The GAP Character Table Library
  
  
                                (Version 1.3.9)
  
  
                                 Thomas Breuer
  
  
  
  Thomas Breuer
      Email:    mailto:sam@math.rwth-aachen.de
      Homepage: https://www.math.rwth-aachen.de/~Thomas.Breuer
  
  -------------------------------------------------------
  Copyright
  © 2003–2024 by Thomas Breuer
  
  This  package  may  be distributed under the terms and conditions of the GNU
  Public License Version 3 or later, see http://www.gnu.org/licenses.
  
  
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  Contents (CTblLib)
  
  1 Introduction to the GAP Character Table Library
    1.1 History of the GAP Character Table Library
    1.2 What's New in CTblLib, Compared to Older Versions?
      1.2-1 What's New in Version 1.3.9? (March 2024)
      1.2-2 What's New in Version 1.3.8? (March 2024)
      1.2-3 What's New in Version 1.3.7? (January 2024)
      1.2-4 What's New in Version 1.3.6? (May 2023)
      1.2-5 What's New in Version 1.3.5? (March 2023)
      1.2-6 What's New in Version 1.3.4? (April 2022)
      1.2-7 What's New in Version 1.3.3? (January 2022)
      1.2-8 What's New in Version 1.3.2? (March 2021)
      1.2-9 What's New in Version 1.3.1? (April 2020)
      1.2-10 What's New in Version 1.3.0? (December 2019)
      1.2-11 What's New in Version 1.2.2? (March 2013)
      1.2-12 What's New in Version 1.2.0 and 1.2.1? (May 2012)
      1.2-13 What's New in Version 1.1? (November 2003)
    1.3 Acknowledgements
  2 Tutorial for the GAP Character Table Library
    2.1 Concepts used in the GAP Character Table Library
    2.2 Accessing a Character Table from the Library
      2.2-1 Accessing a Character Table via a name
      2.2-2 Accessing a Character Table via properties
      2.2-3 Accessing a Character Table via a Table of Marks
      2.2-4 Accessing a Character Table relative to another Character Table
      2.2-5 Different character tables for the same group
    2.3 Examples of Using the GAP Character Table Library
      2.3-1 Example: Ambivalent Simple Groups
      2.3-2 Example: Simple p-pure Groups
      2.3-3 Example: Simple Groups with only one p-Block
      2.3-4 Example:The Sylow 3 subgroup of 3.O'N
      2.3-5 Example: Primitive Permutation Characters of 2.A_6
      2.3-6 Example: A Permutation Character of Fi_23
      2.3-7 Example: Non-commutators in the commutator group
      2.3-8 Example: An irreducible 11-modular character of J_4 (December
      2018)
      2.3-9 Example: Tensor Products that are Generalized Projectives (October
      2019)
      2.3-10 Example: Certain elementary abelian subgroups in quasisimple
      groups (November 2020)
  3 The User Interface to the GAP Character Table Library
    3.1 Accessing Data of the CTblLib Package
      3.1-1 Admissible Names for Character Tables in CTblLib
      3.1-2 CharacterTable
      3.1-3 BrauerTable
      3.1-4 AllCharacterTableNames
      3.1-5 OneCharacterTableName
      3.1-6 NameOfEquivalentLibraryCharacterTable
    3.2 The Interface to the TomLib Package
      3.2-1 TableOfMarks
      3.2-2 CharacterTable
      3.2-3 FusionCharTableTom
      3.2-4 FusionToTom
      3.2-5 NameOfLibraryCharacterTable
    3.3 The Interface to GAP's Group Libraries
      3.3-1 GroupInfoForCharacterTable
      3.3-2 KnowsSomeGroupInfo
      3.3-3 CharacterTableForGroupInfo
      3.3-4 GroupForGroupInfo
      3.3-5 GroupForTom
      3.3-6 AtlasStabilizer
      3.3-7 IsNontrivialDirectProduct
    3.4 Unipotent Characters of Finite Groups of Lie Type
      3.4-1 UnipotentCharacter
      3.4-2 DeligneLusztigNames
      3.4-3 DeligneLusztigName
      3.4-4 KnowsDeligneLusztigNames
    3.5 Browse Applications Provided by CTblLib
      3.5-1 DisplayCTblLibInfo
      3.5-2 BrowseCTblLibInfo
      3.5-3 BrowseCommonIrrationalities
      3.5-4 BrowseCTblLibDifferences
      3.5-5 BrowseAtlasContents
      3.5-6 DisplayAtlasContents
      3.5-7 BrowseAtlasMap
      3.5-8 DisplayAtlasMap
      3.5-9 BrowseAtlasTable
      3.5-10 BrowseAtlasImprovements
    3.6 Duplicates of Library Character Tables
      3.6-1 IsDuplicateTable
      3.6-2 IdentifierOfMainTable
      3.6-3 IdentifiersOfDuplicateTables
    3.7 Attributes for Library Character Tables
      3.7-1 Maxes
      3.7-2 ProjectivesInfo
      3.7-3 ExtensionInfoCharacterTable
      3.7-4 ConstructionInfoCharacterTable
      3.7-5 InfoText
  4 Contents of the GAP Character Table Library
    4.1 Ordinary and Brauer Tables in the GAP Character Table Library
      4.1-1 Ordinary Character Tables
      4.1-2 Brauer Tables
    4.2 Generic Character Tables
      4.2-1 Available generic character tables
      4.2-2 CharacterTableSpecialized
      4.2-3 Components of generic character tables
      4.2-4 Example: The generic table of cyclic groups
      4.2-5 Example: The generic table of the general linear group GL(2,q)
    4.3 Atlas Tables
      4.3-1 Improvements to the Atlas
      4.3-2 Power Maps
      4.3-3 Projective Characters and Projections
      4.3-4 Tables of Isoclinic Groups
      4.3-5 Ordering of Characters and Classes
      4.3-6 AtlasLabelsOfIrreducibles
      4.3-7 Examples of the Atlas Format for GAP Tables
    4.4 CAS Tables
      4.4-1 CASInfo
    4.5 Customizations of the GAP Character Table Library
      4.5-1 Installing the GAP Character Table Library
      4.5-2 Unloading Character Table Data
      4.5-3 Changing the display format of several functions
      4.5-4 User preference MagmaPath
    4.6 Technicalities of the Access to Character Tables from the Library
      4.6-1 Data Files of the GAP Character Table Library
      4.6-2 LIBLIST
      4.6-3 LibInfoCharacterTable
    4.7 How to Extend the GAP Character Table Library
      4.7-1 NotifyNameOfCharacterTable
      4.7-2 LibraryFusion
      4.7-3 LibraryFusionTblToTom
      4.7-4 PrintToLib
      4.7-5 NotifyCharacterTable
      4.7-6 NotifyCharacterTables
    4.8 Sanity Checks for the GAP Character Table Library
    4.9 Maintenance of the GAP Character Table Library
  5 Functions for Character Table Constructions
    5.1 Character Tables of Groups of Structure M.G.A
      5.1-1 PossibleCharacterTablesOfTypeMGA
      5.1-2 BrauerTableOfTypeMGA
      5.1-3 PossibleActionsForTypeMGA
    5.2 Character Tables of Groups of Structure G.S_3
      5.2-1 CharacterTableOfTypeGS3
      5.2-2 PossibleActionsForTypeGS3
    5.3 Character Tables of Groups of Structure G.2^2
      5.3-1 PossibleCharacterTablesOfTypeGV4
      5.3-2 PossibleActionsForTypeGV4
    5.4 Character Tables of Groups of Structure 2^2.G
      5.4-1 PossibleCharacterTablesOfTypeV4G
      5.4-2 BrauerTableOfTypeV4G
    5.5 Character Tables of Subdirect Products of Index Two
      5.5-1 CharacterTableOfIndexTwoSubdirectProduct
      5.5-2 ConstructIndexTwoSubdirectProduct
      5.5-3 ConstructIndexTwoSubdirectProductInfo
    5.6 Brauer Tables of Extensions by p-regular Automorphisms
      5.6-1 IBrOfExtensionBySingularAutomorphism
    5.7 Character Tables of Coprime Central Extensions
      5.7-1 CharacterTableOfCommonCentralExtension
    5.8 Construction Functions used in the Character Table Library
      5.8-1 ConstructMGA
      5.8-2 ConstructMGAInfo
      5.8-3 ConstructGS3
      5.8-4 ConstructV4G
      5.8-5 ConstructProj
      5.8-6 ConstructDirectProduct
      5.8-7 ConstructCentralProduct
      5.8-8 ConstructSubdirect
      5.8-9 ConstructWreathSymmetric
      5.8-10 ConstructIsoclinic
      5.8-11 ConstructPermuted
      5.8-12 ConstructAdjusted
      5.8-13 ConstructFactor
  6 Interfaces to Other Data Formats for Character Tables
    6.1 Interface to the CAS System
      6.1-1 CASString
    6.2 Interface to the MOC System
      6.2-1 MAKElb11
      6.2-2 MOCTable
      6.2-3 MOCString
      6.2-4 ScanMOC
      6.2-5 GAPChars
      6.2-6 MOCChars
    6.3 Interface to GAP 3
      6.3-1 GAP3CharacterTableScan
      6.3-2 GAP3CharacterTableString
      6.3-3 GAP3CharacterTableData
    6.4 Interface to the Cambridge Format
      6.4-1 CambridgeMaps
      6.4-2 StringOfCambridgeFormat
    6.5 Interface to the MAGMA System
      6.5-1 BosmaBase
      6.5-2 GAPTableOfMagmaFile
      6.5-3 CharacterTableComputedByMagma
  7 Utility Functions Provided by the CTblLib Package
    7.1 Write Character Values in Terms of Atomic Atlas Irrationalities
      7.1-1 CTblLib.StringOfAtlasIrrationality
    7.2 Create a String that Describes the Group Structure
      7.2-1 StructureDescriptionCharacterTableName