Magma contains the following databases of groups:
Small Groups: Contains all groups of order up to 1000, excluding orders 512 and 768.
Perfect Groups: This database contains all perfect groups up to order 50000, and many classes of perfect groups up to order one million. Each group is defined by means of a finite presentation. Further information is also provided which allows the construction of permutation representations.
Rational Maximal Matrix Groups: Contains rational maximal finite matrix groups and their invariant forms, for small dimensions (up to 31 at V2.9 and above). Each entry can be accessed either as a matrix group or as a lattice.
Quaternionic Matrix Groups: A database of the finite absolutely irreducible subgroups of GLn((D)) where (D) is a definite quaternion algebra whose centre has degree d over Q and nd leq10. Each entry can be accessed either as a matrix group or as a lattice.
Transitive Permutation Groups: Magma has a database containing all transitive permutation groups having degree up to 47.
Primitive Permutation Groups: Magma has a database containing all primitive permutation groups having degree up to 4095.
For a description of these databases, we refer to Chapter DATABASES OF GROUPS.