  
  [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;0YThe  [11Xdoc[111X  and  [11Xhtm[111X  directories  of  the [5XGAP[105X Character Table Library contain
  several  files with examples of character theoretic computations, in PDF and
  HTML format. Currently these are[133X
  
  [30X    [33X[0;6YAmbiguous        class       fusions,       see       [11Xdoc/ambigfus.pdf[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ambigfus.pdf
        )                         and                         [11Xhtm/ambigfus.htm[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ambigfus.htm
        ).[133X
  
  [30X    [33X[0;6YConstructions  of  character  tables  using  table  automorphisms, see
        [11Xdoc/ctblcons.pdf[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctblcons.pdf
        )                         and                         [11Xhtm/ctblcons.htm[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ctblcons.htm
        ).[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;6YConstructing  the  irreducible  characters  of  [22XJ_4[122X  from one faithful
        character,                      see                     [11Xdoc/ctblj4.pdf[111X
        ([7Xhttp://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctblj4.pdf[107X)
        and                                                     [11Xhtm/ctblj4.htm[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ctblj4.htm[107X).[133X
  
  [30X    [33X[0;6YComputations  of possible permutation characters, see [11Xdoc/ctblpope.pdf[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctblpope.pdf
        )                         and                         [11Xhtm/ctblpope.htm[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ctblpope.htm
        ).[133X
  
  [30X    [33X[0;6YComputations   of  common  central  extensions,  see  [11Xdoc/ctocenex.pdf[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctocenex.pdf
        )                         and                         [11Xhtm/ctocenex.htm[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ctocenex.htm
        ).[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 [11Xdoc/dntgap.pdf[111X
        ([7Xhttp://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/dntgap.pdf[107X)
        and                                                     [11Xhtm/dntgap.htm[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/dntgap.htm[107X).[133X
  
  [30X    [33X[0;6YHamiltonian  cycles  in  the  generating  graphs of finite groups, see
        [11Xdoc/hamilcyc.pdf[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/hamilcyc.pdf
        )                         and                         [11Xhtm/hamilcyc.htm[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/hamilcyc.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;6YA  question  about the group PSO[22X^+(8,5).S_3[122X, see [11Xdoc/o8p2s3_o8p5s3.pdf[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/o8p2s3_o8p5s3.pdf
        )                       and                      [11Xhtm/o8p2s3_o8p5s3.htm[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/o8p2s3_o8p5s3.htm
        ).[133X
  
  [30X    [33X[0;6YProbabilistic  generation of finite simple groups, see [11Xdoc/probgen.pdf[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/probgen.pdf[107X)
        and                                                    [11Xhtm/probgen.htm[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/probgen.htm
        ).[133X
  
  [30X    [33X[0;6YSolvable   subgroups  of  maximal  order  in  sporadic  simple  groups
        [11Xdoc/sporsolv.pdf[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/sporsolv.pdf
        )                         and                         [11Xhtm/sporsolv.htm[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/sporsolv.htm
        ).[133X
  
  [30X    [33X[0;6YMaintenance   issues   concerning  the  [5XGAP[105X  Character  Table  Library
        [11Xdoc/maintain.pdf[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/maintain.pdf
        )                         and                         [11Xhtm/maintain.htm[111X
        (
        http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/maintain.htm
        ).[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{ CTblLib1.2.1,[104X
    [4X  author =       {Breuer, T.},[104X
    [4X  title =        {The \textsf{GAP} {C}haracter {T}able {L}ibrary,[104X
    [4X                  {V}ersion 1.2.1},[104X
    [4X  month =        {May},[104X
    [4X  year =         {2012},[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 [GAP] 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 [CCNPW85] 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 [CCNPW85]
  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
  
  
  [1X1.2-1 [33X[0;0YWhat's New in Version 1.2?[133X[101X
  
  [33X[0;0YThe following bugs were fixed in version 1.2.2.[133X
  
  [30X    [33X[0;6YThe functions [2XAllCharacterTableNames[102X ([14X3.1-3[114X) and [2XOneCharacterTableName[102X
        ([14X3.1-4[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 same character
        table, for example in the case of [22X(A_5 × A_5).2[122X created as a subdirect
        product of two copies of [22XS_5[122X.[133X
  
  [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;0YLike in earlier versions, the PDF file [11Xdoc/ctbldiff.pdf[111X of the package lists
  the  important  changes,  mainly  related  to  the  relevant  simple groups.
  However, a probably more suitable overview is given by the [5XGAP[105X readable file
  [11Xdata/ctbldiff.dat[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   using
  [2XBrowseCTblLibDifferences[102X  ([14X3.5-4[114X)  if  the  [5XBrowse[105X  package  (see [BL12]) is
  available.[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.[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  explicit, see
        Section [14X3.6[114X. As a consequence, the behaviour of [2XAllCharacterTableNames[102X
        ([14X3.1-3[114X)  has changed in situations where [10XIsSimple[110X and [10XIsSporadicSimple[110X
        (see  [14X'Reference:  Group  Operations  Applicable to Character Tables'[114X)
        occur,  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 [BL12]) has
        been  loaded.  See the documentation of [2XAllCharacterTableNames[102X ([14X3.1-3[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 [BL12]) has been loaded.[133X
  
  [30X    [33X[0;6YAn interactive overview of the contents is now available that is based
        on the [5XBrowse[105X package [BL12], 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
  
  
  [1X1.2-2 [33X[0;0YWhat's New in Version 1.1?[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 [WPNBB07]) 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),  and  the
  Schwerpunkt [21XAlgorithmische Zahlentheorie und Algebra[121X (from 1991 until 1997).[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 [Cla05].[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, on which the manual of the [5XCTblLib[105X package is based. The previously
  available documentation format had been completely inappropriate.[133X
  
