The list of groups is given under Groups in /proc/<pid>/status; for example,
$ grep '^Groups' /proc/$$/status
Groups: 4 24 27 30 46 110 115 116 1000
The primary group is given under Gid:
$ grep '^Gid' /proc/$$/status
Gid: 1000 1000 1000 1000
ps is also capable of showing the groups of a process, as the other answers indicate.