- Introduction
- Database of Simple Groups
- Database of Small Groups
- Basic Small Group Functions
- SmallGroupDatabase() : -> DB
- delete D : DB ->
- SmallGroupDatabaseLimit() : -> RngIntElt
- IsInSmallGroupDatabase(o) : RngIntElt -> BoolElt
- NumberOfSmallGroups(o) : RngIntElt -> RngIntElt
- SmallGroup(o, n) : RngIntElt, RngIntElt -> Grp
- SmallGroup(o: parameters) : RngIntElt -> Grp
- SmallGroup(o, f: parameters) : RngIntElt, Program -> Grp
- IsSoluble(D, o, n) : DB, RngIntElt, RngIntElt -> Grp
- SmallGroupIsInsoluble(o, n) : RngIntElt, RngIntElt -> Grp
- SmallGroup(o, f: parameters) : RngIntElt, Program -> Grp
- SmallGroups(o: parameters) : RngIntElt -> [* Grp *]
- SmallGroups(S: parameters) : [RngIntElt] -> [* Grp *]
- SmallGroups(o, f: parameters) : RngIntElt, Program -> [* Grp *]
- SmallGroups(S, f: parameters) : [RngIntElt], Program -> [* Grp *]
- Example GrpData_SmallGroups (H72E1)
- Processes
- Small Group Identification
- Accessing Internal Data
- Groups with Order Divisible by Only 4 Primes
- The p-groups of Order Dividing p7
- Metacyclic p-groups
- Database of Perfect Groups
- Specifying an Entry of the Database
- Creating the Database
- Accessing the Database
- Group(D, i): DB, RngIntElt -> GrpFP, SeqEnum
- IdentificationNumber(D, i): DB, RngIntElt -> RngIntElt
- NumberOfRepresentations(D, i): DB, RngIntElt -> RngIntElt
- PermutationRepresentation(D, i: parameters): DB, RngIntElt -> Hom(Grp), GrpFP, GrpPerm
- PermutationGroup(D, i: parameters): DB, RngIntElt -> GrpPerm
- Finding Legal Keys
- # D : DB -> RngIntElt
- NumberOfGroups(D, o) : DB, RngIntElt -> RngIntElt
- TopQuotients(D) : DB -> SetIndx
- ExtensionPrimes(D, Q) : DB, MonStgElt -> SetEnum
- ExtensionExponents(D, Q, p) : DB, MonStgElt, RngIntElt -> SetEnum
- ExtensionNumbers(D, Q, p, r) : DB, MonStgElt, RngIntElt, RngIntElt -> SetEnum
- ExtensionClasses(D, Q) : DB, MonStgElt -> SetEnum
- Example GrpData_perfgps (H72E8)
- Database of Almost-Simple Groups
- The Record Fields
- Creating the Database
- Accessing the Database
- # D : DB -> RngIntElt
- GroupData(D, i): DB, RngIntElt -> Rec
- ExistsGroupData(D, o1, o2): DB, RngIntElt, RngIntElt -> BoolElt
- NumberOfGroups(D, o1, o2): DB, RngIntElt, RngIntElt -> RngIntElt, RngIntElt
- IdentifyAlmostSimpleGroup(G) : GrpPerm -> Map, GrpPerm
- Example GrpData_sgdb (H72E9)
- Database of Transitive Groups
- Accessing the Databases
- TransitiveGroupDatabaseLimit() : -> RngIntElt
- NumberOfTransitiveGroups(d) : RngIntElt -> RngIntElt
- TransitiveGroup(d, n) : RngIntElt, RngIntElt -> GrpPerm, MonStgElt
- TransitiveGroupDescription(d, n) : RngIntElt, RngIntElt -> MonStgElt
- TransitiveGroupDescription(G) : GrpPerm -> MonStgElt
- TransitiveGroup(d) : RngIntElt -> GrpPerm, MonStgElt
- TransitiveGroup(d, f) : RngIntElt, Program -> GrpPerm, MonStgElt
- TransitiveGroup(S, f) : [RngIntElt], Program -> GrpPerm, MonStgElt
- TransitiveGroups(d: parameters) : RngIntElt -> [GrpPerm]
- TransitiveGroups(S: parameters) : [RngIntElt] -> [GrpPerm]
- TransitiveGroups(d, f) : RngIntElt, Program -> [GrpPerm]
- TransitiveGroups(S, f) : [RngIntElt], Program -> [GrpPerm]
- Example GrpData_Transitive (H72E10)
- Processes
- Transitive Group Identification
- Database of Primitive Groups
- Accessing the Databases
- PrimitiveGroupDatabaseLimit() : -> RngIntElt
- NumberOfPrimitiveGroups(d) : RngIntElt -> RngIntElt
- PrimitiveGroup(d, n) : RngIntElt, RngIntElt -> GrpPerm, MonStgElt, MonStgElt
- PrimitiveGroupDescription(d, n) : RngIntElt, RngIntElt -> MonStgElt
- PrimitiveGroup(d) : RngIntElt -> GrpPerm, MonStgElt, MonStgElt
- PrimitiveGroup(d, f) : RngIntElt, Program -> GrpPerm, MonStgElt
- PrimitiveGroup(S, f) : [RngIntElt], Program -> GrpPerm, MonStgElt
- PrimitiveGroups(d: parameters) : RngIntElt -> [GrpPerm]
- PrimitiveGroups(S: parameters) : [RngIntElt] -> [GrpPerm]
- PrimitiveGroups(d, f: parameters) : RngIntElt, Program -> [GrpPerm]
- Example GrpData_Primitive (H72E13)
- Processes
- Primitive Group Identification
- Database of Rational Maximal Finite Matrix Groups
- RationalMatrixGroupDatabase() : -> DB
- LargestDimension(D) : DB -> RngIntElt
- # D : DB -> RngIntElt
- NumberOfGroups(D, d) : DB, RngIntElt -> RngIntElt
- Group(D, i): DB, RngIntElt -> GrpMat
- Lattice(D, i): DB, RngIntElt -> Lat
- Group(D, d, i): DB, RngIntElt, RngIntElt -> GrpMat
- Lattice(D, d, i): DB, RngIntElt, RngIntElt -> Lat
- Example GrpData_ratgps1 (H72E16)
- Database of Integral Maximal Finite Matrix Groups
- IntegralMatrixGroupDatabase() : -> DB
- LargestDimension(D) : DB -> RngIntElt
- # D : DB -> RngIntElt
- NumberOfGroups(D, d) : DB, RngIntElt -> RngIntElt
- Group(D, i): DB, RngIntElt -> GrpMat
- Lattice(D, i): DB, RngIntElt -> Lat, SeqEnum
- Construction(D, i): DB, RngIntElt -> MonStgElt, SeqEnum
- Group(D, d, i): DB, RngIntElt, RngIntElt -> GrpMat
- Lattice(D, d, i): DB, RngIntElt, RngIntElt -> Lat, SeqEnum
- Construction(D, d, i): DB, RngIntElt, RngIntElt -> MonStgElt, SeqEnum
- Example GrpData_Integral (H72E17)
- Database of Finite Quaternionic Matrix Groups
- QuaternionicMatrixGroupDatabase() : -> DB
- LargestDimension(D) : DB -> RngIntElt
- # D : DB -> RngIntElt
- NumberOfGroups(D, d) : DB, RngIntElt -> RngIntElt
- Group(D, i): DB, RngIntElt -> GrpMat
- Lattice(D, i): DB, RngIntElt -> Lat, SeqEnum
- Construction(D, i): DB, RngIntElt -> MonStgElt, RngIntElt
- Group(D, d, i): DB, RngIntElt, RngIntElt -> GrpMat
- Lattice(D, d, i): DB, RngIntElt, RngIntElt -> Lat, SeqEnum
- Construction(D, d, i): DB, RngIntElt, RngIntElt -> MonStgElt, RngIntElt
- Example GrpData_Quaternionic (H72E18)
- Database of Finite Symplectic Matrix Groups
- SymplecticMatrixGroupDatabase() : -> DB
- LargestDimension(D) : DB -> RngIntElt
- # D : DB -> RngIntElt
- NumberOfGroups(D, d) : DB, RngIntElt -> RngIntElt
- Group(D, i): DB, RngIntElt -> GrpMat
- Lattice(D, i): DB, RngIntElt -> Lat, SeqEnum
- Construction(D, i): DB, RngIntElt -> MonStgElt
- Group(D, d, i): DB, RngIntElt, RngIntElt -> GrpMat
- Lattice(D, d, i): DB, RngIntElt, RngIntElt -> Lat, SeqEnum
- Construction(D, d, i): DB, RngIntElt, RngIntElt -> MonStgElt
- Example GrpData_Symplectic (H72E19)
- Database of Irreducible Matrix Groups
- Database of Quasisimple Matrix Groups
- Database of Soluble Irreducible Groups
- Basic Functions
- IsolGroupDatabase() : -> DB
- IsolGroup(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> GrpMat
- IsolNumberOfDegreeField(n, p) : RngIntElt, RngIntElt -> RngIntElt
- IsolInfo(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> MonStgElt
- IsolOrder(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt
- IsolMinBlockSize(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt
- IsolIsPrimitive(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> BoolElt
- IsolGuardian(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> GrpMat
- Example GrpData_IsolGroup (H72E21)
- Searching with Predicates
- IsolGroupSatisfying(f) : Any -> GrpMat
- IsolGroupOfDegreeSatisfying(d, f) : RngIntElt, Any -> GrpMat
- IsolGroupOfDegreeFieldSatisfying(d, p, f) : RngIntElt, RngIntElt, Any -> GrpMat
- IsolGroupsSatisfying(f) : Any -> SeqEnum
- IsolGroupsOfDegreeSatisfying(d, f) : RngIntElt, Any -> SeqEnum
- IsolGroupsOfDegreeFieldSatisfying(d, p, f) : RngIntElt, RngIntElt, Any -> SeqEnum
- Associated Functions
- Processes
- Database of ATLAS Groups
- Fundamental Groups of 3-Manifolds
- Automatic Groups of 3-Manifolds
- Bibliography
V2.28, 13 July 2023