F4 is a Lie group.

In the mathematical construct (notice the word CON) of HIV which stands for Horribly Incorrect Virology, there are many of these F4‘s.

Wikpedia states: The F4 Lie algebra may be constructed by adding 16 generators transforming as a spinor to the 36-dimensional Lie algebra so(9), in analogy with the construction of E8. In older books and papers, F4 is sometimes denoted by E4.