The GAP Character Table Library (Version 1.3.4) Thomas Breuer Thomas Breuer Email: mailto:sam@math.rwth-aachen.de Homepage: https://www.math.rwth-aachen.de/~Thomas.Breuer ------------------------------------------------------- Copyright © 2003–2022 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. ------------------------------------------------------- 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 1.3.4? (April 2022) 1.2-2 What's New in Version 1.3.3? (January 2022) 1.2-3 What's New in Version 1.3.2? (March 2021) 1.2-4 What's New in Version 1.3.1? (April 2020) 1.2-5 What's New in Version 1.3.0? (December 2019) 1.2-6 What's New in Version 1.2.2? (March 2013) 1.2-7 What's New in Version 1.2.0 and 1.2.1? (May 2012) 1.2-8 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 The path for calling MAGMA 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