Funnily enough a pre-print paper was published just two days ago on this very subject, using a twin study, in Norway!

https://osf.io/preprints/socarxiv/mncet/

TLDR:

> We show that class attainment is strongly influenced by genetics. Shared environmental factors play a modest role. Our study suggests that sociological theories explaining class outcomes in terms of social origins have little explanatory power, and should be reformulated to consider genetics.