Like a group on fb then unlike?

[Claire]

You can't like a group. You can like a page, and join/get added into a group.

If it's a page, it could be seen on their homepage. Sometimes, from personal experience. Sometimes, it doesn't.

If it's a group, there are two ways :
Closed group (group that you are added into and cannot join freely) - nothing is seen.
Open group - People who have joined the group or friends who are also in the group will see the posts and get notifications(if chosen) but it is not shown that you joined the group.