KGT adds "group of people with shared culture." 

nugh is used when referring to a group with a shared culture (common beliefs, values, traditions, knowledge, etc.) and (usually) shared territory whose members interact with each other in accordance with shared norms.

yej'an is an intentionally formed organization of people and is not infrequently used in the name of that organization. (In this usage, it could be translated "society," but also "organization, association, guild" and many other things.)

For "community," meaning a group of people with a shared (and probably relatively narrow) interest or common defining characteristic, such as the "Klingon-speaking community," use the term yuvwan. A yuvwan is generally not a formally or officially organized group.