Yes, you can create a group assignment using the Assignment activity. A group assignment means when one member of the group submits, the submission is applied to all group members. And when you grade, the grade and feedback is given to all group members. Turnitin Assignment does not yet have this capability.
When you set up the Assignment, you will enable group submissions in the Group Submission Settings section. See the Group Submissions Settings section in our help guide on how to create an Assignment for more information.
You will need to create the groups within your course before they begin submitting to the group Assignment. Please see our help guide on how to Create Groups and Groupings.