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<Chapter Label="ch:introduction">
<Heading>Introduction to the &GAP; Character Table Library</Heading>
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 <Q>open</Q> 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 &AUTHOREMAIL;.
<P/>
It depends on your &GAP; installation whether the character table library
is available.
You can check this as follows.
If the result is <K>false</K> 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 <Ref Subsect="subsect:install"/>.
<P/>
For general information about character tables in &GAP;,
see Chapter <Ref Chap="Character Tables" BookName="ref"/>.
<P/>
<Label Name="application-files"/>
<Alt Only="HTML">
<![CDATA[
<a name="application_files">Examples of character theoretic computations</a>
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</Alt>
<Alt Not="HTML">
Examples of character theoretic computations
</Alt>
involving the &GAP; Character Table Library are part of the package.
They are dealing with the following aspects.
<P/>
<List>
<Item>
Maintenance issues concerning the &GAP; Character Table Library
<Ref Chap="Maintenance Issues for the GAP Character Table Library" BookName="CTblLibXpls"/>.
</Item>
<Item>
Constructions of character tables using table automorphisms, see
<Ref Chap="Using Table Automorphisms for Constructing Character Tables in GAP" BookName="CTblLibXpls"/>.
</Item>
<Item>
Computations of common central extensions, see
<Ref Chap="Constructing Character Tables of Central Extensions in GAP" BookName="CTblLibXpls"/>.
</Item>
<Item>
Hamiltonian cycles in the generating graphs of finite groups, see
<Ref Chap="GAP Computations Concerning Hamiltonian Cycles in the Generating Graphs of Finite Groups" BookName="CTblLibXpls"/>.
</Item>
<Item>
A question about the group PSO<M>^+(8,5).S_3</M>, see
<Ref Chap="GAP Computations with O_8^+(5).S_3 and O_8^+(2).S_3" BookName="CTblLibXpls"/>.
</Item>
<Item>
Solvable subgroups of maximal order in sporadic simple groups
<Ref Chap="Solvable Subgroups of Maximal Order in Sporadic Simple Groups" BookName="CTblLibXpls"/>.
</Item>
<Item>
Large Nilpotent Subgroups of sporadic simple groups
<Ref Chap="Large Nilpotent Subgroups of Sporadic Simple Groups" BookName="CTblLibXpls"/>.
</Item>
<Item>
Computations of possible permutation characters, see
<Ref Chap="Permutation Characters in GAP" BookName="CTblLibXpls"/>.
</Item>
<Item>
Ambiguous class fusions, see
<Ref Chap="Ambiguous Class Fusions in the GAP Character Table Library" BookName="CTblLibXpls"/>.
</Item>
<Item>
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
<Ref Chap="gap computations needed in the proof of [dnt theorem 6.1 ii ]" BookName="CTblLibXpls"/>.
</Item>
<Item>
Probabilistic generation of finite simple groups,
see <Cite Key="ProbGenArxiv"/> or an updated version at
<Ref Chap="gap computations concerning probabilistic generation of finite simple groups" BookName="CTblLibXpls"/>.
</Item>
<Item>
Ordinary character tables, Brauer tables, and decomposition matrices, see
<URL>
<Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctbldeco.pdf</Link>
<LinkText><F>doc/ctbldeco.pdf</F></LinkText>
</URL>
and
<URL>
<Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ctbldeco.htm</Link>
<LinkText><F>htm/ctbldeco.htm</F></LinkText>
</URL>.
</Item>
<Item>
Multiplicity-free permutation characters of the sporadic simple groups
and their automorphism groups, see
<URL>
<Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/multfree.pdf</Link>
<LinkText><F>doc/multfree.pdf</F></LinkText>
</URL>
and
<URL>
<Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/multfree.htm</Link>
<LinkText><F>htm/multfree.htm</F></LinkText>
</URL>.
</Item>
<Item>
Multiplicity-free permutation characters of central extensions of
the sporadic simple groups, and their automorphic extensions
(together with Jürgen Müller), see
<URL>
<Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/multfre2.pdf</Link>
<LinkText><F>doc/multfre2.pdf</F></LinkText>
</URL>
and
<URL>
<Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/multfre2.htm</Link>
<LinkText><F>htm/multfre2.htm</F></LinkText>
</URL>.
</Item>
<Item>
The construction of some character tables of &ATLAS; groups,
using character theoretic methods,
see <Cite Key="AtlasVerifyLargeArxiv"/> or an updated version at
<URL>
<Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctblatlas.pdf</Link>
<LinkText><F>doc/ctblatlas.pdf</F></LinkText>
</URL>
and
<URL>
<Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ctblatlas.htm</Link>
<LinkText><F>htm/ctblatlas.htm</F></LinkText>
</URL>.
</Item>
<Item>
The verification of the character table of the Baby Monster group,
see <Cite Key="BMverify"/> or an updated version at
<URL>
<Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctblbm.pdf</Link>
<LinkText><F>doc/ctblbm.pdf</F></LinkText>
</URL>
and
<URL>
<Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ctblbm.htm</Link>
<LinkText><F>htm/ctblbm.htm</F></LinkText>
</URL>.
</Item>
<Item>
The verification of the character table of the Monster group,
see <Cite Key="Mverify"/> or an updated version at
<URL>
<Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctblm.pdf</Link>
<LinkText><F>doc/ctblm.pdf</F></LinkText>
</URL>
and
<URL>
<Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ctblm.htm</Link>
<LinkText><F>htm/ctblm.htm</F></LinkText>
</URL>.
</Item>
</List>
<P/>
If you use the &GAP; Character Table Library to solve a problem then
please send a short e-mail to &AUTHOREMAIL; about it.
The &GAP; Character Table Library database should be referenced
as follows.
For referencing the &GAP; system in general,
use the entry <Cite Key="GAP"/> in the bibliography of this manual,
see also
<P/>
<URL>http://www.gap-system.org</URL>.
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="sec:history">
<Heading>History of the &GAP; Character Table Library</Heading>
The first version of the &GAP; Character Table Library was released with
&GAP; 3.1 in March 1992.
<P/>
It was the first aim of this library to continue the character table library
of the &CAS; system (see <Cite Key="NPP84"/>) in &GAP;,
as a part of the process of reimplementing the algorithms of &CAS; in &GAP;,
see <Ref Sect="History of Character Theory Stuff in GAP"
BookName="ref"/>.
&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.
<P/>
A second aspect of the character table library was to make all character
tables shown in the &ATLAS; of Finite Groups
<Cite Key="CCN85"/> available in &GAP;.
In fact &GAP; turned out to provide a very good environment for
systematic checks of these character tables.
<P/>
To some extent,
the access to the (ordinary) character tables in <Cite Key="CCN85"/>
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 <Q>outside of &GAP;</Q>,
using the methods described in <Cite Key="HJLP92"/>,
and part of the library has been published in the &ATLAS;
of Brauer Characters <Cite Key="JLPW95"/>.
One of the roles of &GAP; was again to perform systematic checks.
<P/>
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., <Cite Key="NPP84"/> and <Cite Key="LP91"/>).
<P/>
Section <Ref Sect="sec:contents"/> 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
<URL>
<Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctbldiff.pdf</Link>
<LinkText><F>doc/ctbldiff.pdf</F></LinkText>
</URL> of the package.
<P/>
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 <Package>AtlasRep</Package> and
<Package>TomLib</Package>)
and &GAP;'s group libraries,
and an improvement of the <Q>database</Q> aspect
of the character table library itself,
see the sections <Ref Sect="sect:accessdata"/> and
<Ref Sect="sect:ctbllib-browse"/>.
<!-- mention also the <Q>WWW table of contents</Q> -->
<P/>
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 <Q>split off</Q> as a &GAP; package.
</Section>
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<Section Label="sect:What's New in CTblLib?">
<Heading>What's New in CTblLib,
Compared to Older Versions?</Heading>
The PDF file <F>doc/ctbldiff.pdf</F> of the package
lists the important changes to the data since October 1996,
mainly related to the relevant simple groups.
<P/>
A perhaps more suitable overview of these changes is given by
the &GAP; readable file <F>data/ctbldiff.json</F>,
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 <Q>from</Q> table and once for the <Q>to</Q> table.)
This list of changes can be shown and evaluated using
<Ref Func="BrowseCTblLibDifferences"/>
if the <Package>Browse</Package> package (see <Cite Key="Browse"/>)
is available.
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<Alt Only="HTML"><![CDATA[<a id="sect:news"/>]]></Alt> <!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Subsection Label="sec:new1.3.10">
<Heading>What's New in Version &VERSIONNUMBER;?
(&RELEASEMONTH; &RELEASEYEAR;)</Heading>
<E>The following bugs were fixed.</E>
<P/>
<List>
<Item>
The paper <Cite Key="DLPP24"/> corrects an error in the classification
of the maximal subgroups of the Monster group:
The Monster has no maximal subgroups of the type <M>L_2(59)</M>,
hence the groups of the structure <M>59:29</M> are maximal.
<P/>
Due to this bugfix, the character tables of the maximal subgroups
had to be reordered.
(Note that a similar reordering had happened in version 1.3.7,
see Section <Ref Subsect="sec:new1.3.7"/>.)
This means that the following changes of relative admissible names
were necessary.
The known information about the primitive permutation characters
of the Monster in the (now no longer important) data file
<F>data/prim_perm_M.json</F> has been updated accordingly.
</Item>
<Item>
The <Q>individual</Q> <Ref Attr="GroupInfoForCharacterTable"/> entry
for the character table with identifier
<C>"3^(1+10)_+:(2x2^(1+6)_-:3^(1+2)_+:2S4)"</C>
had erroneously been assigned to the table with identifier
<C>"3^(1+8).2^(1+6).3^(1+2).2S4"</C>.
(Thanks to Frank Lübeck who pointed out this error.)
</Item>
<Item>
The <Ref Attr="CharacterParameters" BookName="ref"/> value for the
ordinary character table of the symmetric group on six points
(with <Ref Attr="Identifier" BookName="ref"/> value <C>"A_6.2_1"</C>)
was not consistent with the correspnding parameters stored on the
<M>p</M>-modular Brauer tables, for <M>p \in \{ 2, 3, 5 \}</M>.
Now this inconsistency was fixed, by permuting the stored parameters
with the permutation that is induced by the outer automorphism of the group.
</Item>
</List>
<P/>
<E>The following data have been added.</E>
<P/>
<List>
<Item>
The character table of the maximal subgroup of the type
<M>2^{5+10+20}.(S_3 \times L_5(2))</M> in the Monster group
has been computed by Anthony Pisani (see <Cite Key="Pis25"/>)
and is now available in the table library.
<P/>
By the classification of maximal subgroups of the Monster
in <Cite Key="DLP25"/> and <Cite Key="DLPP24"/>,
this means that now the character table library contains the character
tables of all maximal subgroups of the Monster.
Also all their class fusions into the Monster are known
(see for example <Cite Key="PP24"/>),
hence one can now easily compute the primitive permutation characters
of the Monster, as follows.
<P/>
<Example><![CDATA[
gap> m:= CharacterTable( "M" );;
gap> prim:= List( Maxes( m ),
> nam -> TrivialCharacter( CharacterTable( nam ) )^m );;
gap> Length( prim );
46
]]></Example>
</Item>
<Item>
A description of computations that arose in the verification of
the character table of the Monster group is now part of the package,
see the overview at the beginning of Chapter <Ref Chap="ch:introduction"/>.
</Item>
<Item>
The errata list <Cite Key="ABCImp"/> for the
&ATLAS; of Brauer Characters <Cite Key="JLPW95"/> has been updated.
(The contents can be shown by <Ref Func="BrowseAtlasImprovements"/>.)
</Item>
<Item>
<Ref Attr="CharacterParameters" BookName="ref"/> values for all
Brauer character tables of symmetric groups in the library
are now available.
(Thanks to Benjamin Sambale for pointing out that the values were missing
for some tables, and to Jürgen Müller for pointing me to a reference for
the definition of these character parameters.)
</Item>
</List>
<P/>
<E>The following functionality has been changed.</E>
<P/>
<List>
<Item>
When <Ref Func="AllCharacterTableNames"/> is called
with an <C>OrderedBy</C> function,
the returned list is now <E>stably</E> sorted w.r.t. entries
which have the same <C>OrderedBy</C> value.
</Item>
<Item>
The property <Ref Prop="IsAtlasCharacterTable"/> is new.
It can for example be used for filtering,
as an argument of <Ref Func="AllCharacterTableNames"/>.
</Item>
<Item>
Also the Boolean attribute <C>HasFusionToTom</C>
(see <Ref Attr="FusionToTom"/>)
is now a supported argument of <Ref Func="AllCharacterTableNames"/>.
</Item>
<Item>
Now version 4.13 of &GAP; is required,
such that the <Q>package extension</Q> feature can be assumed.
As a consequence, the behaviour of the &CTblLib; package does not depend
on the order in which its needed and suggested packages get
(installed and) loaded.
</Item>
</List>
</Subsection>
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<Subsection Label="sec:new1.3.9">
<Heading>What's New in Version 1.3.9? (March 2024)
The release of Version 1.3.9 was necessary because of a bug in the
changes for version 1.3.8:
Depending on the order in which packages are loaded,
&GAP; ran into an error when it tried to load <Package>CTblLib</Package>.
</Subsection>
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<Subsection Label="sec:new1.3.8">
<Heading>What's New in Version 1.3.8? (March 2024)
<E>The following bug was fixed.</E>
<P/>
<List>
<Item>
The table with identifier <C>"2^2x3^2.2.S4"</C> is encoded as a direct
product.
Up to now, one of the two factors did not fit to the identifier.
Now this has been corrected.
</Item>
</List>
<P/>
<E>The following data have been added.</E>
<P/>
<List>
<Item>
The class fusions from the maximal subgroups
<M>(L_2(11) \times L_2(11)):4</M>,
<M>11^2:(5 \times 2.A_5)</M>,
<M>7^2:2L_2(7)</M>, and
<M>L_2(19).2</M>
of the Monster group have been added.
The proofs can be found in a paper by Anthony Pisani and Tomasz Popiel,
see <Cite Key="PP24"/>.
</Item>
</List>
<P/>
<E>The following functionality has been changed.</E>
<P/>
<List>
<Item>
In order to make <Ref Func="AllCharacterTableNames"/> efficient
also if the <Package>Browse</Package> package is not available,
the relevant code from that package has been copied into
<Package>CTblLib</Package>.
</Item>
</List>
</Subsection>
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<Subsection Label="sec:new1.3.7">
<Heading>What's New in Version 1.3.7? (January 2024)
<E>The following bug was fixed.</E>
<P/>
<List>
<Item>
The <Ref Attr="GroupInfoForCharacterTable"/> entry <C>"SigmaL(2,9)"</C> had
been erroneously attributed to the table with identifier <C>"2.A6.2_2"</C>,
but the correct table is that of <C>"2.A6.2_1"</C>.
(Thanks to Bernhard Böhmler for pointing this out.)
</Item>
</List>
<P/>
<E>The following data have been added.</E>
<P/>
<List>
<Item>
Due to <Cite Key="DLP25"/>,
all classes of maximal subgroups of the Monster group are now known,
their number is <M>46</M>.
Currently not all their character tables (and the class fusions to the
Monster) are available in the character table library.
The known information about the primitive permutation characters
of the Monster in the data file <F>data/prim_perm_M.json</F>
has been updated accordingly.
<P/>
Now the groups with character tables <C>"U3(4).4"</C> and <C>"L2(13).2"</C>
have been found as maximal subgroups of the Monster.
This means that the following changes of relative admissible names
were necessary.
As a consequence, some arguments concerning the Monster in the chapters
<Ref Chap="GAP Computations Concerning Hamiltonian Cycles in the Generating Graphs of Finite Groups" BookName="ctbllibxpls"/> and
<Ref Chap="Solvable Subgroups of Maximal Order in Sporadic Simple Groups"
BookName="ctbllibxpls"/> have been adjusted.
</Item>
<Item>
The following ordinary character tables of maximal subgroups
of the Monster have been added to the library:
<C>"2^(10+16).O10+(2)"</C> was contributed by Alexander Hulpke.
<C>"3^8.O8-(3).2_3"</C>,
<C>"(3^2:2xO8+(3)).S4"</C>,
<C>"3^(2+5+10).(M11x2S4)"</C>,
<C>"3^(3+2+6+6):(L3(3)xSD16)"</C> were contributed by Tim Burness.
<C>"2^[39].(L3(2)x3.S6)"</C> and
<C>"2^(2+11+22).(M24xS3)"</C> were computed using &MAGMA;.
<P/>
As a consequence, the permutation characters induced from these subgroups
can be computed directly.
The relevant subsections in Section
<Ref Sect="Four Primitive Permutation Characters of the Monster Group"
BookName="ctbllibxpls"/> have been extended accordingly.
</Item>
<Item>
The known information about orthogonal discriminants of orthogonally stable
irreducible characters of almost simple groups is now available,
via the data in the file <F>data/odresults.json</F>.
The functions
<Ref Oper="Display" Label="for a character table" BookName="ref"/> and
<Ref Meth="Browse (for character tables)" BookName="browse"/>
support the component <C>OD</C> in the optional second argument,
in order to show a column with the known orthogonal discriminants.
</Item>
<Item>
Three new example sections have been added,
which deal with subgroups of the Monster group:
<Ref Subsect="The Monster group does not contain subgroups of the type 2.U_4(2) (August 2023)" BookName="ctbllibxpls"/>,
<Ref Subsect="Perfect central extensions of L_3(4) (August 2023)" BookName="ctbllibxpls"/>
<Ref Subsect="The character table of (2 × O_8^+(3)).S_4 ≤ 2.B (October 2023)" BookName="ctbllibxpls"/>.
</Item>
</List>
</Subsection>
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<Subsection Label="sec:new1.3.6">
<Heading>What's New in Version 1.3.6? (May 2023)
The release of Version 1.3.6 was necessary for technical reasons:
The code for building the documentation of the package had to be adjusted to
<URL><LinkText>a change in &GAP; 4.13</LinkText>
<Link>https://github.com/gap-system/gap/pull/5178</Link></URL>.
This does not affect most users of the package because the package archive
contains a ready documentation.
(The ability to rebuild the package documentation had been requested
by packagers for Linux distributions.)
</Subsection>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Subsection Label="sec:new1.3.5">
<Heading>What's New in Version 1.3.5? (March 2023)
<List>
<Item>
&GAP; 4.13 will provide the new <Q>package extension</Q> feature,
which allows a package to execute &GAP; code <E>after</E> the package
and some other required packages have been loaded.
In &CTblLib;, this feature is now used for example in order to achieve
that those functions which depend on the <Package>Browse</Package>
package can be used also if this package gets (installed and) loaded
after &CTblLib; has been loaded.
</Item>
<Item>
A few (modular and ordinary) character tables have been added that
were used for the computation of orthogonal discriminants
of characters.
Also a few formerly unknown <M>2</M>-modular indicator values have
been added.
</Item>
<Item>
Character parameters for modular tables of symmetric groups are now
available.
(Thanks to Jürgen Müller for these data.)
</Item>
<Item>
The identifier of one character table had to be changed
from <C>"D8.(S4x2)"</C> to <C>"2^3.(S4×2)"</C> because the old name
suggested a wrong group structure.
This bug had been announced in
<URL><LinkText>a StackExchange discussion</LinkText>
<Link>https://math.stackexchange.com/questions/4577016/group-names-in-gap-character-table-library</Link></URL>.
</Item>
<Item>
The <M>11</M>-modular character tables of <M>HN</M> and <M>HN.2</M>
(and as a consequence also that of <M>(D_{10} \times HN).2</M>)
had to be changed, in order to solve a generality problem.
See <Ref Subsect="A generality problem concerning the group HN (August 2022)" BookName="CTblLibXpls"/>
for the details.
</Item>
<Item>
A few class fusions had to be replaced; they were valid for the
ordinary character tables in question but not for their Brauer tables.
</Item>
</List>
</Subsection>
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<Subsection Label="sec:new1.3.4">
<Heading>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 <F>PackageInfo.g</F> exits &GAP; in the end.
</Subsection>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Subsection Label="sec:new1.3.3">
<Heading>What's New in Version 1.3.3? (January 2022)
The reason for this release was the addition of the new example section
<Ref Subsect="Generation of sporadic simple groups by π- and π'-subgroups (December 2021)" BookName="ctbllibxpls"/>,
which requires the new data file <F>data/prim_perm_M.json</F>.
(The data had already been used before in the example section
<Ref Subsect="The Monster" BookName="ctbllibxpls"/>,
which has now been changed accordingly.)
<P/>
The database attribute <C>IsQuasisimple</C> 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 <Ref Func="AllCharacterTableNames"/>.
Thanks to Gunter Malle for suggesting this addition.
<P/>
No new character tables have been added,
and there are only a few new class fusions, admissible names,
and group constructions.
</Subsection>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Subsection Label="sec:new1.3.2">
<Heading>What's New in Version 1.3.2? (March 2021)
The main new features of this release are technical.
<List>
<Item>
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
<F>data/ctprimar.tbl</F>,
now one calls a few short &GAP; functions,
in the new file <F>gap4/ctprimar.g</F>, which evaluate JSON format files.
This was one more step on the way to make the database
independent of &GAP;.
</Item>
<Item>
Also the files with the precomputed attribute values are now in
JSON format,
since now the <Package>Browse</Package> supports this format.
</Item>
<Item>
The <URL><Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/ctbltoc/index.html</Link>
<LinkText><Q>WWW table of contents</Q></LinkText></URL> of the package
has been updated in the sense that it shows the same as the functions
<Ref Func="DisplayCTblLibInfo" Label="for a name"/> and
<Ref Func="BrowseCTblLibInfo"/>;
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 <F>ctbltoc</F> directory.
</Item>
<Item>
The mechanism for processing the package documentation (which contains
two <Package>GAPDoc</Package> books) has been changed to a more
standard way.
Now it is enough to process one &GAP; input file in the package directory.
</Item>
</List>
<P/>
In several <Ref Meth="InfoText"/> values of character tables,
information about group constructions has been added;
where possible, these constructions are now also available via
<Ref Func="GroupInfoForCharacterTable"/>;
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.)
<P/>
The function <Ref Func="BrowseAtlasImprovements"/> can now show (also)
the improvements for the &ATLAS; of Brauer Characters <Cite Key="JLPW95"/>.
<P/>
The strings <C>"L2(49)"</C> and <C>"L2(81)"</C> are now valid inputs
for <Ref Func="DisplayAtlasMap" Label="for the name of a simple group"/>
and <Ref Func="BrowseAtlasTable"/>,
and <Ref Func="DisplayAtlasContents"/> and <Ref Func="BrowseAtlasContents"/>
now show information about these two and <C>"L6(2)"</C> and <C>"S10(2)"</C>.
<P/>
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 <Ref Subsect="subsect:elabsubgroup"/>,
<Ref Subsect="The Character Table of 4.L_2(49).2_3 (December 2020)" BookName="ctbllibxpls"/>,
<Ref Subsect="The Character Table of 4.L_2(81).2_3 (December 2020)" BookName="ctbllibxpls"/>.
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Subsection Label="sec:new1.3.1">
<Heading>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.
<P/>
Besides that, the function <Ref Func="CharacterTableComputedByMagma"/>
was made more robust.
<P/>
In particular, the data part of the package was not changed at all.
</Subsection>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Subsection Label="sec:new1.3.0">
<Heading>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.
<P/>
<E>The following bugs were fixed.</E>
<P/>
<List>
<Item>
The <M>2</M>-modular Brauer table of the character table with the
identifier <C>"3.(2x2^(1+8)):(U4(2):2x2)"</C> was wrong,
due to an error in the &GAP; function that constructs this Brauer table
from the known Brauer table of <M>U_4(2).2</M>;
this was the only case in the library that was affected by this bug.
(Thanks to Jürgen Müller who pointed out this error.) <!-- in May 2014 -->
</Item>
<Item>
The <M>2</M>-power map of the character table with the identifier
<C>"2.F4(2).2"</C> was wrong, <!-- Subsect="1.1-3" -->
see Section <Ref BookName="ctbllibxpls"
Subsect="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 <Cite Key="BMO17"/>.)
</Item>
<Item>
The character table of <M>E_6(2)</M> was wrong w. r. t. some
irrational character values and power maps
on the classes of element order <M>91</M>, <!-- ref. to "An Error in the Character Table of E_6(2) ...",
in subsection "subsect:errorE62" -->
see Section <Ref BookName="ctbllibxpls"
Subsect="An Error in the Character Table of E_6(2) (March 2016)"/>. <!-- Subsect="1.1-2" -->
(Thanks to Bill Unger who pointed out this error.) <!-- in March 2016 -->
</Item>
<Item>
Character tables with construction info <Ref Func="ConstructAdjusted"/>
had immutable <Ref Attr="ComputedPowerMaps" BookName="ref"/> values,
which made it impossible to add more power maps.
(Thanks to Fabian Gundlach who pointed out this error.) <!-- in May 2019 -->
</Item>
</List>
<P/>
<E>The following features have been added.</E>
<P/>
<List>
<Item>
The functions
<Ref Func="AllCharacterTableNames"/>,
<Ref Func="OneCharacterTableName"/>, and
<Ref Func="BrowseCTblLibInfo"/> support now
the global option <C>OrderedBy</C>.
</Item>
<Item>
The operation
<Ref Oper="BrauerTable" Label="for a string, and a prime integer"/>
now admits also a string as its first argument,
and then delegates to the ordinary character table with this name.
</Item>
<Item>
The operation
<Ref Oper="BrauerTable" Label="for a string, and a prime integer"/>
is now successful also if the ordinary character table in question
has the attribute <Ref Attr="ConstructionInfoCharacterTable"/> set and
the first entry of the attribute value is the string <C>"ConstructGS3"</C>
and the Brauer tables for the character tables involved in the construction
are available, see
Section <Ref Sect="Examples for the Type G.S_3" BookName="ctbllibxpls"/>.
</Item>
<Item>
The function <Ref Func="CambridgeMaps"/> has been improved in the sense
that <Q>relative</Q> class names such as <C>"B*2"</C>
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 <C>"L2(13)"</C> is an example
for which the result is now different.)
</Item>
<Item>
The function <Ref Func="ConstructIsoclinic"/> has been extended,
according to the extended functionality of
<Ref Oper="CharacterTableIsoclinic" BookName="ref"/>.
For examples, see the sections
<Ref Subsect="Groups of the Structures 3.U_3(8).3_1 and 3.U_3(8).6 (February 2017)" BookName="ctbllibxpls"/>
and
<Ref Subsect="The Character Table of 9.U_3(8).3_3 (March 2017)" BookName="ctbllibxpls"/>.
</Item>
<Item>
There is now a default <Ref Meth="InfoText"/> method for
library character tables, which returns an empty string.
This admits searches for properties of the info text via
<Ref Func="AllCharacterTableNames"/>.
Similarly, also properties of
<Ref Attr="Identifier" Label="for character tables" BookName="ref"/>
can now be searched efficiently,
see <Ref Func="AllCharacterTableNames"/> for examples.
</Item>
<Item>
With the user preference <C>DisplayFunction</C>
of the <Package>AtlasRep</Package> package
(see Section <Ref Subsect="subsect:displayfunction"/>),
one can configure how functions like
<Ref Func="DisplayCTblLibInfo" Label="for a name"/>
place their output on the screen.
(Up to now, the function <Ref Func="Pager" BookName="ref"/> had always
been called.)
</Item>
<Item>
The definition of <Q>duplicate tables</Q> has been extended
in order to get a better integration of the <Package>SpinSym</Package>
package,
see Section <Ref Sect="sec:duplicates"/>.
</Item>
<Item>
A new variant of the function
<Ref Func="GAPTableOfMagmaFile" Label="for a string"/> admits
entering a &MAGMA; format string instead of the name of a file
that contains this string.
</Item>
<Item>
The new function <Ref Func="CharacterTableComputedByMagma"/> uses
the &MAGMA; system (if this is available) for computing
the character table of a permutation group.
</Item>
<Item>
The new function <Ref Func="NotifyCharacterTables"/> is more efficient
than <Ref Func="NotifyCharacterTable"/> if one wants to add several
private character tables at the same time.
</Item>
<Item>
In the tables of maximal subgroups and Sylow <M>p</M> normalizers shown
by <Ref Func="DisplayCTblLibInfo" Label="for a name"/>
and <Ref Func="BrowseCTblLibInfo"/>,
the former <C>Name</C> column has been replaced by two columns
<C>Structure</C>
(which tries to show information about the structures of the groups,
using <Ref Func="StructureDescriptionCharacterTableName"/>)
and <C>Name</C>
(which just shows the identifiers of the character tables).
This improvement arose from a discussion with Gabriel Navarro.
</Item>
<Item>
The former &GAP; readable text file <F>data/ctbldiff.dat</F>
has been replaced by the (still &GAP; readable)
JSON format file <F>data/ctbldiff.json</F>.
(It is planned for future releases to replace more data files
by JSON format files,
in order to make the data independent of &GAP;.)
</Item>
<Item>
Two filenames of the package have been changed,
from <F>ctadmin.tbd</F> and <F>ctadmin.tbi</F>
to <F>ctadmin.gd</F> and <F>ctadmin.gi</F>, respectively.
</Item>
</List>
<P/>
Concerning <E>added character table data</E>,
the full list of differences w. r. t. earlier versions can be found
in the file <F>data/ctbldiff.json</F> of the package;
see <Ref Func="BrowseCTblLibDifferences"/> for a way to utilize this list
in a &GAP; session.
<P/>
<E>The following other data have been added.</E>
<P/>
<List>
<Item>
<Ref Func="GroupInfoForCharacterTable"/> works now for more
character tables than before.
<P/>
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 <Cite Key="CCN85"/>, up to isoclinism),
except the groups <M>2.B</M> and <M>M</M>;
several of these representations were computed in the context of the
computations that are described in <Cite Key="BMO17"/>.
<P/>
Also the library tables of groups that occur in
&GAP;'s library of primitive groups
(the &GAP; package <Package>PrimGrp</Package>) know about this fact;
note that older versions of <Package>PrimGrp</Package> contained only
groups of degree at most <M>2499</M>.
<P/>
See Section <Ref BookName="ctbllibxpls"
Sect="Some finite factor groups of perfect space groups (February 2014)"/>
for some other representations that are now available.
</Item>
</List>
<P/>
<E>Finally, the documentation was changed as follows.</E>
<P/>
<List>
<Item>
Several of the files showing
examples of character theoretic computations with &GAP;
have been turned into the <Package>GAPDoc</Package> book
<Q>CTblLibXpls</Q>, see above. <!-- An explicit cross-reference would be possible via <Ref Label="application-files" Text="examples of character theoretic computations with GAP"/>, but I cannot use the entity &GAP; inside the Text attribute,
and the cross-reference looks ugly in the PDF version. -->
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.
</Item>
</List>
</Subsection>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Subsection Label="sec:new1.2.2">
<Heading>What's New in Version 1.2.2? (March 2013)
The following bugs were fixed.
<List>
<Item>
The functions <Ref Func="AllCharacterTableNames"/> and
<Ref Func="OneCharacterTableName"/> ran into an error in certain situations,
if the library had been extended by private tables,
see Section <Ref Sect="sec:extending"/>.
(As a consequence, the description of <Ref Prop="IsDuplicateTable"/>
has been extended.)
Thanks to Alexander Konovalov and Lukas Maas for pointing out this error.
</Item>
<Item>
The function <Ref Func="CharacterTableOfIndexTwoSubdirectProduct"/>
returned a wrong result if the two factors were given by the <E>same</E>
character table.
An example is <M>(A_5 \times A_5).2</M>,
created as a subdirect product of two copies of <M>S_5</M>.
</Item>
</List>
</Subsection>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Subsection Label="sec:new1.2">
<Heading>What's New in Version 1.2.0 and 1.2.1? (May 2012)
Concerning character table data, we have the following.
<List>
<Item>
A few bugs in character tables have been fixed.
</Item>
<Item>
Several class fusions stored in character tables have been changed,
in order to be more consistent with related data,
see Section <Ref Sect="sec:CTblLib Maintenance"/> for reasons of such
changes.
</Item>
<Item>
Many new character tables have been added.
For example, a character table is available for each table of marks in the
<Package>TomLib</Package> package.
</Item>
</List>
<P/>
Besides these changes of the data, the following features are new.
<List>
<Item>
A tutorial for beginners was added to the package manual,
see Chapter <Ref Chap="ch:tutorial"/>,
and the package manual was restructured.
The manual is now based on the <Package>GAPDoc</Package> package
(see <Cite Key="GAPDoc"/>).
</Item>
<Item>
Generic constructions of Brauer tables are now available if the
underlying ordinary table is encoded via <Ref Func="ConstructMGA"/>,
<Ref Func="ConstructIndexTwoSubdirectProduct"/>, or
<Ref Func="ConstructV4G"/>,
and if the Brauer tables of the compound tables are known.
</Item>
<Item>
The attributes <Ref Attr="FusionToTom"/> and <Ref Attr="Maxes"/> 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.
</Item>
<Item>
The consistency checks for character tables have been improved
and are now documented,
see Section <Ref Sect="sec:CTblLib Sanity Checks"/>.
Due to these checks, several class fusions had to be replaced.
</Item>
<Item>
The concept of duplicate character tables is now documented,
see Section <Ref Sect="sec:duplicates"/>.
As a consequence, the behaviour of <Ref Func="AllCharacterTableNames"/>
has changed in situations where
<Ref Prop="IsSimple" Label="for a character table" BookName="ref"/> or
<Ref Prop="IsSporadicSimple" Label="for a character table" BookName="ref"/>
occur as arguments
(see <Ref Subsect="Group Operations Applicable to Character Tables"
BookName="ref"/>), 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.
</Item>
<Item>
Several attribute values for character tables,
such as <Ref Attr="Size" BookName="ref"/> and
<Ref Attr="NrConjugacyClasses" BookName="ref"/> are now available
without reading the character table data files,
provided that the <Package>Browse</Package> package
(see <Cite Key="Browse"/>) has been loaded.
See the documentation of <Ref Func="AllCharacterTableNames"/> 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.
</Item>
<Item>
&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 <Ref Sect="sect:tblgrp"/>,
provided that the <Package>Browse</Package> package
(see <Cite Key="Browse"/>) has been loaded.
</Item>
<Item>
An interactive overview of the contents is now available
that is based on the <Package>Browse</Package> package
<Cite Key="Browse"/>,
see Section <Ref Sect="sect:ctbllib-browse"/>.
</Item>
<Item>
Information about Deligne-Lusztig names of unipotent characters of finite
groups of Lie type is now available,
see Section <Ref Sect="sec:unipotsec"/>.
</Item>
<Item>
An interface for reading &MAGMA; tables was added,
see Section <Ref Sect="sec:interface-magma"/>.
</Item>
</List>
</Subsection>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Subsection Label="sec:new1.1">
<Heading>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 <F>doc/ctbldiff.pdf</F> 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 <M>p</M>-subgroups whenever the tables of the factors are
available;
these maps admit the automatic construction of the <M>p</M>-modular
Brauer tables if the corresponding tables of the factors are available.
For example, the <M>2</M>-modular Brauer table of the maximal subgroup of the type <M>2^{10}:M_{22}</M> in the group <M>Fi_{22}</M> is available
because of the known <M>2</M>-modular table of <M>M_{22}</M>
and the stored factor fusion onto the table of <M>M_{22}</M>.
<P/>
Second, more information has been made more explicit, in the following sense.
<List>
<Item>
<Ref Attr="Identifier" Label="for character tables" BookName="ref"/>
values of tables that are constructed from generic tables are now valid
arguments of <Ref Func="CharacterTable" BookName="ref"/>,
for example <C>CharacterTable( "C10" )</C>
and <C>CharacterTable( "Sym(5)" )</C>
can be used to create the character table of the cyclic group of order
<M>10</M> and of the symmetric group of degree <M>5</M>, respectively.
</Item>
<Item>
Attributes have been introduced that replace more or less hidden
components (see Section <Ref Sect="sec:attributes"/>);
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 <Ref Func="ConstructionInfoCharacterTable"/>).
</Item>
<Item>
The functions that are used for the table constructions have been
documented (see Chapter <Ref Chap="chap:constructions"/>).
</Item>
<Item>
Several consistency checks are now part of the package distribution,
in the files <F>gap4/test.gd</F> and <F>gap4/test.gi</F>.
However, currently they are not documented.
The new file <F>tst/testall.g</F> lists the files that belong to the
<Q>standard test suite</Q>.
Further checks involving the &GAP; Character Table Library are parts
of the &GAP; packages AtlasRep (see <Cite Key="AtlasRep"/>) and TomLib.
</Item>
<Item>
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 <C>text</C> 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.
</Item>
<Item>
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 <C>CTblLibSetUnload</C> had been provided
for that. Since version 1.2, a &GAP; 4.5 user preference replaces this
function.)
</Item>
</List>
<P/>
Third, several errors have been corrected
(again see <F>doc/ctbldiff.pdf</F>).
Most of them affect class fusions, and for most of those,
the term <Q>error</Q> could be regarded as not really appropriate.
See <Ref Sect="sec:CTblLib Maintenance"/> for details.
<P/>
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 <Ref Chap="chap:interfaces"/>),
because they are useful only for library tables.
The &GAP; 3 format is now also supported, mainly for documentation
purposes (see Section <Ref Sect="sec:interface-gap3"/>).
The development of the &GAP; Character Table Library has been supported
by several DFG grants,
in particular the project
<Q>Representation Theory of Finite Groups and Finite Dimensional Algebras</Q>
(until 1991),
the Schwerpunkt <Q>Algorithmische Zahlentheorie und Algebra</Q>
(from 1991 until 1997),
and the <URL><Link>https://www.computeralgebra.de/sfb/</Link>
<LinkText>SFB-TRR 195
<Q>Symbolic Tools in Mathematics and their Applications</Q></LinkText></URL>
(Project-ID 286237555, since 2017).
<P/>
The functions for the conversion of &CAS; tables
to &GAP; format have been written by Götz Pfeiffer.
The functions for converting the so-called <Q>Cambridge format</Q>
(in which the original data of the &ATLAS; of Finite Groups had been stored)
to &GAP; format have been written by Christoph Jansen.
<P/>
The generic character tables of double covers of alternating and
symmetric groups were contributed by Felix Noeske,
see <Cite Key="Noe02"/>.
<P/>
The functions in Section <Ref Sect="sec:unipotsec"/>
(<Ref Func="DeligneLusztigName"/>, <Ref Func="DeligneLusztigNames"/>,
and <Ref Func="UnipotentCharacter"/>)
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 <Cite Key="Cla05"/>.
<P/>
Several character tables of maximal subgroups of covering groups of
simple groups have been computed by Sebastian Dany,
see <Cite Key="Dan06"/>. <!-- now complete: maxes of 2.A5, A9, 2.A9, A10, 2.A10, ... -->
<P/>
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 <C>TtH</C> was used to
provide these HTML files.
<P/>
Thanks to Frank Lübeck and Max Neunhöffer also for developing the
<Package>GAPDoc</Package> package (see <Cite Key="GAPDoc"/>),
on which the manual of the &CTblLib; package is based.
The previously available documentation format had been completely
inappropriate.
Die Informationen auf dieser Webseite wurden
nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit,
noch Qualität der bereit gestellten Informationen zugesichert.
Bemerkung:
Die farbliche Syntaxdarstellung ist noch experimentell.
