Tables of Marks
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More about Tables of Marks
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Table of Marks Objects in GAP
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Several examples in this chapter require the &GAP; package `TomLib` (the &GAP; Library of Tables of Marks) to be available. If it is not yet loaded then we load it now.

gap> LoadPackage( "tomlib" ); true
Constructing Tables of Marks
<#Include Label="TableOfMarks"> <#Include Label="TableOfMarksByLattice"> <#Include Label="LatticeSubgroupsByTom">

Printing Tables of Marks
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Sorting Tables of Marks
<#Include Label="SortedTom"> <#Include Label="PermutationTom">

Technical Details about Tables of Marks
<#Include Label="InfoTom"> <#Include Label="IsTableOfMarks"> <#Include Label="TableOfMarksFamily"> <#Include Label="TableOfMarksComponents"> <#Include Label="ConvertToTableOfMarks">

Attributes of Tables of Marks
<#Include Label="MarksTom"> <#Include Label="NrSubsTom"> <#Include Label="LengthsTom"> <#Include Label="ClassTypesTom"> <#Include Label="ClassNamesTom"> <#Include Label="FusionsTom"> <#Include Label="UnderlyingGroup:tom"> <#Include Label="IdempotentsTom"> <#Include Label="Identifier:tom"> <#Include Label="MatTom"> <#Include Label="MoebiusTom"> <#Include Label="WeightsTom">

Properties of Tables of Marks
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Other Operations for Tables of Marks
<#Include Label="[7]{tom}"> <#Include Label="DerivedSubgroupTom"> <#Include Label="DerivedSubgroupsTomPossible"> <#Include Label="NormalizerTom"> <#Include Label="ContainedTom"> <#Include Label="ContainingTom"> <#Include Label="CyclicExtensionsTom"> <#Include Label="DecomposedFixedPointVector"> <#Include Label="EulerianFunctionByTom"> <#Include Label="IntersectionsTom"> <#Include Label="FactorGroupTom"> <#Include Label="MaximalSubgroupsTom"> <#Include Label="MinimalSupergroupsTom">

Accessing Subgroups via Tables of Marks
<#Include Label="[8]{tom}"> <#Include Label="GeneratorsSubgroupsTom"> <#Include Label="StraightLineProgramsTom"> <#Include Label="IsTableOfMarksWithGens"> <#Include Label="RepresentativeTom">

The Interface between Tables of Marks and Character Tables

The following examples require the &GAP; Character Table Library to be available. If it is not yet loaded then we load it now.

gap> LoadPackage( "ctbllib" ); true

<#Include Label="FusionCharTableTom"> <#Include Label="PermCharsTom">

Generic Construction of Tables of Marks
<#Include Label="[9]{tom}"> <#Include Label="TableOfMarksCyclic"> <#Include Label="TableOfMarksDihedral"> <#Include Label="TableOfMarksFrobenius">

The Library of Tables of Marks

The &GAP; package `TomLib` provides access to several hundred tables of marks of almost simple groups and their maximal subgroups. If this package is installed then the tables from this database can be accessed via with argument a string. If also the &GAP; Character Table Library is installed and contains the ordinary character table of the group for which one wants to fetch the table of marks then one can also call with argument the character table.

A list of all names of tables of marks that are provided by the `TomLib` package can be obtained via .

gap> names:= AllLibTomNames();; gap> "A5" in names; true