AbelianGroup

construct a finitely generated Abelian group

AllAbelianGroups

return a list of all the Abelian groups of a given order

AlternatingGroup

construct the alternating group of a given order

BabyMonster

construct the Baby Monster sporadic finite simple group

ConwayGroup

construct a Conway sporadic simple group

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

FreeGroup

construct a free group

FrobeniusGroup

construct a Frobenius group from the database

GaloisGroup

construct the Galois group of a polynomial

GeneralLinearGroup

construct the general linear group over a finite field

GeneralOrthogonalGroup

construct the general orthogonal 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

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

PGL

construct a projective linear 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

ProjectiveGeneralUnitaryGroup

construct a projective general unitary group over a finite field

ProjectiveSpecialLinearGroup

construct a projective special linear 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

PSL

construct a projective special linear 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

QuaternionGroup

construct the quaternion group of order eight

RubiksCubeGroup

construct the group of the Rubik's Cube

RudvalisGroup

construct the Rudvalis simple group

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

SpecialUnitaryGroup

construct a special unitary group over a finite field

Stabilizer

compute the stabilizer of a point under a permutation group

Subgroup

construct a subgroup of a given group

Supergroup

construct a supergroup of a given group

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

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
