# The GAP 4 Reference Manual - Index C

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c_N 18.4
Calculating with Group Automorphisms 38.8
Calendar Arithmetic 26.8
CallFuncList 5.2.1
Calling a function with a list argument that is interpreted as several arguments 5.2
Cancellation Tests for Rational Functions 64.23
CanComputeIndex 37.25.4
CanComputeIsSubset 37.25.5
CanComputeSize 37.25.2
CanComputeSizeAnySubgroup 37.25.3
candidates, for permutation characters 70.13 70.14
CanEasilyCompareElements 30.11.2
CanEasilyCompareElementsFamily 30.11.2
CanEasilyComputePcgs 43.2.3
CanEasilySortElements 30.11.2
CanEasilySortElementsFamily 30.11.2
CanEasilyTestMembership 37.25.1
canonical basis, for matrix spaces 59.8
canonical basis, for row spaces 59.8
CanonicalBasis 59.4.3
CanonicalGenerators 61.7.14
CanonicalPcElement 43.5.9
CanonicalPcgs 43.8.2
CanonicalPcgsByGeneratorsWithImages 43.9.7
CanonicalRepresentativeDeterminatorOfExternalSet 39.11.14
CanonicalRepresentativeOfExternalSet 39.11.13
CanonicalRightCosetElement 37.7.3
Carmichael's lambda function 15.1
carriage return character 26.1
CartanMatrix 61.7.12
CartanSubalgebra 61.3.7
Cartesian 21.20.15
Categories 13.3
Categories and Properties of Algebras 60.7
Categories for Streams and the StreamsFamily 10.1
Categories of Associative Words 35.1
Categories of Matrices 24.1
Categories of Words and Nonassociative Words 34.1
CategoriesOfObject 13.3.1
CategoryCollections 28.1.4
Center 33.4.5
center 33.4
central character 70.8
CentralCharacter 70.8.17
CentralIdempotentsOfAlgebra 60.8.17
centraliser 33.4
Centralizer 33.4.4
Centralizer, for groups with pcgs 43.16
CentralizerInGLnZ 42.5.8
CentralizerModulo 37.18.7
CentralizerSizeLimitConsiderFunction 43.17.2
CentralNormalSeriesByPcgs 43.11.8
Centre 33.4.5
Centre, for groups with pcgs 43.16
centre, of a character 70.8
CentreOfCharacter 70.8.11
CF 58.1
ChangeStabChain 41.10.3
Changing Presentations 46.6
Changing the Help Viewer 2.3
Changing the Representation 30.5
Changing the Structure 30.4
CHAR_INT 26.6.2
CHAR_SINT 26.6.4
Character 70.6.3
Character Conversion 26.6
Character Degrees and Derived Length 72.1
Character Table Categories 69.4
Character Tables 69.0
character tables 69.3
character tables, access to 69.3
character tables, calculate 69.3
character tables, infix operators 69.7
character tables, of groups 69.3
character value, of group element using powering operator 70.4
CharacterDegrees 69.8.1
Characteristic 30.10.1
characteristic polynomial, for field elements 56.3
characteristic, for class functions 70.4
CharacteristicPolynomial 24.12.1
CharacterNames 69.8.10
characters 70.0
characters, permutation 70.13 70.14
characters, symmetrizations of 70.11
CharacterTable 69.3.1
CharacterTableDirectProduct 69.18.1
CharacterTableFactorGroup 69.18.3
CharacterTableIsoclinic 69.18.4
CharacterTableWithSortedCharacters 69.19.1
CharacterTableWithSortedClasses 69.19.3
CharacterTableWreathSymmetric 69.18.6
CharsFamily 26.2.4
CheapFactorsInt 14.3
CheckFixedPoints 71.3.10
CheckForHandlingByNiceBasis 59.11.3
CheckPermChar 71.5.2
ChevalleyBasis 61.7.2
ChiefNormalSeriesByPcgs 43.11.16
ChiefSeries 37.17.1
ChiefSeriesThrough 37.17.2
ChiefSeriesUnderAction 37.17.3
Chinese remainder 14.2
ChineseRem 14.2.9
Chomp 26.5.11
CIUnivPols 64.1.5
class function 70.0
class function objects 70.0
Class Functions 70.0
class functions 71.3
class functions, as ring elements 70.4
Class Fusions between Character Tables 71.2
class multiplication coefficient 69.10
ClassElementLattice 37.20.2
classes, real 69.8
ClassesSolvableGroup 43.17.1
ClassFunction 70.6.1
ClassFunctionSameType 70.6.4
Classical Groups 48.2
ClassMultiplicationCoefficient, for character tables 69.10.6
ClassNames 69.8.10
ClassNamesTom 68.7.5
ClassOrbit 69.8.15
ClassPermutation 69.19.5
ClassPositionsOfAgemo 69.8.18
ClassPositionsOfCentre, for character tables 69.8.19
ClassPositionsOfCentre, for characters 70.8.12
ClassPositionsOfDerivedSubgroup 69.8.21
ClassPositionsOfDirectProductDecompositions 69.8.20
ClassPositionsOfElementaryAbelianSeries 69.8.22
ClassPositionsOfFittingSubgroup 69.8.23
ClassPositionsOfKernel 70.8.10
ClassPositionsOfLowerCentralSeries 69.8.24
ClassPositionsOfMaximalNormalSubgroups 69.8.17
ClassPositionsOfMinimalNormalSubgroups 69.8.17
ClassPositionsOfNormalClosure 69.8.27
ClassPositionsOfNormalSubgroup 69.21.2
ClassPositionsOfNormalSubgroups 69.8.17
ClassPositionsOfSupersolvableResiduum 69.8.26
ClassPositionsOfUpperCentralSeries 69.8.25
ClassRoots 69.8.16
ClassStructureCharTable 69.10.7
ClassTypesTom 68.7.4
CleanedTailPcElement 43.5.11
ClearCacheStats 7.7.12
ClearProfile 7.7.10
clone, an object 12.7
CloseMutableBasis 59.7.6
CloseStream 10.2.1
Closure Operations and Other Constructors 32.4
ClosureGroup 37.4.1
ClosureGroupAddElm 37.4.2
ClosureGroupCompare 37.4.2
ClosureGroupDefault 37.4.3
ClosureGroupIntest 37.4.2
ClosureLeftModule 55.2.3
ClosureNearAdditiveGroup 53.4.1
ClosureRing 54.1.9
Closures of (Sub)groups 37.4
ClosureStruct 30.3.6
ClosureSubgroup 37.4.4
ClosureSubgroupNC 37.4.4
Coboundaries 61.12.8
Cochain 61.12.3
CochainSpace 61.12.4
Cocycles 61.12.7
cocycles 37.23
CodePcGroup 44.9.2
CodePcgs 44.9.1
Coding a Pc Presentation 44.9
Coefficient List Arithmetic 23.3
coefficient, binomial 17.1
Coefficients 59.5.3
coefficients, for cyclotomics 18.1
CoefficientsAndMagmaElements 63.2.3
CoefficientsFamily 64.18.3
CoefficientsMultiadic 14.2.8
CoefficientsOfLaurentPolynomial 64.12.2
CoefficientsOfUnivariatePolynomial 64.4.9
CoefficientsOfUnivariateRationalFunction 64.4.7
CoefficientsQadic 14.2.7
CoefficientsRing 64.14.3
CoeffsCyc 18.1.8
CoeffsMod 23.3.4
cohomology 37.23
COHORTS_PRIMITIVE_GROUPS 48.9.4
CoKernelOfAdditiveGeneralMapping 31.9.6
CoKernelOfMultiplicativeGeneralMapping 31.8.6
CollapsedMat 71.3.16
Collected 21.20.3
Collection Families 28.1
Collections 28.0
CollectionsFamily 28.1.1
Coloring the Prompt and Input 3.12
ColorPrompt 3.12.1
ColumnIndexOfReesMatrixSemigroupElement 49.6.8
ColumnIndexOfReesZeroMatrixSemigroupElement 49.6.8
Combinations 17.2.1
Combinations, Arrangements and Tuples 17.2
Combinatorial Numbers 17.1
CombinatorialCollector 44.4.2
Combinatorics 17.0
Comm 30.12.3
Comm, for words 35.4
Command Line Options 3.1
comments 4.4
CommutativeDiagram 71.3.9
CommutatorFactorGroup 37.18.3
CommutatorLength 37.12.4
CommutatorLength, for character tables 69.8
CommutatorSubgroup 37.12.2
Compacted 21.20.2
CompanionMat 24.12.5
CompareVersionNumbers 74.3.6
Comparison of Associative Words 35.3
Comparison of Class Functions 70.3
Comparison of Elements of Finitely Presented Groups 45.2
Comparison of Elements of Finitely Presented Semigroups 51.2
Comparison of Permutations 40.1
Comparison of Rational Functions 64.3
Comparison of Words 34.2
Comparison Operations for Elements 30.11
comparison, fp semigroup elements 51.2.1
comparison, operation 30.11.1
comparison, rational functions 64.3.1
Comparisons 4.11
Comparisons of Booleans 20.2
Comparisons of Cyclotomics 18.3
Comparisons of Lists 21.10
Comparisons of Records 27.4
Comparisons of Strings 26.4
comparisons, of booleans 20.2.1
comparisons, of lists 21.10
CompatibleConjugacyClasses 69.6.5
CompatiblePairs 44.8.8
Compilation 73.4
Compiling Library Code 3.9
Complementclasses 37.11.6
ComplementclassesEA 37.23.4
ComplementIntMat 25.1.6
ComplementSystem 37.13.5
Completion Files 3.5
ComplexConjugate 18.5.2
ComplexConjugate, for class functions 70.4
ComplexificationQuat 60.4.2
Components of a Dixon Record 69.16
CompositionMapping 31.1.4
CompositionMapping, for Frobenius automorphisms 57.4
CompositionMapping2 31.1.5
CompositionMaps 71.3.1
CompositionOfStraightLinePrograms 35.8.7
CompositionSeries 37.17.5
CompositionSeries, for groups with pcgs 43.16
ComputedBrauerTables 69.3.2
ComputedClassFusions 71.2.2
ComputedIndicators 69.10.4
ComputedIsPSolvableCharacterTables 69.10.2
ComputedPowerMaps 71.1.1
ComputedPrimeBlockss 69.9.1
Computing a Pcgs 43.2
Computing a Permutation Representation 41.2
Computing Pc Groups 44.5
Computing Possible Permutation Characters 70.14
Computing the Irreducible Characters of a Group 69.12
Concatenation 21.20.1
concatenation, of lists 21.20
Conductor 18.1.5
ConfluentRws 36.1.6
Congruences for semigroups 49.3
Congruences, for character tables 71.4.2
Conjugacy Classes 37.10
Conjugacy Classes in Classical Groups 48.3
Conjugacy Classes in Solvable Groups 43.17
ConjugacyClass 37.10.1
ConjugacyClasses, attribute 37.10.2
ConjugacyClasses, for character tables 69.6.2
ConjugacyClasses, for groups with pcgs 43.16
ConjugacyClasses, for linear groups 48.3
ConjugacyClassesByOrbits 37.10.4
ConjugacyClassesByRandomSearch 37.10.3
ConjugacyClassesMaximalSubgroups 37.19.4
ConjugacyClassesPerfectSubgroups 37.20.6
ConjugacyClassesSubgroups 37.19.3
ConjugacyClassSubgroups 37.19.1
conjugate, matrix 24.2.10
conjugate, of a word 35.4
ConjugateDominantWeight 61.7.20
ConjugateDominantWeightWithWord 61.7.20
ConjugateGroup 37.2.5
Conjugates 56.3.6
ConjugateSubgroup 37.3.8
ConjugateSubgroups 37.3.9
conjugation 39.2
ConjugatorAutomorphism 38.6.2
ConjugatorAutomorphismNC 38.6.2
ConjugatorIsomorphism 38.6.1
ConjugatorOfConjugatorIsomorphism 38.6.5
ConnectGroupAndCharacterTable 69.6.4
ConsiderKernels 71.4.3
ConsiderSmallerPowerMaps 71.4.4
ConsiderStructureConstants 71.2.9
ConsiderTableAutomorphisms 71.5.3
ConstantTimeAccessList 21.17.6
constituent, of a group character 70.8
ConstituentsCompositionMapping 31.1.7
ConstituentsOfCharacter 70.8.8
Constructing Algebras as Free Algebras 60.2
Constructing Algebras by Generators 60.1
Constructing Algebras by Structure Constants 60.3
Constructing Character Tables from Others 69.18
Constructing Domains 30.3
Constructing Lie algebras 61.2
Constructing Pc Groups 44.4
Constructing Subdomains 30.8
Constructing Tables of Marks 68.3
Constructing Vector Spaces 59.1
Construction of Abelian Number Fields 58.1
Construction of Stabilizer Chains 41.7
Constructors for Basic Groups 48.4
ContainedCharacters 71.3.17
ContainedDecomposables 71.3.17
ContainedMaps 71.3.6
ContainedPossibleCharacters 71.3.15 71.3
ContainedPossibleVirtualCharacters 71.3.15 71.3
ContainedSpecialVectors 71.3.15 71.3
ContainedTom 68.9.5
ContainingTom 68.9.6
Continue 4.21
continue statement 4.21.1
Continued Fractions 15.5
ContinuedFractionApproximationOfRoot 15.5.2
ContinuedFractionExpansionOfRoot 15.5.1
Conventions for Character Tables 69.5
convert, to a string 26.2
Converting Groups to Finitely Presented Groups 45.10
ConvertToCharacterTable 69.3.4
ConvertToCharacterTableNC 69.3.4
ConvertToMatrixRep 24.13.2
ConvertToMatrixRepNC 24.13.2
ConvertToRangeRep 21.22.2
ConvertToStringRep 26.2.2
ConvertToTableOfMarks 68.6.5
ConvertToVectorRep 23.2.1
ConvertToVectorRepNC 23.2.1
Conway Polynomials 57.5
ConwayPolynomial 57.5.1
coprime 4.12
Copy 12.7
copy, an object 12.7
COPY_LIST_ENTRIES 21.4.6
CopyOptionsDefaults 41.10.2
Copyright 76.0
Copyright Notice 76.0
Copyrights 73.18
CopyStabChain 41.10.1
Core 37.11.2
CorrespondingGeneratorsByModuloPcgs 43.9.6
coset 37.7
Coset Tables and Coset Enumeration 45.5
Coset tables for subgroups in the whole group 45.7
CosetLeadersMatFFE 23.5.6
Cosets 37.7
CosetTable 45.5.1
CosetTableBySubgroup 45.5.4
CosetTableDefaultLimit 45.5.7
CosetTableDefaultMaxLimit 45.5.6
CosetTableFromGensAndRels 45.5.5
CosetTableInWholeGroup 45.7.1
CosetTableOfFpSemigroup 51.6.1
CosetTableStandard 45.6.1
CRC 3.10
CRC Numbers 3.10
CrcFile 9.7.11
CrcFile, example 3.10
CreateCompletionFiles 3.5.1
CreateCompletionFilesPkg 75.2
Creating Character Tables 69.3
Creating Class Functions from Values Lists 70.6
Creating Class Functions using Groups 70.7
Creating Finite Fields 57.3
Creating Finitely Presented Groups 45.1
Creating Finitely Presented Semigroups 51.1
Creating Group Homomorphisms 38.1
Creating Groups 37.2
Creating Mappings 31.1
Creating Permutations 40.4
Creating Presentations 46.1
Creation of Algebraic Extensions 65.1
Creation of Rational Functions 64.21
Credit 1.2
CrystGroupDefaultAction 42.6.1
Cycle 39.8.3
CycleLength 39.8.4
CycleLengths 39.8.6
Cycles 39.8.5
CycleStructureClass 70.8.14
CycleStructurePerm 40.3.2
CyclicExtensionsTom 68.9.7
CyclicGroup 48.1.2
cyclotomic field elements 18.0
cyclotomic fields, CanonicalBasis 58.3
Cyclotomic Numbers 18.0
Cyclotomic Polynomials 64.9
CyclotomicField 58.1.1
CyclotomicPolynomial 64.9.1
Cyclotomics 18.1.2
cyclotomics, DefaultField 58.2

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GAP 4 manual
September 2006