If your application service is not running on Windows, you will not be able to read the PAC without jumping through some serious hoops. The PAC is built using Microsoft proprietary code, which is something Microsoft introduced into their flavor of Kerberos IAW RFC 1510 but their words, "slightly modified". Shortly after the release of Windows 2000 [Active Directory], Microsoft received some negative press attention because of the proprietary way they used the PAC field in a Kerberos ticket. [Microsoft] explicitly forbids the creation of software that implements the PAC as described in the specifications.
I spent a long time trying to find something open source and reliable which could read the PAC anyway, and I found that JAASLounge does this. It's an old article though (from 2010). Be aware that, it appears, based on my interpretation based on Microsoft's statement, to be a violation of their terms and conditions.
Anyway, I've also bookmarked two threads from right here in this forum by people who claim to have gotten JAASLounge this working, and some of the troubles they had to work through.
Decrypt kerberos ticket using Spnego
Malformed PAC logon info on new KerberosToken
In case you don't want to go down this route, and want to bypass the PAC to determine the AD user's group memberships, then you will have to resort to making an LDAP call back to the AD domain controller.
I'll close by saying that if you're running on a Windows-based application server such as IIS or SharePoint, Kerberos decoding of the PAC takes place automatically, so no special code, configuration, or keytab file is ever required.