The mission: the Jesus Groups were dynamic. We have very little information about a mission by James’ group. Acts contains several mentions
of baptismal communities: in Samaria: Acts 8:16 and in Ephesus: Acts 19:1ff. The latter are said to be baptised only in the name of Jesus, in other words, by John’s baptism; they did not yet have the Holy Spirit.
The most impressive mission was that of Peter’s group. Peter himself is depicted as a missionary in Acts 10; baptism is integrated into Peter’s mission, so we can interpret Peter’s mission as the final stage of mission that was then continued in the general Christian mission.