In a Gii-generated view the object passed from the controller is usually named [font="Courier New"]$model[/font]. Assuming in your view [font="Courier New"]$model[/font] is an instance of [font="Courier New"]Member[/font] then [font="Courier New"]$model->group->name[/font] is probably what you want.
If you are trying to access the group name in a grid then you can use “dot notation” as shown here. If I understand your case, you can use [font=“Courier New”]‘group.name’[/font] as an attribute name.
See also the [font="Courier New"]$value[/font] and [font="Courier New"]$content[/font] properties of DataColumn