How do I view the members of a group?

You can use getent to display the group's information. getent uses library calls to fetch the group information, so it will honour settings in /etc/nsswitch.conf as to the sources of group data.

Example:

$ getent group simpsons
simpsons:x:742:homer,marge,bart,lisa,maggie

The fields, separated by :, are—

1. Group name
2. Encrypted password (not normally used)
3. Numerical group ID
4. Comma-separated list of members

list members:

getent group <group>

And what rights? On filesystem, sudo, ssh? On filesystem:

find / -xdev -group <group>