how to use join & group by in liq

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LINQ

my table structure is like this

1)list_table

id      int
list_name   string

2)item_table

id      int
list_name   string
item_name   string
price       double
qty     int
amt     double

i want to disply it like

list_name ( Count)

i want item count group by list name and also want to include those list_name whose
item is not there in item_table.(i.e. list_name (0) )

till i have done

public class MyListItem
    	{
        public string category { get; set; }
        public double total { get; set; }
    	}

	public List<mylistitem> jinal;

	public void listcountwise1()
        {
	var qur = from lst in db.List1
                      join it in db.Item1 on lst.List_name equals it.list_name
                      group lst by new { lst.List_name } into g
                      from c in g.DefaultIfEmpty()
                      select new MyListItem() { category = g.Key.List_name, total  = (c == null ? 0 : g.Count()) };
            jinal = qur.ToList();
	}

the result is not true.
there is one list repeting no of items it have.
and the list which has no items is not displying it shows null insted of name.