In addition to IgC the antibodies that can fix complement are?

IgG and IgM can fix complement by activating the C3 protein at the end of the complement cascade allowing ADCC (antibody dependent cell- mediated cytoxicity) to occur.

I have never heard of an IgC antibody.

In humans there are only 5 classes of antibodies: IgM, IgG, IgA. IgD & IgE.