The "group" to which I refer is the demand for centralized organization, authority of Rome. That does not exist in the Scriptures. There were hundreds of separate, independent gatherings, congregations, assemblies meeting all over the world by the end of the first century. Paul saw no one group as superior or controlling the believers. He had little regard for reputations and apparently neither did God Himself (Gal. 2:6).
So, gathering together with other believers and attending to the teaching of the apostles, fellowship, breaking of bread, and prayer is not the same thing as needing a "group" (Acts 2:42).
The hundreds of separate bodies such as you mention to not appear in the New Testament, which has a definite hierarchy, starting with Jesus’ calling of the 12 and extending to his dispatch of the 70. Paul was very exercised by those who challenge his authority as apostle and instructed Timothy how to behave as a “bishop.” The very purpose of the canon of the New Testament is to limit the disparity of what was taught,which is to say, it is the book of THE Church. I say this leaving aside the matter of authority of the bishop of Rome.