We've run into this several times in our applications and we usually push the user to the new "group" they've created. The reason for this is because creating that "group" is not just about naming it but about setting it up in it's entirety.
I don't know about all the details of your application but for us, we allow people in the insurance industry to create a new "group" of forms that will be associated with various policies. When the user clicks "Create New Form Group", it immediately takes them to a screen where they not only choose the name of the group and the categories it applies to but also all of the forms associated with this group. Just to explain further, we actually implemented a swap box below that shows all of the forms on the left and the forms they associate with this group dragged or selected to the right. Once the user is done naming the new group, choosing a category, moving over associated forms, they can then "finish" the task and the user is taken back to their "groups" page where the new form group sits at the very top.
While this isn't exactly what you are doing since yours are people and ours are forms, what it does show is that if the user clicks "New Group" and there are other actions they must take to define that group, then it makes sense to take them straight to it in order to complete the task.
Think of it this way—If it was just tagging or a very simple task, you could easily just place that new tag at the top since there isn't really much else the user has to do to that new item. But in this case, there are still things that need to be defined in that group. While you could still create the group, place the name at the top of the list, and then make the user choose a menu item ("Edit Group") to enter that view; doing so does add an extra click and it also sort of implies that you're done and no further action is really required. For us, that wouldn't be the case since the name is just one part of defining our type of grouping. It sounds like the more efficient way would be take them straight to the view/screen where the user can add the new group name, add members, edit other settings, etc., allow them to "finish" group creation and that takes the user back to the list view of the groups with the new one sitting at the top.
Hopefully this helps.