In my book The 2-Hour Job Search, I recommend using Group connections as a bit of a last resort (after grad/undergrad connections and 2nd degree connections). My thinking has evolved a bit.
The problem with 2nd-degree connections is they’re slow. You need two people’s help instead of just one. Group connections may be “colder,” but they’re faster.
Your options for contacting a Group or 3rd degree connection in LinkedIn’s search results are limited to 1) Invite them to connect (which is an awkward way to approach a stranger) or 2) Send them an InMail (which costs money). With Group connections, there is a way to message them directly for free, but only if you access their profile correctly.
To take advantage of this, find a Group connection you’d like to message. Then, click on the name of the Group you share with them. You’ll default to the Group’s “Discussions” page, which still won’t give you free access.
However, if you click on the Members page, something magical happens. Look up your contact’s name in the search box on the left and find their profile. Hover your cursor over their profile, and a new option will appear on the right: “Send a message”. Bingo.
What if a person isn’t a Group connection?
What if they’re a 3rd degree connection, or worse? What if you don’t even have a last name to work with? Just first name and last initial, or generic “LinkedIn Member”? Don’t fret — try this instead.
In these cases, copy and paste your desired contact’s job title into Google, putting quotes around it (e.g., “Lead Graphic Designer”). Do the same for their employer’s name, and finally add “LinkedIn.” This will make your search field look like this: “Lead Graphic Designer” “Graphix Consulting Co.” LinkedIn
The results should give you your desired contact’s full name (your results are only restricted to first initial & last name or “LinkedIn Member” within LinkedIn’s infrastructure — public profiles found through Google search are not usually restricted in the same fashion). If you click on this public page and scroll down to the bottom of the page, a list of that contact’s Groups memberships will appear at the bottom. (It appears blank at first, but give it a second.)
At this point, you may request membership to whichever of those Groups appears most applicable to your interests and goals. Once approved for membership, you may take advantage of the process outlined above.