Here's how to create a Domain Local Group in Active Directory using C#
using (DirectoryEntry myDE =
    new DirectoryEntry(LDAPPath, LDAPUsername, LDAPPassword))
{
   DirectoryEntries myEntries = myDE.Children;
   using (DirectoryEntry group = myEntries.Add("CN=" + Name, "group"))
   {
      group.Properties["sAMAccountName].Add(Name);
      group.Properties["groupType].Add("-2147483644"); //DOMAIN LOCAL GROUP
      group.CommitChanges();
   }
}
Also one thing to note - if the Name ends in a full stop it will fail with a really non-helpful message of "A device attached to the system is not functioning."