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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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