The properties will depend largely on the thermoplastic resin used, but also on the type of carbon fibre, fibre length and other additives.
Most common carrier resin is Nylon 6.6, but nylon 6 is also common.
The people who specialise in these compounds are, DSM in the Netherlands and in Evansville Indiana, RTP (i think in Florida) ans LNP, whom I think now belong to GE, but don't quote me on that
Depending on what properties you are looking for, sometimes long glass fibre can out perform carbon
I have quite a few old data sheets if you can tell me what you really want