Is the word group a prepositional phrase?

I'm not sure if your question is whether a prepositional phrase is the same thing as a Word group, or if "group" is a prepositional phrase.

The answer is no in either case.

A Word group must express a complete thought.

A prepositional phrase is part of a sentence and it has to start with a preposition. "In the group" is a prepositional phrase beginning with the preposition "in."