A complex that contains kinase activity directed towards the C-terminal Domain (CTD) of the largest subunit of RNA polymerase II and is essential for initiation at RNA polymerase II promoters in vitro. In S. cerevisiae, it is composed of the 5-subunit core (Rad3p, Tfb1p, Tfb2p, Ssl1p and Tfb4p), Ssl2p, and TFIIK (Kin28p, Ccl1p, and Tfb3p). All of the subunits have equivalents in humans: the 5 subunit core is composed of ERCC2, p62, p55, p44, p34; the equivalent of the TFIIK subcomplex is composed of MO15, Mat1, and a cyclin; the human equivalent of Ssl2p is XPB.