Databases of Structure Definitions

These are Magma's databases of structure definitions.

Polynomials with given Galois groups. For each transitive group G with degree between 2 and 11, the database contains a univariate polynomial over the integers which has G as its Galois group.

glnzgps

The maximal finite subgroups of GL(n, Z) for n = 2, 3, 4, 5. The groups are taken from the tables which appear in R. Buelow, "Ueber Dadegruppen in GL(5, Z)", Diss, RWTH Aachen 1973.

gps100

The non-abelian soluble groups having orders in the range 1 to 100 but excluding 64.

isolgps

The irreducible soluble subgroups of GL(n, p) for n > 1 and p^n < 256.

matgps

Various useful matrix groups, almost all over finite fields (the only exception is the Weyl group E6).

perfpgs

This database was intended to contain all finite perfect groups of order up to one million. In fact, due to the very large number of groups involved, it is incomplete in certain places. It is totally complete up to order 50000.

pergps

A number of permutation representations for finite groups. A particular group is included either if (a) It is an "interesting" group. In practice this means a simple group or a close relative of a simple group; or (b) It is representative of some class of groups which is useful for testing conjectures and algorithms.

prmgps

Primitive groups of degree up to 50. The list has been prepared by C. C. Sims and, while it is believed to be complete, users assuming the completeness of the list do so at their own risk.

simgps

Presentations for all simple groups of order less than a million. The database was prepared by Jamali, Robertson and Campbell.

solgps

Power-conjugate presentations of 13 soluble groups constructed by S.P. Glasby.

thrgps

The groups of order dividing 729. The stored description for each group can be used to calculate a power-conjugate presentation for the group.

trngps

The transitive permutation groups of degrees from 2 to 12.

twogps

The groups of order dividing 256. The stored description for each group can be used to calculate a power-conjugate presentation for the group.

Magma also has a library of files containing functions and procedures written in the Magma language. See Libraries of Functions in the Magma Language.

Subscreens

• Database of Galois Group Polynomials
• Database of Maximal Finite Subgroups of GL(n, Z)
• Database of Groups of Order up to 100
• Database of Irreducible Soluble Subgroups of GL(n,p) for n > 1 and p^n < 256
• Database of Matrix Groups
• Database of Finite Perfect Groups
• Database of Some Permutation Groups
• Database of Primitive Groups
• Database of Simple Groups: Permutations, Presentations, Conjugacy Classes, Maximal Subgroups and Sylow Subgroups
• Database of Soluble Groups
• Database of Groups of Order Dividing 729
• Database of the Transitive Groups of Degrees from 2 to 22
• Database of Groups of Order Dividing 256

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