Let's say I have a 'group of people', let's call it 'Group A'. Group A consists of people (concrete) suggesting it is concrete, yet any member of Group A can be at any place in the world, and their membership of Group A implies its existence, however in this case Group A has no physical spatial location, suggesting an abstract nature.
Is there a way we can determine this metaphysically?
The group does have a physical spatial location (aka a location), namely the Earth, so your supposed reason for considering the group to have an abstract nature does not apply. Lest you still think otherwise, imagine a thought experiment in which the scattered members of the group are asked to head for the room- at what point in their individual journeys toward the room would they morph from being abstract to concrete?
The group is purely abstract: it is a convenient name we give for a collection of particular people. We use that name "group A" in communications and reasoning to avoid having to explicitly list the particulars each time, but only the particulars exist, and the group is a pure subject-side abstraction that does not "exist" outside our minds.
In the thought experiment in which the scattered members of the group are asked to head for the room, there is no "group" entity that physically enters the room, but only particular individuals.