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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?

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There is the GAP package repsn (gap-system.org/Packages/repsn.html), which computes irreducible representations in characteristic zero (not a database though). The atlas of finite group representations (brauer.maths.qmul.ac.uk/Atlas/v3) has representations of finite simple groups in characteristic 0 (though by far not all of them). –  Florian Eisele Jul 4 '12 at 22:35
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To add to Florian's comment, I can say that GAP also has an interface to the atlas of finite group representations, the package AtlasRep. I don't think anyone works with this data in floating point, as it would be quite impossible due to rounding errors creeping in. –  Dima Pasechnik Jul 5 '12 at 4:59

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