Wireless support has never been great in Knoppix, and even some NICs that did work in 4.2 seems to not be working for many in 5.0.1. In addition there are many problems installing Knoppix to hard disk, one of them frequently being networking. I would advise you that there is no good reason at all to install Knoppix and that if you want a copy of Linux installed to hard disk, use one of the distros that is intended for hard disk install. For many users, particularly those who like Knoppix, Debian is a good choice, since Knoppix is actually based on Debian and you can install of all the apts included with Knoppix (and many many more) into Debian quickly and easily. This is not a ststement that Deian or any other Linux distro is the best, I'm just suggesting that you may find it a good place to start. Indeed, some other distros that get updated more frequently might have better support for your network card. But Knoppix will not have better support than Debian.

Some also suggesting installining Kanotix rather than Knoppix. While I agree completely that Kanotix addresses some of the problems that are known to exist with a Knoppix "install", I have never heard any good argument for install Katonix over Debian itself and then installing exactly the software that you want.