What is the adjectival form of group?

Using group as an adjective is grammatical, as in group effort, but there can be an ambiguity: is a "group study" a study of a group or a study by a group? It is often used to refer to the former.

For the sake of clarity, you might want to say "The study was undertaken by a group... " and then go on to identify or describe the group in some way.

Whilst I cannot think of an adverb which applies to something having been done by a specific group, collectively would be a suitable one to indicate that a group, in a loose sense, had been involved.

If you wanted to say, for example, that the new library facilities had been provided by the Literacy Group, you could say that they were not the work of a single individual but were a group-wide achievement.

OED lists three adjectival derivatives of group...

grouped - Arranged, placed, or situated in a group or groups; forming a group or groups.
Most recent citation 2000 N.Y. Rev. Bks. 24 Feb. 29/1:
Enright later found affinities with ‘the Movement’—a loosely grouped school of poets that advocated terseness and public subjects in verse.

groupist - Characterized by the desire or tendency to belong to a group; (also) that tends to view people as members of a group, rather than as individuals.
Most recent citation 2005 R. Brubaker in J. Adams et al. Remaking Modernity v. 472
Everyday talk..routinely [frames]..accounts of ethnic, racial, and national conflict in groupist terms as the struggles ‘of’ ethnic groups, races, and nations.

groupy - Of the nature of or characteristic of a group or groups; spec. (somewhat depreciative) characteristic of the Oxford Group¹ movement or its members (now rare).
Most recent citation 2010 S. T. Fiske Social Beings (ed. 2) xii. 483
They perceive themselves as more groupy, more of a psychological unit or entity, if the elevator stalls, because they develop a common fate.

Plus obviously the root word itself can be used attributively as a noun adjunct in, for example, We made a group decision and We conducted a group study. In such usages, the exact relationship between the adjunct and the main noun depends on context (so those could be decisions or studies by or of a group or groups).

¹Oxford Group Movement - A religious revivalist movement founded in 1921 by Frank Buchman (see Buchmanism n.), emphasizing the importance of leading a spiritual life under the guidance of God, and characterized esp. by the discussion of one's moral dilemmas and failings in small groups.