Magma has a database containing characteristic 0 representations of some finite quasisimple groups.
OverZ: BoolElt Default: true <=> p = 0
Automorphisms: BoolElt Default: false
RepNo: RngIntElt Default: 1
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.
Returns a list of tuples specifying the names of the groups in the quasisimple matrix group database, together with the dimension and the number of stored representations of the group in that dimension.