Someone has to be GROUPED in the first place in order to exclude certain persons. Social strata are not "grouped." They are an aggregate....as is language, looks, sexuality....etc.
An aggregate is a body of people with similar characteristics but no enduring ties. You gave many examples.
A group is a body with identifiable binding ties. A group would be "the workers at Ford Plant #23." The "Eagles" football team. If the eagles had a picnic for the whites only, they'd be going out of their way to exclude.