How do I find out what groups I belong to under Linux operating systems?

/etc/group is a text file which defines the groups on the system. You can use the groups command to display group memberships for any user using the following syntax.

groups
groups userName-Here

Example

pen a command-line terminal (select Applications > Accessories > Terminal), and then type:
$ groups
Sample outputs:

vivek cdrom floppy audio dip video plugdev netdev bluetooth scanner

You are part of all of the above groups. To find group memebership for root user, enter:
$ groups root
Sample outputs:

root : root

Please note that (from the groups man page):

Primary and supplementary groups for a process are normally inherited from its parent and are usually unchanged since login. This means that if you change the group database after logging in, groups will not reflect your changes within your existing login session. Running `groups’ with a list of users causes the user and group database to be consulted afresh, and so will give a different result.

You can also use the id command as follows to get the same information:
$ id -Gn
$ id -Gn userName
$ id -Gn vivek

How Do I Find Out My Primary Group Membership?

Type the following command:
$ getent group userName
$ getent group vivek
Sample outputs:

vivek:x:1000:

In this example, user vivek has group id # 1000 and has group name vivek for primary group membership.