Today, there are no reports or notifications of tasks assigned to groups. The only way to have visibility of tasks is if they are assigned to a person. Please allow a task view of unassigned tasks for groups you are part of in order to assign those tasks.
We are proposing going further with it there are several requests over the last few years. Would you go like our latest request? https://support.freshservice.com/support/discussions/topics/50000000087