48 Character Tables

This chapter contains

Some Notes on Character Theory in GAP, Character Table Records, Brauer Table Records, Operators for Character Tables) and some conventions for their usage (see Conventions for Character Tables),

Getting Character Tables, CharTable; for the contents of the table library, see Chapter Character Table Libraries), matrix representations (see MatRepresentationsPGroup).

the description of some functions which give information about the conjugacy classes of character tables, that is, to compute classlengths (see InitClassesCharTable), inverse classes (see InverseClassesCharTable) and classnames (see ClassNamesCharTable), structure constants (see ClassMultCoeffCharTable, MatClassMultCoeffsCharTable, ClassStructureCharTable), the set of real classes (see RealClassesCharTable), orbits of the Galois group on the classes (see ClassOrbitCharTable) and roots of classes (see ClassRootsCharTable),

the description how character tables or parts of them can be displayed (see DisplayCharTable) and sorted (see SortCharactersCharTable, SortClassesCharTable, SortCharTable).

the description of functions which compute the automorphism group of a matrix (see MatAutomorphisms) or character table (see TableAutomorphisms), or which compute permutations relating permutation equivalent matrices (see TransformingPermutations) or character tables (see TransformingPermutationsCharTables),

the description of functions which get fusions from and store fusions on tables (see GetFusionMap, StoreFusion, FusionConjugacyClasses),

the description of the interface between GAP and the MOC3 system (see MAKElb11, ScanMOC, MOCChars, GAPChars, MOCTable, PrintToMOC ), and of a function which converts GAP tables to CAS tables (see PrintToCAS).

This chapter does not contain information about

functions to construct characters (see Chapter Characters), or Maps and Parametrized Maps).

For some elaborate examples how character tables are handled in GAP, see About Character Tables.

Subsections

  1. Some Notes on Character Theory in GAP
  2. Character Table Records
  3. Brauer Table Records
  4. IsCharTable
  5. PrintCharTable
  6. TestCharTable
  7. Operations Records for Character Tables
  8. Functions for Character Tables
  9. Operators for Character Tables
  10. Conventions for Character Tables
  11. Getting Character Tables
  12. CharTable
  13. Advanced Methods for Dixon Schneider Calculations
  14. An Example of Advanced Dixon Schneider Calculations
  15. CharTableFactorGroup
  16. CharTableNormalSubgroup
  17. CharTableDirectProduct
  18. CharTableWreathSymmetric
  19. CharTableRegular
  20. CharTableIsoclinic
  21. CharTableSplitClasses
  22. CharTableCollapsedClasses
  23. CharDegAgGroup
  24. CharTableSSGroup
  25. MatRepresentationsPGroup
  26. CharTablePGroup
  27. InitClassesCharTable
  28. InverseClassesCharTable
  29. ClassNamesCharTable
  30. ClassMultCoeffCharTable
  31. MatClassMultCoeffsCharTable
  32. ClassStructureCharTable
  33. RealClassesCharTable
  34. ClassOrbitCharTable
  35. ClassRootsCharTable
  36. NrPolyhedralSubgroups
  37. DisplayCharTable
  38. SortCharactersCharTable
  39. SortClassesCharTable
  40. SortCharTable
  41. MatAutomorphisms
  42. TableAutomorphisms
  43. TransformingPermutations
  44. TransformingPermutationsCharTables
  45. GetFusionMap
  46. StoreFusion
  47. FusionConjugacyClasses
  48. MAKElb11
  49. ScanMOC
  50. MOCChars
  51. GAPChars
  52. MOCTable
  53. PrintToMOC
  54. PrintToCAS
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Index

GAP 3.4.4
April 1997