Unfortunately there is no command to list names of groups which particular user is part. But you can use combination some commands to get that.
One of the ways is
rahul@rahul-Aspire-4736Z:~$ cat /etc/group | grep rahul adm:x:4:rahul cdrom:x:24:rahul sudo:x:27:rahul dip:x:30:rahul plugdev:x:46:rahul lpadmin:x:108:rahul rahul:x:1000: sambashare:x:124:rahul
User “rahul” is part of groups shown above, first part is group name, second one is password which is not shown, third is group ID and last one is list of users part of a group.