Here are the classes, structs, unions and interfaces with brief descriptions:

[detail level 123]

permlib
classic
BacktrackSearch	Searching in a group with classical backtracking
IntersectionSearch	Subgroup search for a group intersection based on classical backtracking
LexSmallerImageSearch	Coset representative search for a lex-smaller set images
SetImageSearch	Coset representative search for a set image based on classical backtracking
SetStabilizerSearch	Subgroup search for a set stabilizer based on classical backtracking
exports
BSGSSchreierData	Data structure with elementary data types to represent a BSGS based on SchreierTreeTransversal
BSGSSchreierBase	Base class for import/export of a BSGS based on SchreierTreeTransversal
BSGSSchreierExport	Export of a BSGS based on SchreierTreeTransversal
BSGSSchreierImport	Import of a BSGS based on SchreierTreeTransversal
helpers
SupportRestriction	Helper class to decide when an permutation action on a set is trivial or can be reduced to a subset
BaseSupportRestriction	This class never imposes a restriction on any set
ReducedSupportRestriction	This class implements canBeIgnored() but has a trivial set()
FullSupportRestriction	This class implements both canBeIgnored() and set()
partition
BacktrackRefinement	Backtrack refinement
GroupRefinement	Concrete $\mathcal P$ -refinements for group membership
IntersectionSearch	Subgroup search for a group intersection based on partition backtracking
MatrixAutomorphismSearch	Subgroup search for the automorphism group of a symmetric matrix based on partition backtracking
MatrixRefinement1	Concrete $\mathcal P$ -refinement for symmetric matrix automorphisms
MatrixRefinement2	Concrete $\mathcal P$ -refinement for symmetric matrix automorphisms
Partition	Partition
RBase	R-base for partition backtracking
Refinement	Base class for a $\mathcal P$ -refinement which is used in an R-base and bound to an initial partition
RefinementFamily	Class of $\mathcal P$ -refinements for a given problem
GroupRefinementFamily	$\mathcal P$ -refinements for group membership
SetStabilizeRefinementFamily	$\mathcal P$ -refinements for set stabilization
SetImageRefinementFamily	$\mathcal P$ -refinements for set stabilization
MatrixAutomorphismRefinementFamily	$\mathcal P$ -refinements for symmetric matrix automorphisms
SetImageRefinement
SetImageSearch	Coset representative search for a set image based on partition backtracking
SetStabilizeRefinement	Concrete $\mathcal P$ -refinements for set stabilization
SetStabilizerSearch	Subgroup search for a set stabilizer based on partition backtracking
VectorStabilizerSearch	Subgroup search for a stabilizer of an integer vector based on partition backtracking
AbstractBSGS	A high level interface implementing a group represented by a BSGS data structure
AbstractPermutationGroup	A high level interface for a permutation group
AbstractSymmetricProduct	A high level interface implementing a direct product of symmetric groups
BSGS	Represents a base and strong generating set (BSGS)
StrongGeneratingSetSorter	Class that can be used to sort a strong generating set
BSGSCore	Core data of a base and strong generating set (BSGS)
BaseChange	Abstract base class for base change algorithms
BaseTranspose	Abstract base class for base transposition
SymmetricGroup	Representation of a symmetric group
ConjugatingBaseChange	Base change by conjugation and, if necessary, transpositions
DeterministicBaseTranspose	Implementation of a deterministic base transposition algorithm
NewBaseChange	Base change by constructing a new base with random schreier sims
RandomBaseTranspose	Implementation of a randomized base transposition algorithm
SimpleBaseChange	Base change by a sequence of point insertions and transpositions
delete_object	Callable object to delete a pointer
BaseConstruction	Base class for BSGS construction algorithms
CyclicGroupConstruction	BSGS construction for a cyclic group of given order
KnownBSGSConstruction	BSGS construction from a known base and strong generating set
RandomSchreierSimsConstruction	BSGS construction with Random Schreier-Sims algorithm
SchreierSimsConstruction	BSGS construction with classic Schreier-Sims algorithm
BSGSGenerator	Stateful generator of BSGS elements
BSGSRandomGenerator	Generates uniformly distributed random group elements based on an existing BSGS
Generator	Interface for group element generators
ProductReplacementGenerator	Generates nearly-uniformly distributed random group elements using the product replacement algorithm
RandomGenerator	Abstract base class for random group element generators
RandomSchreierGenerator	Generates a uniformly distributed random element of $G^{[i]}_\alpha$
SchreierGenerator	Stateful generator of Schreier generators
Permutation	Permutation class storing all values explicitly
PermutationWord	Permutation class storing permutations as words of elementary Permutation 's
GroupIntersectionPredicate	Predicate for the subgroup that arises as the intersection of two given groups
IdentityPredicate	Predicate matching a permutation if it stabilizes a given list of points pointwise
LexSmallerImagePredicate	Coset-type predicate for group elements that map one set of zeros and ones to a lex-smaller set (w.r.t. to the indices)
MatrixAutomorphismPredicate	Predicate for the automorphisms of a symmetric matrix
PointwiseStabilizerPredicate	Predicate matching a permutation if it stabilizes a given list of points pointwise
SetImagePredicate	Coset-type predicate for group elements that map one set of points onto another given set of points
SetwiseStabilizerPredicate	Predicate for the subgroup that stabilizes a given point set
StabilizesPointPredicate	Predicate matching points that are stabilized by given permutations
RefinementFamily
SubgroupPredicate	Abstract base class for subgroup (and coset) predicates
VectorStabilizerPredicate	Predicate for the subgroup that stabilizes a given integer vector
PrimeHelper	Helper class for primality checks
RedundantBasePointInsertionStrategy	Strategy for redundant base point insertion
TrivialRedundantBasePointInsertionStrategy	Insertion position after first non-trivial transversal
FirstRedundantBasePointInsertionStrategy	Insertion position at first position i such that $G^{[i]}$ stabilizes beta
BaseSearch	Base class for searching in a group
DSetAction	Action of a permutation on a dynamic bitset
OrbitLexMinSearch	Algorithm to find the lexicographically minimal set in an orbit
OrderedSorter	A sorter that sorts a sequence with respect to a given input ordering
BaseSorter	A sorter that sorts a sequence (e.g. $\Omega$ ) with respect to a given input ordering (e.g. a base)
BaseSorterByReference	A sorter that sorts a sequence (e.g. $\Omega$ ) with respect to a given input ordering (e.g. a base)
GroupSorter	A sorter that sorts a sequence of permutations with respect to a ordering induced by a base
TrivialSorter	A sorter that sorts a sequence in natural numerical order (1 < 2 < 3 < ...)
GiantTestBase
GiantTest	Tests a group given by generators for being an Alternating Group or a Symmetric Group
GroupType	Abstract base class for permutation group types
TrivialGroupType	Group type for a trivial permutation group
AnonymousGroupType	Group type for a permutation group whose type could not be determined
NamedGroupType	Abstract base class for named groups (such as cyclic and symmetric groups)
SymmetricGroupType	Group type for symmetric groups
AlternatingGroupType	Group type for alternating groups
CyclicGroupType	Group type for cyclic groups
WreathSymmetricGroupType	Group type for a wreath product of symmetric groups
DirectProductGroupType	Group type for a direct product of two groups
PrimitivitySGSTest	Tests a transitive group for which a strong generating set is availble for primitivity
PrimitivityTest	Tests a transitive group is availble for primitivity
TypeRecognition	Class for a basic type recognition of permutation groups
BlockVectorAction
SymmetricGroupRecognitionHeuristic	Fast recognition of symmetric group subgroups
ExplicitTransversal	Transversal class that stores all transversal elements explicitly
Orbit	Abstract base class for orbit computation
OrbitList	Stores an orbit in a sorted list
OrbitSet	Stores an orbit in a set for fast contains() operation
SchreierTreeTransversal	Transversal class that stores transversal elements in a Schreier tree
ShallowSchreierTreeTransversal	Transversal class that stores elements in a shallow Schreier tree
SymmetricGroupTransversal	Transversal of a symmetric group
Transversal	Transversal base class corresponding to a base element $\alpha$
TrivialAction	Action of a PERM on unsigned long element