Magma has a database containing characteristic 0 representations of
some finite quasisimple groups.
Return an absolutely irreducible matrix group in characteristic p, which
may be a prime number or 0, derived from the reduction modulo p of
of an absolutely irreducible representation in characteristic 0 and
dimension d of the quasisimple group G with name N.
The generators of G used are its standard generators.
For those quasisimple groups in the ATLAS-database (Section Database of ATLAS Groups),
the same names are used as there.
Other quasisimple groups are named according to the same conventions.
If there is more than one representation of G in dimension d in the
database, then the first such is used by default, and the others can
be accessed by using the RepNo option.
If the reduction modulo p of the representation is not irreducible, then
a random non-trivial irreducible constituent is used. (This behaviour may change
in the future.)
For those representations that are not realisable over Z in
dimension d, a representation in dimension d over a minimal extension
of the rationals and also an irreducible representation in a higher dimension
over Z are both stored in the database. The representation used is
the one over Z if the parameter OverZ is true, and the
one over the number field otherwise. Reduction modulo p is generally faster
using the integral representation, so that is the default when p>0.
If the parameter Automorphisms is set, then extra generators inducing
those outer automorphisms of G that stabilise the representation are
included in the group returned. This may result in extra scalars being
present in the group returned, and when p=0 this scalar subgroup can
sometimes be infinite.