Generation and Population of values in DropdownList

Hii,
I have a problem with generation of dropdownlist and populating it with values.I have a Model called GroupsModel written in AdminModel inherited from HeaderModel.

 public class GroupsModel : HeaderModel
    {
      public Guid Id { get; set; }
      public String GroupName { get; set; }
      public Guid GroupId { get; set; }
      public IEnumerable<SelectListItem> GroupsList { get; set; 
      }

I have a view called groups.cshtml which uses groupsmodel and i also have a partialview _groupspartial where i need to generate a dropdown list which must populate Groupslist according to GroupId .
I have a controller to fetch groupslist in which i have written code as

public ActionResult GetGroups()
        {
          var groupsmodel = new GroupsModel();
          var groupsList = new List<SelectListItem>();
            groupsList = _adminSystemServices.GetGroups().ToList();
            groupsList.Insert(0, new SelectListItem { Text = "Select Group", Value = "" });
            groupsmodel.GroupsList = groupsList;
           return PartialView("_MyGroupsPartial",groupsmodel);
        }

Can anyone please help me with the dropdownlist generation.