The following has some useful details on the history of primary groups: -
http://dunnry.com/blog/DeterminingYourPrimaryGroupInActiveDirectoryUsingNET.aspx

SID Structure: -
http://msdn.microsoft.com/en-us/library/cc230371%28v=PROT.10%29.aspx

To obtain SID in binary format the following may be required: -
env.put("java.naming.ldap.attributes.binary","objectSID");

Using the primary group ID to locate the primary group: -
http://support.microsoft.com/kb/297951