Sorry if this would be more appropriate as a stackoverflow and not a mathoverflow question, but I think it's more likely to be known in this community.

There are plenty of places on the internet or in books where you can find character tables for standard finite groups $G$ (say, linear groups). However I'm looking for a database of the actual matrices by which elements of $G$ act on representations of small dimensions ($\text{dim} V<20$, and with $|G|<5000$ or so), and can't find any, either with floating-point values or algebraic ones. Anyone know of such?