Can QC run on FireFox?
I'll go get the version.
No, IE or the QCExplorer stand alone.
Quality Center relies on ActiveX plugins to communicate with the DLLs that you've downloaded on your system when you first go to your QC website.
Regardless of whether you can tweak your system in some way to make it work, running QC in any browser other than IE is unsupported.
(Opinions and information contained in this post are wholly my own and do not reflect the opinions of my employer.)