CCTab

Constructing Character Tables

Version 0.4

October 2026

CCTab is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

1 The CCTab-Package

1.1 Installation of the CCTab package

1.1-1 InfoCCTable

2 The main functionality of CCTab

3 Utility functions from the CCTab package

3.1 Identifying conjugacy classes of elements

3.1-1 PositionConjugacyClass
3.1-2 ConjugacyClassInvariants

3.2 Power maps and rational classes

  3.2-1 PowerMapsOfAllClasses
  3.2-2 RationalClassSets
  3.2-3 NrRationalClasses
  3.2-4 RationalClassesInfo
  3.2-5 MaximalCyclics
  3.2-6 InduceAllFromCyclicSubgroup
  3.2-7 InducedFromAllMaximalCyclicSubgroups
  3.2-8 PowerMapCharacters
  3.2-9 SmallPowerMapCharacters
  3.2-10 ActionAutomorphismsOnConjugacyClasses

3.3 Induction from elementary subgroups

  3.3-1 MaximalNonCyclicElementarySubgroups
  3.3-2 InducedFromElementary
  3.3-3 FusionElementaryCCTable
  3.3-4 InductionDataFromElementaryCCTable

3.4 Some utilities for integer matrices

  3.4-1 HermiteIntMat
  3.4-2 PermutedFractionFreeIntegerGaussPositiveDefinite
  3.4-3 InverseUnimodularMat
  3.4-4 LLLTransformUnimodularGram

4 Computing character tables with CCTab

4.1 The IsCCTable (???) object

  4.1-1 CCTable
  4.1-2 EncodeForCCTable
  4.1-3 ImportToCCTable
  4.1-4 UpdateHNFCCTable
  4.1-5 HasFullRankCCTable
  4.1-6 FindIndexCCTable
  4.1-7 ImportInducedFromAllMaximalCyclicToCCTable
  4.1-8 FindIrreduciblesInFullLattices
  4.1-9 IrrCCTableHNF
  4.1-10 AddVectorToHNF

4.2 Scalar products

4.2-1 CCTScalarProduct

4.3 Splitting by the centre

4.3-1 SplitByCentre
4.3-2 SplitCharacterByCentre

4.4 Natural characters

4.4-1 NaturalCharacters

References

Index

CCTab

Constructing Character Tables

Copyright

Contents