step on the way to make the
        database independent of GAP.
  
      Also  the  files with the precomputed attribute values are now in JSON
        format, since now the Browse supports this format.
  
      The             WWW            table            of            contents
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/ctbltoc/index.html
        )  of the package has been updated in the sense that it shows the same
        as  the  functions  DisplayCTblLibInfo  (3.5-1)  and BrowseCTblLibInfo
        (3.5-2); at the same time, these functions have been extended in order
        to  link  each table to its main table and to its duplicates. The code
        for  creating  the  HTML files is now distributed with the package, in
        the ctbltoc directory.
  
      The mechanism for processing the package documentation (which contains
        two  GAPDoc  books) has been changed to a more standard way. Now it is
        enough to process one GAP input file in the package directory.
  
  In  several  InfoText  (3.7-5) values of character tables, information about
  group  constructions has been added; where possible, these constructions are
  now also available via GroupInfoForCharacterTable (3.3-1); for example, this
  function  now  supports also the construction of a group as the automorphism
  group  of  a simple group. (Thanks to Gunter Malle for ideas and discussions
  about this feature.)
  
  The  function  BrowseAtlasImprovements  (3.5-10)  can  now  show  (also) the
  improvements for the Atlas of Brauer Characters [JLPW95].
  
  The  strings  "L2(49)" and "L2(81)" are now valid inputs for DisplayAtlasMap
  (3.5-8)  and  BrowseAtlasTable (3.5-9), and DisplayAtlasContents (3.5-6) and
  BrowseAtlasContents (3.5-5) now show information about these two and "L6(2)"
  and "S10(2)".
  
  Besides these changes, a few new tables and class fusions have been added. A
  few  new  examples of applications have been added, see the sections 2.3-10,
  'CTblLibXpls:   The  Character  Table  of  4.L_2(49).2_3  (December  2020)',
  'CTblLibXpls: The Character Table of 4.L_2(81).2_3 (December 2020)'.
  
  
  1.2-4 What's New in Version 1.3.1? (April 2020)
  
  This  release  was  motivated  by  small technical changes: A few typos were
  fixed,  an  acknowledgement was added, the directory name of the package now
  contains  the version number (in order not to overwrite older versions), and
  the  process  to  generate the package documentation was made independent of
  other packages.
  
  Besides  that,  the  function CharacterTableComputedByMagma (6.5-3) was made
  more robust.
  
  In particular, the data part of the package was not changed at all.
  
  
  1.2-5 What's New in Version 1.3.0? (December 2019)
  
  We  distinguish  bug fixes, new features, new character table data, new data
  of other kind, and changed documentation.
  
  The following bugs were fixed.
  
      The  2-modular Brauer table of the character table with the identifier
        "3.(2x2^(1+8)):(U4(2):2x2)"  was  wrong,  due  to  an error in the GAP
        function that constructs this Brauer table from the known Brauer table
        of  U_4(2).2;  this was the only case in the library that was affected
        by this bug. (Thanks to Jürgen Müller who pointed out this error.)
  
      The 2-power map of the character table with the identifier "2.F4(2).2"
        was  wrong,  see  Section 'CTblLibXpls: An Error in a Power Map of the
        Character  Table  of 2.F_4(2).2 (November 2015)'. (This error has been
        found  in  the  context  of  the  computations  that  are described in
        [BMO17].)
  
      The  character  table  of  E_6(2)  was  wrong w. r. t. some irrational
        character  values  and  power maps on the classes of element order 91,
        see  Section  'CTblLibXpls:  An Error in the Character Table of E_6(2)
        (March 2016)'. (Thanks to Bill Unger who pointed out this error.)
  
      Character tables with construction info ConstructAdjusted (5.8-12) had
        immutable  ComputedPowerMaps  (Reference:  ComputedPowerMaps)  values,
        which  made  it  impossible  to add more power maps. (Thanks to Fabian
        Gundlach who pointed out this error.)
  
  The following features have been added.
  
      The  functions  AllCharacterTableNames  (3.1-4), OneCharacterTableName
        (3.1-5),  and  BrowseCTblLibInfo (3.5-2) support now the global option
        OrderedBy.
  
      The  operation  BrauerTable  (3.1-3)  now  admits also a string as its
        first  argument,  and  then  delegates to the ordinary character table
        with this name.
  
      The  operation  BrauerTable  (3.1-3)  is  now  successful  also if the
        ordinary    character    table   in   question   has   the   attribute
        ConstructionInfoCharacterTable  (3.7-4) set and the first entry of the
        attribute value is the string "ConstructGS3" and the Brauer tables for
        the  character  tables involved in the construction are available, see
        Section 'CTblLibXpls: Examples for the Type G.S_3'.
  
      The function CambridgeMaps (6.4-1) has been improved in the sense that
        relative  class  names  such as "B*2" occur whenever this is possible,
        where  the  element  order  does  not  appear in the class name, and a
        Galois  automorphism  describes  the  relation  to another class. (The
        character  table  with identifier "L2(13)" is an example for which the
        result is now different.)
  
      The  function ConstructIsoclinic (5.8-10) has been extended, according
        to  the  extended functionality of CharacterTableIsoclinic (Reference:
        CharacterTableIsoclinic). For examples, see the sections 'CTblLibXpls:
        Groups  of the Structures 3.U_3(8).3_1 and 3.U_3(8).6 (February 2017)'
        and 'CTblLibXpls: The Character Table of 9.U_3(8).3_3 (March 2017)'.
  
      There  is  now a default InfoText (3.7-5) method for library character
        tables,  which  returns  an  empty  string.  This  admits searches for
        properties  of  the  info  text  via  AllCharacterTableNames  (3.1-4).
        Similarly,  also  properties  of Identifier (Reference: Identifier for
        character    tables)    can   now   be   searched   efficiently,   see
        AllCharacterTableNames (3.1-4) for examples.
  
      With  the user preference DisplayFunction of the AtlasRep package (see
        Section    4.5-3),    one    can    configure   how   functions   like
        DisplayCTblLibInfo  (3.5-1)  place  their output on the screen. (Up to
        now, the function Pager (Reference: Pager) had always been called.)
  
      The definition of duplicate tables has been extended in order to get a
        better integration of the SpinSym package, see Section[14 X3.6.
  
      A  new  variant  of  the  function  GAPTableOfMagmaFile (6.5-2) admits
        entering  a  MAGMA  format  string  instead of the name of a file that
        contains this string.
  
      The  new function CharacterTableComputedByMagma (6.5-3) uses the MAGMA
        system  (if  this is available) for computing the character table of a
        permutation group.
  
      The  new function NotifyCharacterTables (4.7-6) is more efficient than
        NotifyCharacterTable  (4.7-5)  if  one  wants  to  add several private
        character tables at the same time.
  
      In  the  tables  of maximal subgroups and Sylow p normalizers shown by
        DisplayCTblLibInfo  (3.5-1)  and BrowseCTblLibInfo (3.5-2), the former
        Name column has been replaced by two columns Structure (which tries to
        show   information   about   the   structures  of  the  groups,  using
        StructureDescriptionCharacterTableName  (7.2-1))  and Name (which just
        shows the identifiers of the character tables). This improvement arose
        from a discussion with Gabriel Navarro.
  
      The  former GAP readable text file data/ctbldiff.dat has been replaced
        by  the  (still GAP readable) JSON format file data/ctbldiff.json. (It
        is  planned  for  future  releases  to replace more data files by JSON
        format files, in order to make the data independent of GAP.)
  
      Two  filenames  of the package have been changed, from ctadmin.tbd and
        ctadmin.tbi to ctadmin.gd and ctadmin.gi, respectively.
  
  Concerning added character table data, the full list of differences w. r. t.
  earlier versions can be found in the file data/ctbldiff.json of the package;
  see BrowseCTblLibDifferences (3.5-4) for a way to utilize this list in a GAP
  session.
  
  The following other data have been added.
  
      GroupInfoForCharacterTable (3.3-1) works now for more character tables
        than before.
  
        In particular there are representations for all Atlas groups (bicyclic
        extensions  of  simple  groups whose character tables are shown in the
        Atlas  of Finite Groups [CCN+85], up to isoclinism), except the groups
        2.B  and  M;  several  of  these  representations were computed in the
        context of the computations that are described in [BMO17].
  
        Also  the  library  tables  of  groups  that occur in GAP's library of
        primitive  groups (the GAP package PrimGrp) know about this fact; note
        that older versions of PrimGrp contained only groups of degree at most
        2499.
  
        See  Section  'CTblLibXpls: Some finite factor groups of perfect space
        groups  (February  2014)'  for some other representations that are now
        available.
  
  Finally, the documentation was changed as follows.
  
      Several   of   the  files  showing  examples  of  character  theoretic
        computations   with   GAP  have  been  turned  into  the  GAPDoc  book
        CTblLibXpls, see above. Some advantages of this new setup are that the
        contents  can  be  accessed  also  in GAP's interactive help, and that
        cross-referencing is simpler.
  
  
  1.2-6 What's New in Version 1.2.2? (March 2013)
  
  The following bugs were fixed.
  
      The functions AllCharacterTableNames (3.1-4) and OneCharacterTableName
        (3.1-5)  ran  into  an error in certain situations, if the library had
        been  extended  by private tables, see Section 4.7. (As a consequence,
        the description of IsDuplicateTable (3.6-1) has been extended.) Thanks
        to Alexander Konovalov and Lukas Maas for pointing out this error.
  
      The function CharacterTableOfIndexTwoSubdirectProduct (5.5-1) returned
        a  wrong  result  if  the two factors were given by the same character
        table.  An example is (A_5 × A_5).2, created as a subdirect product of
        two copies of S_5.
  
  
  1.2-7 What's New in Version 1.2.0 and 1.2.1? (May 2012)
  
  Concerning character table data, we have the following.
  
      A few bugs in character tables have been fixed.
  
      Several class fusions stored in character tables have been changed, in
        order  to  be  more  consistent with related data, see Section 4.9 for
        reasons of such changes.
  
      Many  new  character  tables have been added. For example, a character
        table is available for each table of marks in the TomLib package.
  
  Besides these changes of the data, the following features are new.
  
      A  tutorial for beginners was added to the package manual, see Chapter
        2, and the package manual was restructured. The manual is now based on
        the GAPDoc package (see [LN18]).
  
      Generic  constructions  of  Brauer  tables  are  now  available if the
        underlying   ordinary  table  is  encoded  via  ConstructMGA  (5.8-1),
        ConstructIndexTwoSubdirectProduct  (5.5-2),  or  ConstructV4G (5.8-4),
        and if the Brauer tables of the compound tables are known.
  
      The attributes FusionToTom (3.2-4) and Maxes (3.7-1) 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.
  
      The consistency checks for character tables have been improved and are
        now  documented,  see  Section[14 X4.8. Due to these checks, several class
        fusions had to be replaced.
  
      The  concept  of  duplicate  character  tables  is now documented, see
        Section[14 X3.6. As a consequence, the behaviour of AllCharacterTableNames
        (3.1-4)  has changed in situations where IsSimple (Reference: IsSimple
        for    a    character    table)    or   IsSporadicSimple   (Reference:
        IsSporadicSimple  for  a  character  table)  occur  as  arguments (see
        'Reference:  Group  Operations  Applicable  to  Character Tables'), 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.
  
      Several   attribute   values   for  character  tables,  such  as  Size
        (Reference:      Size)      and     NrConjugacyClasses     (Reference:
        NrConjugacyClasses)  are  now  available without reading the character
        table  data  files,  provided that the Browse package (see [BL18]) has
        been  loaded.  See the documentation of AllCharacterTableNames (3.1-4)
        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.
  
      GAP'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[14 X3.3, provided that the Browse package
        (see [BL18]) has been loaded.
  
      An interactive overview of the contents is now available that is based
        on the Browse package [BL18], see Section 3.5.
  
      Information  about  Deligne-Lusztig  names  of unipotent characters of
        finite groups of Lie type is now available, see Section 3.4.
  
      An interface for reading MAGMA tables was added, see Section 6.5.
  
  
  1.2-8 What's New in Version 1.1? (November 2003)
  
  First  of  all,  of  course  several  character  tables  were  added; for an
  overview,  see  the  file  doc/ctbldiff.pdf  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 p-subgroups
  whenever  the  tables  of  the  factors  are available; these maps admit the
  automatic  construction  of the p-modular Brauer tables if the corresponding
  tables of the factors are available. For example, the 2-modular Brauer table
  of  the  maximal  subgroup  of  the  type  2^10:M_22  in  the group Fi_22 is
  available because of the known 2-modular table of M_22 and the stored factor
  fusion onto the table of M_22.
  
  Second,  more  information  has  been  made  more explicit, in the following
  sense.
  
      Identifier  (Reference:  Identifier  for  character  tables) values of
        tables  that  are  constructed  from  generic  tables  are  now  valid
        arguments  of  CharacterTable (Reference: CharacterTable), for example
        CharacterTable(  "C10" ) and CharacterTable( "Sym(5)" ) can be used to
        create  the character table of the cyclic group of order 10 and of the
        symmetric group of degree 5, respectively.
  
      Attributes  have  been  introduced  that  replace  more or less hidden
        components (see Section[14 X3.7); 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[2 XConstructionInfoCharacterTable (3.7-4)).
  
      The  functions  that  are  used  for the table constructions have been
        documented (see Chapter[14 X5).
  
      Several  consistency  checks are now part of the package distribution,
        in  the  files  gap4/test.gd and gap4/test.gi. However, currently they
        are  not  documented.  The new file tst/testall.g lists the files that
        belong  to  the  standard test suite. Further checks involving the GAP
        Character  Table  Library  are  parts  of  the  GAP  packages AtlasRep
        (see [WPN+19]) and TomLib.
  
      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 text 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.
  
      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  CTblLibSetUnload  had  been  provided  for  that. Since
        version 1.2, a GAP 4.5 user preference replaces this function.)
  
  Third, several errors have been corrected (again see[11 Xdoc/ctbldiff.pdf). Most
  of them affect class fusions, and for most of those, the term error could be
  regarded as not really appropriate. See 4.9 for details.
  
  Finally,  the  GAP  functions  for  reading  and  writing  other  formats of
  character  tables  have been moved from the main GAP library to this package
  (see  Chapter[14 X6), because they are useful only for library tables. The GAP 3
  format  is  now  also  supported,  mainly  for  documentation  purposes (see
  Section[14 X6.3).
  
  
  1.3 Acknowledgements
  
  The  development  of  the  GAP 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), the Schwerpunkt
  Algorithmische  Zahlentheorie  und  Algebra  (from 1991 until 1997), and the
  SFB-TRR   195   Symbolic   Tools   in  Mathematics  and  their  Applications
  (https://www.computeralgebra.de/sfb/) (Project-ID 286237555, since 2017).
  
  The  functions  for  the  conversion  of  CAS tables to GAP format have been
  written  by  Götz  Pfeiffer.  The  functions  for  converting  the so-called
  Cambridge  format  (in which the original data of the Atlas of Finite Groups
  had been stored) to GAP format have been written by Christoph Jansen.
  
  The  generic  character tables of double covers of alternating and symmetric
  groups were contributed by Felix Noeske, see [Noe02].
  
  The     functions     in     Section[14 X3.4     (DeligneLusztigName    (3.4-3),
  DeligneLusztigNames  (3.4-2), and UnipotentCharacter (3.4-1)) as well as the
  corresponding  data  for  the finite groups of Lie type in the GAP Character
  Table Library have been contributed by Michael Claßen-Houben, see [CH05].
  
  Several  character  tables of maximal subgroups of covering groups of simple
  groups have been computed by Sebastian Dany, see [Dan06].
  
  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 TtH was used to provide these HTML files.
  
  Thanks  to  Frank  Lübeck  and Max Neunhöffer also for developing the GAPDoc
  package  (see [LN18]),  on which the manual of the CTblLib package is based.
  The   previously   available   documentation   format  had  been  completely
  inappropriate.
  

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