How to use Generic with SqlDataReader

I'm trying to come up with a way just to load a table from SQL Server into a class, without having to tell it anything. Basically, just create the class and have it know what to load, based on that. Here's what I have so far.

My question is, is there some way to keep from having to hard code the types, to call reader.readString, reader. readInt32, etc.. based on the FieldType?

 private Int32? readInt32(SqlDataReader reader, string columnName)
    {
        Int32? result = null;


        if (!reader.IsDBNull(reader.GetOrdinal(columnName)))
        {
            result = reader.GetInt32(reader.GetOrdinal(columnName));
        };

        return result;
    }

  public List<T> readTable(string table, string wherecls, string connStr)
    {
        List<T> result = new List<T>();
        using (SqlConnection connection = new SqlConnection(connStr))
        {
            using (SqlCommand command = connection.CreateCommand())
            {
                command.CommandText = "select * from " + table;
                if (wherecls.Length > 0) command.CommandText += " where " + wherecls;
                connection.Open();
                using (var reader = command.ExecuteReader())
                {
                    while (reader.Read())
                    {
                        Object i = Activator.CreateInstance(typeof(T));

                        System.Reflection.FieldInfo[] fieldInfoList = typeof(T).GetFields();
                        foreach (System.Reflection.FieldInfo f in fieldInfoList)
                        {
                            if (f.FieldType == typeof(string)) f.SetValue(i, readString(reader, f.Name));
                            if (f.FieldType == typeof(Int32)) f.SetValue(i, readInt32(reader, f.Name));
                            if (f.FieldType == typeof(Int16)) f.SetValue(i, readInt16(reader, f.Name));
                            if (f.FieldType == typeof(byte)) f.SetValue(i, readByte(reader, f.Name));
                            if (f.FieldType == typeof(short)) f.SetValue(i, readShort(reader, f.Name));
                        }
                        result.Add((T)i);
                    }
                }
            }
        }
        return result;
    }

Thank you, Dan Chase