- if you're interested in gravi-GUTs I recommend Krasnov and Percacci's paper for a very deep review:
https://arxiv.org/abs/1712.03061
They discuss SO(3, 11) starting on page 37.
By the way, mathematicians hardly ever talk about so(1,9,C) because it's isomorphic to so(10,C) and so(4,4,C) and so(7,2,C) - complexifying washes out the signature, so we just say so(10,C).