Thanks for your reply, Melanie.
I did a test with a student who is in more than one group, one for the class group and one for the presentation group. When I tried to have this student do a grouped assignment, I got an error message saying that the student was in more than one group, so the assignment couldn't be done. When I removed the student from one of the groups, it was possible to do the assignment.
So students can be in more than one group, but how can we specify which group is to be used for an assignment? This might not be the same question as I asked before, but I feel like it's the same problem
So, it sounds like you have forced groups, which is fine, but can result in behavior like that. Do you have separate groups enabled for the activity, too? The groups settings for activities has changed since last I fiddled with it (last was...maybe 2.5?, I do a lot with plain old groups but advanced groups/groupings was never a priority) and they are much cooler. I did a small test run and it seemed to work okay, but I didn't do a complete test (submissions, etc) with each group.
This might be a place to use groupings with groups, it is a little more complicated but might improve functionality.