AbelianGroup

construct a finitely generated Abelian group

AffineGeneralLinearGroup

construct the affine general linear group over a finite field

AffineSpecialLinearGroup

construct the affine special linear group over a finite field

AGL

construct the affine general linear group over a finite field

AllAbelianGroups

return all the Abelian groups of a given order

AlternatingGroup

construct the alternating group of a given order

ASL

construct the affine special linear group over a finite field

BabyMonster

construct the Baby Monster sporadic finite simple group

CayleyTableGroup

construct a Cayley table group

ChevalleyE6

construct a Chevalley group of type E6

ChevalleyE7

construct a Chevalley group of type E7

ChevalleyE8

construct a Chevalley group of type E8

ChevalleyF4

construct a Chevalley group of type F4

ChevalleyG2

construct a Chevalley group of type G2

ConwayGroup

construct a Conway sporadic simple group

CustomGroup

construct a custom group, given its operations

CyclicGroup

construct a cyclic group of a given order

DicyclicGroup

construct a dicyclic group

DihedralGroup

construct the dihedral group of a given degree

DirectProduct

construct a direct product of groups

ElementaryGroup

construct an elementary Abelian group

ExceptionalGroup

construct one of the exceptional finite simple groups

FischerGroup

construct one of the Fischer groups

FPGroup

construct a finitely presented group from generators and defining relators

FreeGroup

construct a free group

FrobeniusGroup

construct a Frobenius group from the database

GaloisGroup

construct the Galois group of a polynomial

GammaL

construct the general semilinear group over a finite field

GeneralLinearGroup

construct the general linear group over a finite field

GeneralOrthogonalGroup

construct the general orthogonal group over a finite field

GeneralSemilinearGroup

construct the general semilinear group over a finite field

GeneralUnitaryGroup

construct a general unitary group over a finite field

GL

construct the general linear group over a finite field

Group

construct a group from various data

HamiltonianGroup

construct a finite Hamiltonian group

HaradaNortonGroup

construct the HaradaNorton simple group

HeldGroup

construct the Held simple group

HigmanSimsGroup

construct the HigmanSims simple group

JankoGroup

construct one of the Janko sporadic finite simple groups

LyonsGroup

construct the Lyons simple group

MathieuGroup

construct one of the Mathieu finite simple groups

McLaughlinGroup

construct the McLaughlin simple group

MetacyclicGroup

construct a metacyclic group

Monster

construct the Monster simple group

ONanGroup

construct the O'Nan simple group

Orbit

construct the orbit of an element under a permutation group

OrthogonalGroup

construct an orthogonal group

PerfectGroup

construct a perfect group from the database

Perm

create a permutation

PermutationGroup

construct a permutation group given generating permutations

PGammaL

construct the general semilinear group over a finite field

PGL

construct a projective linear group over a finite field

PGO

construct the projective general orthogonal group over a finite field

PGU

construct a projective general unitary group over a finite field

ProjectiveGeneralLinearGroup

construct a projective general linear group over a finite field

ProjectiveGeneralOrthogonalGroup

construct the projective general orthogonal group over a finite field

ProjectiveGeneralSemilinearGroup

construct the general semilinear group over a finite field

ProjectiveGeneralUnitaryGroup

construct a projective general unitary group over a finite field

ProjectiveSpecialLinearGroup

construct a projective special linear group over a finite field

ProjectiveSpecialOrthogonalGroup

construct the projective special orthogonal group over a finite field

ProjectiveSpecialSemilinearGroup

construct the special semilinear group over a finite field

ProjectiveSpecialUnitaryGroup

construct a projective special unitary group over a finite field

ProjectiveSymplecticGroup

construct a projective symplectic group over a finite field

ProjectiveSymplecticSemilinearGroup

construct the projective symplectic semilinear group over a finite field

PSigmaL

construct the special semilinear group over a finite field

PSigmap

construct the projective symplectic semilinear group over a finite field

PSL

construct a projective special linear group over a finite field

PSO

construct the projective special orthogonal group over a finite field

PSp

construct a projective symplectic group over a finite field

PSU

construct a projective special unitary group over a finite field

QuasicyclicGroup

construct a quasicyclic pgroup

QuasiDihedralGroup

construct a quasidihedral group

QuaternionGroup

construct a generalized quaternion group

Ree2F4

construct a large Ree group of Lie type

Ree2G2

construct a small Ree group of Lie type

RubiksCubeGroup

construct the group of the Rubik's Cube

RudvalisGroup

construct the Rudvalis simple group

SemiDihedralGroup

construct a semidihedral group

SigmaL

construct the special semilinear group over a finite field

Sigmap

construct the symplectic semilinear group over a finite field

SL

construct a special linear group over a finite field

SmallGroup

construct a specific group of small order

SpecialLinearGroup

construct a special linear group over a finite field

SpecialOrthogonalGroup

construct a special orthogonal group over a finite field

SpecialSemilinearGroup

construct the special semilinear group over a finite field

SpecialUnitaryGroup

construct a special unitary group over a finite field

Stabilizer

compute the stabilizer of a point, list or set under a permutation group

Steinberg2E6

construct a Steinberg group of type 2E6

Steinberg3D4

construct a Steinberg group of type G2

Subgroup

construct a subgroup of a given group

Supergroup

construct a supergroup of a given group

Suzuki2B2

construct a Suzuki group of Lie type

SuzukiGroup

construct the Suzuki simple group

Symm

construct the symmetric group of a given degree

SymmetricGroup

construct the symmetric group of a given degree

SymplecticGroup

construct a symplectic group over a finite field

SymplecticSemilinearGroup

construct the symplectic semilinear group over a finite field

ThompsonGroup

construct the Thompson simple group

TitsGroup

construct the Tits simple group

TransitiveGroup

construct a specific transitive permutation group

TrivialGroup

construct the trivial group

TrivialSubgroup

construct the trivial subgroup of a given group

WreathProduct

construct a wreath product of permutation groups
