[1XThe [5XGAP[105X Character Table Library[101X (Version 1.3.4) Thomas Breuer Thomas Breuer Email: [7Xmailto:sam@math.rwth-aachen.de[107X Homepage: [7Xhttps://www.math.rwth-aachen.de/~Thomas.Breuer[107X ------------------------------------------------------- [1XCopyright[101X [33X[0;0Y© 2003–2022 by Thomas Breuer[133X [33X[0;0YThis package may be distributed under the terms and conditions of the GNU Public License Version 3 or later, see [7Xhttp://www.gnu.org/licenses[107X.[133X ------------------------------------------------------- [1XContents (CTblLib)[101X 1 [33X[0;0YIntroduction to the [5XGAP[105X Character Table Library[133X 1.1 [33X[0;0YHistory of the [5XGAP[105X Character Table Library[133X 1.2 [33X[0;0YWhat's New in [5XCTblLib[105X, Compared to Older Versions?[133X 1.2-1 [33X[0;0YWhat's New in Version 1.3.4? (April 2022)[133X 1.2-2 [33X[0;0YWhat's New in Version 1.3.3? (January 2022)[133X 1.2-3 [33X[0;0YWhat's New in Version 1.3.2? (March 2021)[133X 1.2-4 [33X[0;0YWhat's New in Version 1.3.1? (April 2020)[133X 1.2-5 [33X[0;0YWhat's New in Version 1.3.0? (December 2019)[133X 1.2-6 [33X[0;0YWhat's New in Version 1.2.2? (March 2013)[133X 1.2-7 [33X[0;0YWhat's New in Version 1.2.0 and 1.2.1? (May 2012)[133X 1.2-8 [33X[0;0YWhat's New in Version 1.1? (November 2003)[133X 1.3 [33X[0;0YAcknowledgements[133X 2 [33X[0;0YTutorial for the [5XGAP[105X Character Table Library[133X 2.1 [33X[0;0YConcepts used in the [5XGAP[105X Character Table Library[133X 2.2 [33X[0;0YAccessing a Character Table from the Library[133X 2.2-1 [33X[0;0YAccessing a Character Table via a name[133X 2.2-2 [33X[0;0YAccessing a Character Table via properties[133X 2.2-3 [33X[0;0YAccessing a Character Table via a Table of Marks[133X 2.2-4 [33X[0;0YAccessing a Character Table relative to another Character Table[133X 2.2-5 [33X[0;0YDifferent character tables for the same group[133X 2.3 [33X[0;0YExamples of Using the [5XGAP[105X Character Table Library[133X 2.3-1 [33X[0;0YExample: Ambivalent Simple Groups[133X 2.3-2 [33X[0;0YExample: Simple [22Xp[122X-pure Groups[133X 2.3-3 [33X[0;0YExample: Simple Groups with only one [22Xp[122X-Block[133X 2.3-4 [33X[0;0YExample:The Sylow [22X3[122X subgroup of [22X3.O'N[122X[133X 2.3-5 [33X[0;0YExample: Primitive Permutation Characters of [22X2.A_6[122X[133X 2.3-6 [33X[0;0YExample: A Permutation Character of [22XFi_23[122X[133X 2.3-7 [33X[0;0YExample: Non-commutators in the commutator group[133X 2.3-8 [33X[0;0YExample: An irreducible [22X11[122X-modular character of [22XJ_4[122X (December 2018)[133X 2.3-9 [33X[0;0YExample: Tensor Products that are Generalized Projectives (October 2019)[133X 2.3-10 [33X[0;0YExample: Certain elementary abelian subgroups in quasisimple groups (November 2020)[133X 3 [33X[0;0YThe User Interface to the [5XGAP[105X Character Table Library[133X 3.1 [33X[0;0YAccessing Data of the [5XCTblLib[105X Package[133X 3.1-1 [33X[0;0YAdmissible Names for Character Tables in [5XCTblLib[105X[133X 3.1-2 CharacterTable 3.1-3 BrauerTable 3.1-4 AllCharacterTableNames 3.1-5 OneCharacterTableName 3.1-6 NameOfEquivalentLibraryCharacterTable 3.2 [33X[0;0YThe Interface to the [5XTomLib[105X Package[133X 3.2-1 TableOfMarks 3.2-2 CharacterTable 3.2-3 FusionCharTableTom 3.2-4 FusionToTom 3.2-5 NameOfLibraryCharacterTable 3.3 [33X[0;0YThe Interface to [5XGAP[105X's Group Libraries[133X 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 [33X[0;0YUnipotent Characters of Finite Groups of Lie Type[133X 3.4-1 UnipotentCharacter 3.4-2 DeligneLusztigNames 3.4-3 DeligneLusztigName 3.4-4 KnowsDeligneLusztigNames 3.5 [33X[0;0Y[5XBrowse[105X Applications Provided by [5XCTblLib[105X[133X 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 [33X[0;0YDuplicates of Library Character Tables[133X 3.6-1 IsDuplicateTable 3.6-2 IdentifierOfMainTable 3.6-3 IdentifiersOfDuplicateTables 3.7 [33X[0;0YAttributes for Library Character Tables[133X 3.7-1 Maxes 3.7-2 ProjectivesInfo 3.7-3 ExtensionInfoCharacterTable 3.7-4 ConstructionInfoCharacterTable 3.7-5 InfoText 4 [33X[0;0YContents of the [5XGAP[105X Character Table Library[133X 4.1 [33X[0;0YOrdinary and Brauer Tables in the [5XGAP[105X Character Table Library[133X 4.1-1 [33X[0;0YOrdinary Character Tables[133X 4.1-2 [33X[0;0YBrauer Tables[133X 4.2 [33X[0;0YGeneric Character Tables[133X 4.2-1 [33X[0;0YAvailable generic character tables[133X 4.2-2 CharacterTableSpecialized 4.2-3 [33X[0;0YComponents of generic character tables[133X 4.2-4 [33X[0;0YExample: The generic table of cyclic groups[133X 4.2-5 [33X[0;0YExample: The generic table of the general linear group GL[22X(2,q)[122X[133X 4.3 [33X[0;0Y[5XAtlas[105X Tables[133X 4.3-1 [33X[0;0YImprovements to the [5XAtlas[105X[133X 4.3-2 [33X[0;0YPower Maps[133X 4.3-3 [33X[0;0YProjective Characters and Projections[133X 4.3-4 [33X[0;0YTables of Isoclinic Groups[133X 4.3-5 [33X[0;0YOrdering of Characters and Classes[133X 4.3-6 AtlasLabelsOfIrreducibles 4.3-7 [33X[0;0YExamples of the [5XAtlas[105X Format for [5XGAP[105X Tables[133X 4.4 [33X[0;0Y[5XCAS[105X Tables[133X 4.4-1 CASInfo 4.5 [33X[0;0YCustomizations of the [5XGAP[105X Character Table Library[133X 4.5-1 [33X[0;0YInstalling the [5XGAP[105X Character Table Library[133X 4.5-2 [33X[0;0YUnloading Character Table Data[133X 4.5-3 [33X[0;0YChanging the display format of several functions[133X 4.5-4 [33X[0;0YThe path for calling [5XMAGMA[105X[133X 4.6 [33X[0;0YTechnicalities of the Access to Character Tables from the Library[133X 4.6-1 [33X[0;0YData Files of the [5XGAP[105X Character Table Library[133X 4.6-2 LIBLIST 4.6-3 LibInfoCharacterTable 4.7 [33X[0;0YHow to Extend the [5XGAP[105X Character Table Library[133X 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 [33X[0;0YSanity Checks for the [5XGAP[105X Character Table Library[133X 4.9 [33X[0;0YMaintenance of the [5XGAP[105X Character Table Library[133X 5 [33X[0;0YFunctions for Character Table Constructions[133X 5.1 [33X[0;0YCharacter Tables of Groups of Structure [22XM.G.A[122X[133X 5.1-1 PossibleCharacterTablesOfTypeMGA 5.1-2 BrauerTableOfTypeMGA 5.1-3 PossibleActionsForTypeMGA 5.2 [33X[0;0YCharacter Tables of Groups of Structure [22XG.S_3[122X[133X 5.2-1 [33X[0;0YCharacterTableOfTypeGS3[133X 5.2-2 PossibleActionsForTypeGS3 5.3 [33X[0;0YCharacter Tables of Groups of Structure [22XG.2^2[122X[133X 5.3-1 [33X[0;0YPossibleCharacterTablesOfTypeGV4[133X 5.3-2 PossibleActionsForTypeGV4 5.4 [33X[0;0YCharacter Tables of Groups of Structure [22X2^2.G[122X[133X 5.4-1 [33X[0;0YPossibleCharacterTablesOfTypeV4G[133X 5.4-2 [33X[0;0YBrauerTableOfTypeV4G[133X 5.5 [33X[0;0YCharacter Tables of Subdirect Products of Index Two[133X 5.5-1 CharacterTableOfIndexTwoSubdirectProduct 5.5-2 ConstructIndexTwoSubdirectProduct 5.5-3 ConstructIndexTwoSubdirectProductInfo 5.6 [33X[0;0YBrauer Tables of Extensions by [22Xp[122X-regular Automorphisms[133X 5.6-1 IBrOfExtensionBySingularAutomorphism 5.7 [33X[0;0YCharacter Tables of Coprime Central Extensions[133X 5.7-1 CharacterTableOfCommonCentralExtension 5.8 [33X[0;0YConstruction Functions used in the Character Table Library[133X 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 [33X[0;0YInterfaces to Other Data Formats for Character Tables[133X 6.1 [33X[0;0YInterface to the [5XCAS[105X System[133X 6.1-1 CASString 6.2 [33X[0;0YInterface to the [5XMOC[105X System[133X 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 [33X[0;0YInterface to [5XGAP[105X 3[133X 6.3-1 GAP3CharacterTableScan 6.3-2 GAP3CharacterTableString 6.3-3 GAP3CharacterTableData 6.4 [33X[0;0YInterface to the Cambridge Format[133X 6.4-1 CambridgeMaps 6.4-2 StringOfCambridgeFormat 6.5 [33X[0;0YInterface to the [5XMAGMA[105X System[133X 6.5-1 BosmaBase 6.5-2 GAPTableOfMagmaFile 6.5-3 CharacterTableComputedByMagma 7 [33X[0;0YUtility Functions Provided by the [5XCTblLib[105X Package[133X 7.1 [33X[0;0YWrite Character Values in Terms of Atomic [5XAtlas[105X Irrationalities[133X 7.1-1 CTblLib.StringOfAtlasIrrationality 7.2 [33X[0;0YCreate a String that Describes the Group Structure[133X 7.2-1 StructureDescriptionCharacterTableName [32X
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