Well, when we say community, we refer to a large number of people or entities, who may be affiliated to many smaller or disparate sub-structures.Community almost always refers to a varied and large audience, yet with certain things, which maybe certain interests, opinions, or religion or ethnicity.
On the other hand, group is indeed most often used for a small number of people or other entities, each of which may or may not be large. Also, a group is not as natural a collection as community. A group maybe formed by some of us just now, but a community arises on its own and comes together, and has more naturally common attributes. Similarly, one can be expelled from a group, if he disrespects the rules, but one cannot be banned from a community per se, unless it is something very artificial like a virtual social networking aggregate that is moderated etc.
E.g. we talk about the international community of researchers of a certain field, say Physics, or the international community of institutional investors (each of which is an institution like a bank and consists of millions of people), whereas we say G8- a group of nations.
If you like your 'T-Top' you could use 'T-Shaft' or 'T-Leg'.
Shaft or column and capital or cap or lintel would describe the joint in terms of the T and keep it in the architectural domain—but it might create confusion with vertical elements.
If the wall which constitutes the horizontal of the T is the primary load-bearer, you might write of a main and an intersecting or butted or abutting wall—or a mainwall and a buttwall.
If the wall which constitutes the vertical of the T is primary, you might write of a main(wall) and a crosswall or crossing wall.
Or it might be best to consult an architect for appropriate terms of art.
Best Answer
Both terms are valid and I'm not sure either would be preferred. Given that you are talking about fees explicitly, I'd lean towards the "largest fee". You might also want to consider the "maximum fee".