According to Official Guinness Records,
The most somersaults through a hoop in one minute by a team is 43 and was achieved by Team Kinetix (UK) on the set of Officially Amazing in Suffolk, UK, on 13 July 2015. The record was achieved on the team's 3rd attempt.
For a complete list of 2015 records, please visit 2015 Guinness Records in United Kingdom.