What is the word for "idiosyncrasies of a specific group"?

The word idios comes from Greek, meaning one's own.

Can I use "idiosyncrasies of [group]", despite the subject being a group rather than an individual?

I don't see any reason not to say that a group has idiosyncrasies as you would for an individual. You would, of course, run the risk of making a broad generalisation that is unlikely to apply to every individual in the group.

If you're looking for a single word to describe the shared idiosyncrasies or characteristics of a group, then perhaps subculture is appropriate.

One of the definitions of idiosyncrasy:

A structural or behavioral characteristic peculiar to an individual or group.