  
  [1X1 [33X[0;0YIntroduction to the [5XGAP[105X[101X[1X Character Table Library[133X[101X
  
  [33X[0;0YThe  usefulness  of  [5XGAP[105X  for  character  theoretic  tasks  depends  on  the
  availability  of  many  known  character  tables,  and  there  are  a lot of
  character  tables  in the [5XGAP[105X table library. Of course, this library is [21Xopen[121X
  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
  [7Xmailto:sam@math.rwth-aachen.de[107X.[133X
  
  [33X[0;0YIt  depends  on your [5XGAP[105X installation whether the character table library is
  available. You can check this as follows.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XInstalledPackageVersion( "ctbllib" ) <> fail;[127X[104X
    [4X[28Xtrue[128X[104X
  [4X[32X[104X
  
  [33X[0;0YIf  the  result  is [9Xfalse[109X 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 [14X4.5-1[114X.[133X
  
  [33X[0;0YFor    general    information   about   character   tables   in   [5XGAP[105X,   see
  Chapter [14X'Reference: Character Tables'[114X.[133X
  
  [33X[0;0YExamples  of  character  theoretic  computations involving the [5XGAP[105X Character
  Table  Library  are part of the package. They are dealing with the following
  aspects.[133X
  
  [30X    [33X[0;6YMaintenance   issues   concerning  the  [5XGAP[105X  Character  Table  Library
        [14X'CTblLibXpls: Maintenance Issues for the GAP Character Table Library'[114X.[133X
  
  [30X    [33X[0;6YConstructions  of  character  tables  using  table  automorphisms, see
        [14X'CTblLibXpls:  Using  Table  Automorphisms  for Constructing Character
        Tables in GAP'[114X.[133X
  
  [30X    [33X[0;6YComputations   of   common   central   extensions,  see  [14X'CTblLibXpls:
        Constructing Character Tables of Central Extensions in GAP'[114X.[133X
  
  [30X    [33X[0;6YHamiltonian  cycles  in  the  generating  graphs of finite groups, see
        [14X'CTblLibXpls:  GAP  Computations  Concerning Hamiltonian Cycles in the
        Generating Graphs of Finite Groups'[114X.[133X
  
  [30X    [33X[0;6YA  question  about  the  group  PSO[22X^+(8,5).S_3[122X,  see [14X'CTblLibXpls: GAP
        Computations with O_8^+(5).S_3 and O_8^+(2).S_3'[114X.[133X
  
  [30X    [33X[0;6YSolvable   subgroups  of  maximal  order  in  sporadic  simple  groups
        [14X'CTblLibXpls:  Solvable  Subgroups of Maximal Order in Sporadic Simple
        Groups'[114X.[133X
  
  [30X    [33X[0;6YLarge  Nilpotent  Subgroups  of  sporadic  simple groups [14X'CTblLibXpls:
        Large Nilpotent Subgroups of Sporadic Simple Groups'[114X.[133X
  
  [30X    [33X[0;6YComputations  of  possible  permutation  characters, see [14X'CTblLibXpls:
        Permutation Characters in GAP'[114X.[133X
  
  [30X    [33X[0;6YAmbiguous  class fusions, see [14X'CTblLibXpls: Ambiguous Class Fusions in
        the GAP Character Table Library'[114X.[133X
  
  [30X    [33X[0;6YSome  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 [14X'CTblLibXpls: GAP
        computations needed in the proof of [DNT13, Theorem 6.1 (ii)]'[114X.[133X
  
  [30X    [33X[0;6YProbabilistic  generation  of  finite  simple groups, see [Bree] or an
        updated   version   at   [14X'CTblLibXpls:   GAP  Computations  Concerning
        Probabilistic Generation of Finite Simple Groups'[114X.[133X
  
  [30X    [33X[0;6YOrdinary  character tables, Brauer tables, and decomposition matrices,
        see                                                   [11Xdoc/ctbldeco.pdf[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctbldeco.pdf
        )                         and                         [11Xhtm/ctbldeco.htm[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ctbldeco.htm
        ).[133X
  
  [30X    [33X[0;6YMultiplicity-free permutation characters of the sporadic simple groups
        and     their     automorphism     groups,     see    [11Xdoc/multfree.pdf[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/multfree.pdf
        )                         and                         [11Xhtm/multfree.htm[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/multfree.htm
        ).[133X
  
  [30X    [33X[0;6YMultiplicity-free  permutation characters of central extensions of the
        sporadic  simple  groups,  and  their automorphic extensions (together
        with         Jürgen        Müller),        see        [11Xdoc/multfre2.pdf[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/multfre2.pdf
        )                         and                         [11Xhtm/multfre2.htm[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/multfre2.htm
        ).[133X
  
  [30X    [33X[0;6YThe  construction  of  some  character  tables  of [5XAtlas[105X groups, using
        character  theoretic  methods,  see  [Brec]  or  an updated version at
        [11Xdoc/ctblatlas.pdf[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctblatlas.pdf
        )                         and                        [11Xhtm/ctblatlas.htm[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ctblatlas.htm
        ).[133X
  
  [30X    [33X[0;6YThe verification of the character table of the Baby Monster group, see
        [BMW20]     or     an     updated     version     at    [11Xdoc/ctblbm.pdf[111X
        ([7Xhttp://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctblbm.pdf[107X)
        and                                                     [11Xhtm/ctblbm.htm[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ctblbm.htm[107X).[133X
  
  [33X[0;0YIf  you  use  the [5XGAP[105X Character Table Library to solve a problem then please
  send  a  short  e-mail  to  [7Xmailto:sam@math.rwth-aachen.de[107X about it. The [5XGAP[105X
  Character Table Library database should be referenced as follows.[133X
  
  [4X[32X[104X
    [4X@misc{ CTblLib1.3.4,[104X
    [4X  author =       {Breuer, T.},[104X
    [4X  title =        {The \textsf{GAP} {C}haracter {T}able {L}ibrary,[104X
    [4X                  {V}ersion 1.3.4},[104X
    [4X  month =        {April},[104X
    [4X  year =         {2022},[104X
    [4X  note =         {\textsf{GAP} package},[104X
    [4X  howpublished = {http://www.math.rwth-aachen.de/\~{}Thomas.Breuer/ctbllib}[104X
    [4X}[104X
  [4X[32X[104X
  
  [33X[0;0YFor  referencing  the  [5XGAP[105X  system  in general, use the entry [GAP21] in the
  bibliography of this manual, see also[133X
  
  [33X[0;0Y[7Xhttp://www.gap-system.org[107X.[133X
  
  
  [1X1.1 [33X[0;0YHistory of the [5XGAP[105X[101X[1X Character Table Library[133X[101X
  
  [33X[0;0YThe  first  version  of  the  [5XGAP[105X  Character Table Library was released with
  [5XGAP[105X 3.1 in March 1992.[133X
  
  [33X[0;0YIt was the first aim of this library to continue the character table library
  of  the  [5XCAS[105X  system  (see  [NPP84])  in  [5XGAP[105X,  as  a part of the process of
  reimplementing  the  algorithms  of  [5XCAS[105X  in [5XGAP[105X, see [14X'Reference: History of
  Character  Theory  Stuff  in  GAP'[114X.  [5XGAP[105X 3.1  provided  only very restricted
  methods  for computing character tables from groups, so its character theory
  part was concerned mainly with library tables.[133X
  
  [33X[0;0YA  second  aspect  of  the character table library was to make all character
  tables  shown  in  the  [5XAtlas[105X of Finite Groups [CCN+85] available in [5XGAP[105X. In
  fact [5XGAP[105X turned out to provide a very good environment for systematic checks
  of these character tables.[133X
  
  [33X[0;0YTo  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 [5XGAP[105X Character Table Library. Already [5XGAP[105X 3.1 contained many of
  these  tables.  They  have  been  computed  mainly [21Xoutside of [5XGAP[105X[121X, using the
  methods  described  in [HJLP], and part of the library has been published in
  the  [5XAtlas[105X  of Brauer Characters [JLPW95]. One of the roles of [5XGAP[105X was again
  to perform systematic checks.[133X
  
  [33X[0;0YBesides  these projects, many individual character tables have been added to
  the  [5XGAP[105X  Character  Table  Library  since  the  times of [5XGAP[105X 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]).[133X
  
  [33X[0;0YSection [14X4.1[114X  lists  some  of  the  sources. The changes in the [5XGAP[105X Character
  Table  Library  since the release of [5XGAP[105X 4.1 (in July 1999) are individually
  documented           in          the          file          [11Xdoc/ctbldiff.pdf[111X
  ([7Xhttp://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctbldiff.pdf[107X)  of
  the package.[133X
  
  [33X[0;0YCurrently  the  main  focus  in  the  development of the [5XGAP[105X Character Table
  Library  is  –besides  the addition of tables that appear to be interesting–
  the  better  interaction  with  other  databases, such as the [5XAtlas[105X of Group
  Representations and the [5XGAP[105X Library of Tables of Marks (see the [5XGAP[105X packages
  [5XAtlasRep[105X  and  [5XTomLib[105X)  and [5XGAP[105X's group libraries, and an improvement of the
  [21Xdatabase[121X  aspect of the character table library itself, see the sections [14X3.1[114X
  and [14X3.5[114X.[133X
  
  [33X[0;0YUntil the release of [5XGAP[105X 4.3 in spring 2002, the [5XGAP[105X Character Table Library
  had been a part of the main [5XGAP[105X library. With [5XGAP[105X 4.3, it was [21Xsplit off[121X as a
  [5XGAP[105X package.[133X
  
  
  [1X1.2 [33X[0;0YWhat's New in [5XCTblLib[105X[101X[1X, Compared to Older Versions?[133X[101X
  
  [33X[0;0YThe  PDF file [11Xdoc/ctbldiff.pdf[111X of the package lists the important changes to
  the data since October 1996, mainly related to the relevant simple groups.[133X
  
  [33X[0;0YA  perhaps  more  suitable  overview  of  these  changes is given by the [5XGAP[105X
  readable  file [11Xdata/ctbldiff.json[111X, 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 [21Xfrom[121X table and
  once  for  the  [21Xto[121X  table.)  This list of changes can be shown and evaluated
  using [2XBrowseCTblLibDifferences[102X ([14X3.5-4[114X) if the [5XBrowse[105X package (see [BL18]) is
  available.[133X
  
  
  [1X1.2-1 [33X[0;0YWhat's New in Version 1.3.4? (April 2022)[133X[101X
  
  [33X[0;0YThe  release  of  Version 1.3.4 was necessary for technical reasons: Now the
  testfile mentioned in [11XPackageInfo.g[111X exits [5XGAP[105X in the end.[133X
  
  
  [1X1.2-2 [33X[0;0YWhat's New in Version 1.3.3? (January 2022)[133X[101X
  
  [33X[0;0YThe  reason  for  this  release  was the addition of the new example section
  [14X'CTblLibXpls:  Generation  of  sporadic simple groups by π- and π'-subgroups
  (December 2021)'[114X,  which  requires  the new data file [11Xdata/prim_perm_M.json[111X.
  (The  data had already been used before in the example section [14X'CTblLibXpls:
  The Monster'[114X, which has now been changed accordingly.)[133X
  
  [33X[0;0YThe database attribute [10XIsQuasisimple[110X 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
  [2XAllCharacterTableNames[102X  ([14X3.1-4[114X).  Thanks to Gunter Malle for suggesting this
  addition.[133X
  
  [33X[0;0YNo  new character tables have been added, and there are only a few new class
  fusions, admissible names, and group constructions.[133X
  
  
  [1X1.2-3 [33X[0;0YWhat's New in Version 1.3.2? (March 2021)[133X[101X
  
  [33X[0;0YThe main new features of this release are technical.[133X
  
  [30X    [33X[0;6YThe  initialization of the database (at the time when the package gets
        loaded)  has  been  changed.  Instead  of  executing  [5XGAP[105X  code in the
        formerly  available (huge) file [11Xdata/ctprimar.tbl[111X, now one calls a few
        short  [5XGAP[105X  functions, in the new file [11Xgap4/ctprimar.g[111X, which evaluate
        JSON  format  files.  This  was  one  more step on the way to make the
        database independent of [5XGAP[105X.[133X
  
  [30X    [33X[0;6YAlso  the  files with the precomputed attribute values are now in JSON
        format, since now the [5XBrowse[105X supports this format.[133X
  
  [30X    [33X[0;6YThe             [21XWWW            table            of            contents[121X
        (
        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  [2XDisplayCTblLibInfo[102X  ([14X3.5-1[114X)  and [2XBrowseCTblLibInfo[102X
        ([14X3.5-2[114X); 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 [11Xctbltoc[111X directory.[133X
  
  [30X    [33X[0;6YThe mechanism for processing the package documentation (which contains
        two  [5XGAPDoc[105X  books) has been changed to a more standard way. Now it is
        enough to process one [5XGAP[105X input file in the package directory.[133X
  
  [33X[0;0YIn  several  [2XInfoText[102X  ([14X3.7-5[114X) values of character tables, information about
  group  constructions has been added; where possible, these constructions are
  now also available via [2XGroupInfoForCharacterTable[102X ([14X3.3-1[114X); 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.)[133X
  
  [33X[0;0YThe  function  [2XBrowseAtlasImprovements[102X  ([14X3.5-10[114X)  can  now  show  (also) the
  improvements for the [5XAtlas[105X of Brauer Characters [JLPW95].[133X
  
  [33X[0;0YThe  strings  [10X"L2(49)"[110X and [10X"L2(81)"[110X are now valid inputs for [2XDisplayAtlasMap[102X
  ([14X3.5-8[114X)  and  [2XBrowseAtlasTable[102X ([14X3.5-9[114X), and [2XDisplayAtlasContents[102X ([14X3.5-6[114X) and
  [2XBrowseAtlasContents[102X ([14X3.5-5[114X) now show information about these two and [10X"L6(2)"[110X
  and [10X"S10(2)"[110X.[133X
  
  [33X[0;0YBesides these changes, a few new tables and class fusions have been added. A
  few  new  examples of applications have been added, see the sections [14X2.3-10[114X,
  [14X'CTblLibXpls:   The  Character  Table  of  4.L_2(49).2_3  (December  2020)'[114X,
  [14X'CTblLibXpls: The Character Table of 4.L_2(81).2_3 (December 2020)'[114X.[133X
  
  
  [1X1.2-4 [33X[0;0YWhat's New in Version 1.3.1? (April 2020)[133X[101X
  
  [33X[0;0YThis  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.[133X
  
  [33X[0;0YBesides  that,  the  function [2XCharacterTableComputedByMagma[102X ([14X6.5-3[114X) was made
  more robust.[133X
  
  [33X[0;0YIn particular, the data part of the package was not changed at all.[133X
  
  
  [1X1.2-5 [33X[0;0YWhat's New in Version 1.3.0? (December 2019)[133X[101X
  
  [33X[0;0YWe  distinguish  bug fixes, new features, new character table data, new data
  of other kind, and changed documentation.[133X
  
  [33X[0;0Y[13XThe following bugs were fixed.[113X[133X
  
  [30X    [33X[0;6YThe  [22X2[122X-modular Brauer table of the character table with the identifier
        [10X"3.(2x2^(1+8)):(U4(2):2x2)"[110X  was  wrong,  due  to  an error in the [5XGAP[105X
        function that constructs this Brauer table from the known Brauer table
        of  [22XU_4(2).2[122X;  this was the only case in the library that was affected
        by this bug. (Thanks to Jürgen Müller who pointed out this error.)[133X
  
  [30X    [33X[0;6YThe [22X2[122X-power map of the character table with the identifier [10X"2.F4(2).2"[110X
        was  wrong,  see  Section [14X'CTblLibXpls: An Error in a Power Map of the
        Character  Table  of 2.F_4(2).2 (November 2015)'[114X. (This error has been
        found  in  the  context  of  the  computations  that  are described in
        [BMO17].)[133X
  
  [30X    [33X[0;6YThe  character  table  of  [22XE_6(2)[122X  was  wrong w. r. t. some irrational
        character  values  and  power maps on the classes of element order [22X91[122X,
        see  Section  [14X'CTblLibXpls:  An Error in the Character Table of E_6(2)
        (March 2016)'[114X. (Thanks to Bill Unger who pointed out this error.)[133X
  
  [30X    [33X[0;6YCharacter tables with construction info [2XConstructAdjusted[102X ([14X5.8-12[114X) had
        immutable  [2XComputedPowerMaps[102X  ([14XReference:  ComputedPowerMaps[114X)  values,
        which  made  it  impossible  to add more power maps. (Thanks to Fabian
        Gundlach who pointed out this error.)[133X
  
  [33X[0;0Y[13XThe following features have been added.[113X[133X
  
  [30X    [33X[0;6YThe  functions  [2XAllCharacterTableNames[102X  ([14X3.1-4[114X), [2XOneCharacterTableName[102X
        ([14X3.1-5[114X),  and  [2XBrowseCTblLibInfo[102X ([14X3.5-2[114X) support now the global option
        [10XOrderedBy[110X.[133X
  
  [30X    [33X[0;6YThe  operation  [2XBrauerTable[102X  ([14X3.1-3[114X)  now  admits also a string as its
        first  argument,  and  then  delegates to the ordinary character table
        with this name.[133X
  
  [30X    [33X[0;6YThe  operation  [2XBrauerTable[102X  ([14X3.1-3[114X)  is  now  successful  also if the
        ordinary    character    table   in   question   has   the   attribute
        [2XConstructionInfoCharacterTable[102X  ([14X3.7-4[114X) set and the first entry of the
        attribute value is the string [10X"ConstructGS3"[110X and the Brauer tables for
        the  character  tables involved in the construction are available, see
        Section [14X'CTblLibXpls: Examples for the Type G.S_3'[114X.[133X
  
  [30X    [33X[0;6YThe function [2XCambridgeMaps[102X ([14X6.4-1[114X) has been improved in the sense that
        [21Xrelative[121X  class  names  such as [10X"B*2"[110X 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 [10X"L2(13)"[110X is an example for which the
        result is now different.)[133X
  
  [30X    [33X[0;6YThe  function [2XConstructIsoclinic[102X ([14X5.8-10[114X) has been extended, according
        to  the  extended functionality of [2XCharacterTableIsoclinic[102X ([14XReference:
        CharacterTableIsoclinic[114X). For examples, see the sections [14X'CTblLibXpls:
        Groups  of the Structures 3.U_3(8).3_1 and 3.U_3(8).6 (February 2017)'[114X
        and [14X'CTblLibXpls: The Character Table of 9.U_3(8).3_3 (March 2017)'[114X.[133X
  
  [30X    [33X[0;6YThere  is  now a default [2XInfoText[102X ([14X3.7-5[114X) method for library character
        tables,  which  returns  an  empty  string.  This  admits searches for
        properties  of  the  info  text  via  [2XAllCharacterTableNames[102X  ([14X3.1-4[114X).
        Similarly,  also  properties  of [2XIdentifier[102X ([14XReference: Identifier for
        character    tables[114X)    can   now   be   searched   efficiently,   see
        [2XAllCharacterTableNames[102X ([14X3.1-4[114X) for examples.[133X
  
  [30X    [33X[0;6YWith  the user preference [10XDisplayFunction[110X of the [5XAtlasRep[105X package (see
        Section    [14X4.5-3[114X),    one    can    configure   how   functions   like
        [2XDisplayCTblLibInfo[102X  ([14X3.5-1[114X)  place  their output on the screen. (Up to
        now, the function [2XPager[102X ([14XReference: Pager[114X) had always been called.)[133X
  
  [30X    [33X[0;6YThe definition of [21Xduplicate tables[121X has been extended in order to get a
        better integration of the [5XSpinSym[105X package, see Section [14X3.6[114X.[133X
  
  [30X    [33X[0;6YA  new  variant  of  the  function  [2XGAPTableOfMagmaFile[102X ([14X6.5-2[114X) admits
        entering  a  [5XMAGMA[105X  format  string  instead of the name of a file that
        contains this string.[133X
  
  [30X    [33X[0;6YThe  new function [2XCharacterTableComputedByMagma[102X ([14X6.5-3[114X) uses the [5XMAGMA[105X
        system  (if  this is available) for computing the character table of a
        permutation group.[133X
  
  [30X    [33X[0;6YThe  new function [2XNotifyCharacterTables[102X ([14X4.7-6[114X) is more efficient than
        [2XNotifyCharacterTable[102X  ([14X4.7-5[114X)  if  one  wants  to  add several private
        character tables at the same time.[133X
  
  [30X    [33X[0;6YIn  the  tables  of maximal subgroups and Sylow [22Xp[122X normalizers shown by
        [2XDisplayCTblLibInfo[102X  ([14X3.5-1[114X)  and [2XBrowseCTblLibInfo[102X ([14X3.5-2[114X), the former
        [10XName[110X column has been replaced by two columns [10XStructure[110X (which tries to
        show   information   about   the   structures  of  the  groups,  using
        [2XStructureDescriptionCharacterTableName[102X  ([14X7.2-1[114X))  and [10XName[110X (which just
        shows the identifiers of the character tables). This improvement arose
        from a discussion with Gabriel Navarro.[133X
  
  [30X    [33X[0;6YThe  former [5XGAP[105X readable text file [11Xdata/ctbldiff.dat[111X has been replaced
        by  the  (still [5XGAP[105X readable) JSON format file [11Xdata/ctbldiff.json[111X. (It
        is  planned  for  future  releases  to replace more data files by JSON
        format files, in order to make the data independent of [5XGAP[105X.)[133X
  
  [30X    [33X[0;6YTwo  filenames  of the package have been changed, from [11Xctadmin.tbd[111X and
        [11Xctadmin.tbi[111X to [11Xctadmin.gd[111X and [11Xctadmin.gi[111X, respectively.[133X
  
  [33X[0;0YConcerning [13Xadded character table data[113X, the full list of differences w. r. t.
  earlier versions can be found in the file [11Xdata/ctbldiff.json[111X of the package;
  see [2XBrowseCTblLibDifferences[102X ([14X3.5-4[114X) for a way to utilize this list in a [5XGAP[105X
  session.[133X
  
  [33X[0;0Y[13XThe following other data have been added.[113X[133X
  
  [30X    [33X[0;6Y[2XGroupInfoForCharacterTable[102X ([14X3.3-1[114X) works now for more character tables
        than before.[133X
  
        [33X[0;6YIn particular there are representations for all [5XAtlas[105X groups (bicyclic
        extensions  of  simple  groups whose character tables are shown in the
        [5XAtlas[105X  of Finite Groups [CCN+85], up to isoclinism), except the groups
        [22X2.B[122X  and  [22XM[122X;  several  of  these  representations were computed in the
        context of the computations that are described in [BMO17].[133X
  
        [33X[0;6YAlso  the  library  tables  of  groups  that occur in [5XGAP[105X's library of
        primitive  groups (the [5XGAP[105X package [5XPrimGrp[105X) know about this fact; note
        that older versions of [5XPrimGrp[105X contained only groups of degree at most
        [22X2499[122X.[133X
  
        [33X[0;6YSee  Section  [14X'CTblLibXpls: Some finite factor groups of perfect space
        groups  (February  2014)'[114X  for some other representations that are now
        available.[133X
  
  [33X[0;0Y[13XFinally, the documentation was changed as follows.[113X[133X
  
  [30X    [33X[0;6YSeveral   of   the  files  showing  examples  of  character  theoretic
        computations   with   [5XGAP[105X  have  been  turned  into  the  [5XGAPDoc[105X  book
        [21XCTblLibXpls[121X, see above. Some advantages of this new setup are that the
        contents  can  be  accessed  also  in [5XGAP[105X's interactive help, and that
        cross-referencing is simpler.[133X
  
  
  [1X1.2-6 [33X[0;0YWhat's New in Version 1.2.2? (March 2013)[133X[101X
  
  [33X[0;0YThe following bugs were fixed.[133X
  
  [30X    [33X[0;6YThe functions [2XAllCharacterTableNames[102X ([14X3.1-4[114X) and [2XOneCharacterTableName[102X
        ([14X3.1-5[114X)  ran  into  an error in certain situations, if the library had
        been  extended  by private tables, see Section [14X4.7[114X. (As a consequence,
        the description of [2XIsDuplicateTable[102X ([14X3.6-1[114X) has been extended.) Thanks
        to Alexander Konovalov and Lukas Maas for pointing out this error.[133X
  
  [30X    [33X[0;6YThe function [2XCharacterTableOfIndexTwoSubdirectProduct[102X ([14X5.5-1[114X) returned
        a  wrong  result  if  the two factors were given by the [13Xsame[113X character
        table.  An example is [22X(A_5 × A_5).2[122X, created as a subdirect product of
        two copies of [22XS_5[122X.[133X
  
  
  [1X1.2-7 [33X[0;0YWhat's New in Version 1.2.0 and 1.2.1? (May 2012)[133X[101X
  
  [33X[0;0YConcerning character table data, we have the following.[133X
  
  [30X    [33X[0;6YA few bugs in character tables have been fixed.[133X
  
  [30X    [33X[0;6YSeveral class fusions stored in character tables have been changed, in
        order  to  be  more  consistent with related data, see Section [14X4.9[114X for
        reasons of such changes.[133X
  
  [30X    [33X[0;6YMany  new  character  tables have been added. For example, a character
        table is available for each table of marks in the [5XTomLib[105X package.[133X
  
  [33X[0;0YBesides these changes of the data, the following features are new.[133X
  
  [30X    [33X[0;6YA  tutorial for beginners was added to the package manual, see Chapter
        [14X2[114X, and the package manual was restructured. The manual is now based on
        the [5XGAPDoc[105X package (see [LN18]).[133X
  
  [30X    [33X[0;6YGeneric  constructions  of  Brauer  tables  are  now  available if the
        underlying   ordinary  table  is  encoded  via  [2XConstructMGA[102X  ([14X5.8-1[114X),
        [2XConstructIndexTwoSubdirectProduct[102X  ([14X5.5-2[114X),  or  [2XConstructV4G[102X ([14X5.8-4[114X),
        and if the Brauer tables of the compound tables are known.[133X
  
  [30X    [33X[0;6YThe attributes [2XFusionToTom[102X ([14X3.2-4[114X) and [2XMaxes[102X ([14X3.7-1[114X) 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.[133X
  
  [30X    [33X[0;6YThe consistency checks for character tables have been improved and are
        now  documented,  see  Section [14X4.8[114X. Due to these checks, several class
        fusions had to be replaced.[133X
  
  [30X    [33X[0;6YThe  concept  of  duplicate  character  tables  is now documented, see
        Section [14X3.6[114X. As a consequence, the behaviour of [2XAllCharacterTableNames[102X
        ([14X3.1-4[114X)  has changed in situations where [2XIsSimple[102X ([14XReference: IsSimple
        for    a    character    table[114X)    or   [2XIsSporadicSimple[102X   ([14XReference:
        IsSporadicSimple  for  a  character  table[114X)  occur  as  arguments (see
        [14X'Reference:  Group  Operations  Applicable  to  Character Tables'[114X), 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.[133X
  
  [30X    [33X[0;6YSeveral   attribute   values   for  character  tables,  such  as  [2XSize[102X
        ([14XReference:      Size[114X)      and     [2XNrConjugacyClasses[102X     ([14XReference:
        NrConjugacyClasses[114X)  are  now  available without reading the character
        table  data  files,  provided that the [5XBrowse[105X package (see [BL18]) has
        been  loaded.  See the documentation of [2XAllCharacterTableNames[102X ([14X3.1-4[114X)
        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.[133X
  
  [30X    [33X[0;6Y[5XGAP[105X'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 [14X3.3[114X, provided that the [5XBrowse[105X package
        (see [BL18]) has been loaded.[133X
  
  [30X    [33X[0;6YAn interactive overview of the contents is now available that is based
        on the [5XBrowse[105X package [BL18], see Section [14X3.5[114X.[133X
  
  [30X    [33X[0;6YInformation  about  Deligne-Lusztig  names  of unipotent characters of
        finite groups of Lie type is now available, see Section [14X3.4[114X.[133X
  
  [30X    [33X[0;6YAn interface for reading [5XMAGMA[105X tables was added, see Section [14X6.5[114X.[133X
  
  
  [1X1.2-8 [33X[0;0YWhat's New in Version 1.1? (November 2003)[133X[101X
  
  [33X[0;0YFirst  of  all,  of  course  several  character  tables  were  added; for an
  overview,  see  the  file  [11Xdoc/ctbldiff.pdf[111X  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 [22Xp[122X-subgroups
  whenever  the  tables  of  the  factors  are available; these maps admit the
  automatic  construction  of the [22Xp[122X-modular Brauer tables if the corresponding
  tables of the factors are available. For example, the [22X2[122X-modular Brauer table
  of  the  maximal  subgroup  of  the  type  [22X2^10:M_22[122X  in  the group [22XFi_22[122X is
  available because of the known [22X2[122X-modular table of [22XM_22[122X and the stored factor
  fusion onto the table of [22XM_22[122X.[133X
  
  [33X[0;0YSecond,  more  information  has  been  made  more explicit, in the following
  sense.[133X
  
  [30X    [33X[0;6Y[2XIdentifier[102X  ([14XReference:  Identifier  for  character  tables[114X) values of
        tables  that  are  constructed  from  generic  tables  are  now  valid
        arguments  of  [2XCharacterTable[102X ([14XReference: CharacterTable[114X), for example
        [10XCharacterTable(  "C10" )[110X and [10XCharacterTable( "Sym(5)" )[110X can be used to
        create  the character table of the cyclic group of order [22X10[122X and of the
        symmetric group of degree [22X5[122X, respectively.[133X
  
  [30X    [33X[0;6YAttributes  have  been  introduced  that  replace  more or less hidden
        components (see Section [14X3.7[114X); 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 [2XConstructionInfoCharacterTable[102X ([14X3.7-4[114X)).[133X
  
  [30X    [33X[0;6YThe  functions  that  are  used  for the table constructions have been
        documented (see Chapter [14X5[114X).[133X
  
  [30X    [33X[0;6YSeveral  consistency  checks are now part of the package distribution,
        in  the  files  [11Xgap4/test.gd[111X and [11Xgap4/test.gi[111X. However, currently they
        are  not  documented.  The new file [11Xtst/testall.g[111X lists the files that
        belong  to  the  [21Xstandard test suite[121X. Further checks involving the [5XGAP[105X
        Character  Table  Library  are  parts  of  the  [5XGAP[105X  packages AtlasRep
        (see [WPN+19]) and TomLib.[133X
  
  [30X    [33X[0;6YAs  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 [10Xtext[110X 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.[133X
  
  [30X    [33X[0;6YOne  can  now  avoid  unloading  the contents of data files, which can
        speed  up computations involving many library tables. (In version 1.1,
        the  function  [10XCTblLibSetUnload[110X  had  been  provided  for  that. Since
        version 1.2, a [5XGAP[105X 4.5 user preference replaces this function.)[133X
  
  [33X[0;0YThird, several errors have been corrected (again see [11Xdoc/ctbldiff.pdf[111X). Most
  of them affect class fusions, and for most of those, the term [21Xerror[121X could be
  regarded as not really appropriate. See [14X4.9[114X for details.[133X
  
  [33X[0;0YFinally,  the  [5XGAP[105X  functions  for  reading  and  writing  other  formats of
  character  tables  have been moved from the main [5XGAP[105X library to this package
  (see  Chapter [14X6[114X), because they are useful only for library tables. The [5XGAP[105X 3
  format  is  now  also  supported,  mainly  for  documentation  purposes (see
  Section [14X6.3[114X).[133X
  
  
  [1X1.3 [33X[0;0YAcknowledgements[133X[101X
  
  [33X[0;0YThe  development  of  the  [5XGAP[105X Character Table Library has been supported by
  several  DFG  grants,  in  particular  the  project [21XRepresentation Theory of
  Finite  Groups and Finite Dimensional Algebras[121X (until 1991), the Schwerpunkt
  [21XAlgorithmische  Zahlentheorie  und  Algebra[121X  (from 1991 until 1997), and the
  SFB-TRR   195   [21XSymbolic   Tools   in  Mathematics  and  their  Applications[121X
  ([7Xhttps://www.computeralgebra.de/sfb/[107X) (Project-ID 286237555, since 2017).[133X
  
  [33X[0;0YThe  functions  for  the  conversion  of  [5XCAS[105X tables to [5XGAP[105X format have been
  written  by  Götz  Pfeiffer.  The  functions  for  converting  the so-called
  [21XCambridge  format[121X  (in which the original data of the [5XAtlas[105X of Finite Groups
  had been stored) to [5XGAP[105X format have been written by Christoph Jansen.[133X
  
  [33X[0;0YThe  generic  character tables of double covers of alternating and symmetric
  groups were contributed by Felix Noeske, see [Noe02].[133X
  
  [33X[0;0YThe     functions     in     Section [14X3.4[114X     ([2XDeligneLusztigName[102X    ([14X3.4-3[114X),
  [2XDeligneLusztigNames[102X  ([14X3.4-2[114X), and [2XUnipotentCharacter[102X ([14X3.4-1[114X)) as well as the
  corresponding  data  for  the finite groups of Lie type in the [5XGAP[105X Character
  Table Library have been contributed by Michael Claßen-Houben, see [CH05].[133X
  
  [33X[0;0YSeveral  character  tables of maximal subgroups of covering groups of simple
  groups have been computed by Sebastian Dany, see [Dan06].[133X
  
  [33X[0;0YThanks  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 [10XTtH[110X was used to provide these HTML files.[133X
  
  [33X[0;0YThanks  to  Frank  Lübeck  and Max Neunhöffer also for developing the [5XGAPDoc[105X
  package  (see [LN18]),  on which the manual of the [5XCTblLib[105X package is based.
  The   previously   available   documentation   format  had  been  completely
  inappropriate.[133X
  
