Database of the Transitive Groups of Degrees from 2 to 22

This database contains all transitive permutation groups having degrees in the range 2 to 22 inclusive. The transitive groups up to degree 15 were determined by Greg Butler and John McKay, while the groups having degrees in the range 16 to 22 have recently (1997) been determined by Alexander Hulpke.

Each group is labelled according to its degree. For example, the label of the 3rd transitive group of degree 9 is 9, 3.

The groups are accessed through the following functions only.

TrnGroup(d, n)

This function returns the n-th group of degree d.

TrnNumberOfDegree(d)

This function returns the number of groups of degree d which are stored in the library.

TrnGroupSatisfying(f)

Given a boolean valued function f: GrpPerm --> BoolElt (which may either be an intrinsic function or a user defined function), return a group satisfying f(G). This function runs through all the stored groups, expanding each from the stored generators and applies the predicate f until it finds a suitable one. If no group is found, an error message is printed.

TrnGroupOfDegreeSatisfying(d, f)

As TrnGroupSatisfying(f), except it only runs through the groups of degree d.

TrnGroupsSatisfying(f)

As TrnGroupSatisfying(f), except a sequence of all such groups is returned.

TrnGroupsOfDegreeSatisfying(d, f)

As TrnGroupOfDegreeSatisfying(d, f), except a sequence of all such groups is returned.

TrnProcess()

Return a "process" for looping over all the stored groups. Initially it points to the first group (of degree 2).

TrnProcessOfDegree(d)

Return a "process" for looping over all the stored groups of degree d. Initially it points to the first group of degree d.

TrnGroupOfDegreeProcess()

Return a "process" for looping over all the stored groups of degree d where lo <= d <= hi. Initially it points to the first group of degree lo.

TrnProcessIsEmpty(P)

Return whether the process P currently points to a group.

TrnProcessGroup(P)

Given a process P which currently points to a group, return that group.

TrnProcessLabel(P)

Given a process P which currently points to a group, return the label d, n of the group.

TrnProcessNext(~P)

Given a process P which currently points to a group, modify it so that it points to the next group if there is one or make it empty if there is not.

Example

load trngps;
P := TrnProcessOfDegree(5);
while not TrnProcessIsEmpty(P) do
    G := TrnProcessGroup(P);
    ... do computations with G ...
    TrnProcessNext(~P);
end while;