How would I run a report that shows all tickets belonging to a group?

What do you mean by "belonging"? Responsible? Primary responsible? Reveiwing?

Either way, you can run a simple ticket search in the Tickets application -> cilck "Tickets" in the left-side navigator with any of three group filters set in the "Filter" secton on the right side: Responsible Group, Primary Responsible Group, and Reviewing Group.

You can also create a custom ticket reporting in Tickets -> New -> Report -> Tickets report using any of these three filters to pull a custom set of data for that group.

Refer to this knowledge base article for more information on the difference between responsible and primary responsible:

https://solutions.teamdynamix.com/TDClient/KB/ArticleDet?ID=512