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Databases of Groups

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 22.

Primitive Permutation Groups: Magma has a database containing all primitive permutation groups having degree up to 50.

For a description of these databases, we refer to Chapter DATABASES OF GROUPS.

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Version: V2.19 of Wed Apr 24 15:09:57 EST 2013