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Convert Datatable to Object with Linq and Group by

I try to convert datatable into JSON with special format

Data in DataTable is as follow

col1 col2 col3 col4
---------------------
 A    B    c    D1
 A    B    c    D2
 A    B    c    D3

Try to convert it to a object array like

class obj {
 var col1;
 var col2;
 var col3;
 list<string> col4;
}

I try to use linq, but kinda get stuck.

 var result = from row in dt.AsEnumerable()
                         group row by new
                         {
                             c1 = row["col1"],
                             c2 = row["col2"],
                             c3 = row["col3"]
                         }
                             into section
                             select new
                                 {
                                     item = section.Key

                                 };
var result = from row in dt.AsEnumerable()
             group row by new
             {
                 c1 = r.Field<string>("col1"),
                 c2 = r.Field<string>("col2"),
                 c3 = r.Field<string>("col3")
             } into section
             select new
             {
                 col1 = section.Key.c1,
                 col2 = section.Key.c2,
                 col3 = section.Key.c2,
                 col4 = section.Select(r => r.Field<string>("col4")).ToList()
             };

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