I sympathize with your situation---though at least the problem is only people! At one point when I was a graduate student, there was a building under construction right next to the lab, the noise was continuous for many months. The worst was the weeks when they were setting the foundation with pile-drivers and every few seconds a loud metallic "Ping!" would go right through your bones and make the building vibrate. The only thing to do to get focus was to abandon the building and work elsewhere.
Which is the same thing that I would suggest to you to do in your situation. Find a good quiet place where you can be highly productive (maybe the library, maybe somewhere else---there are usually lots of good hidey-holes around a campus) and use it strategically. If it were one or two people, then you might think of talking with them, but it sounds like the group has an established culture of interaction, and it's appropriate for you to adjust your behavior to work with that culture, rather than asking the whole rest of the group to cater to your needs. It would be different if there were bigger issues involved (e.g., a culture of offensive jokes), but this is just a value-neutral matter of preferred working style.
That then leaves the question of how to maintain connection and visibility. First of all, it's probably important that you spend only a minority of your time away in your quiet place. If you're there all the time, you most certainly will become isolated from your group, and will miss out on all of the benefits of interaction. As a relatively new graduate student, you may think you should spend all of your time reading, but that it very unlikely to be the case.
I think that you should have a conversation with your professor---not to ask for anything to change, but just to say that you intend to spend occasional time away from the lab doing your reading for better focus, and to express the same concern that you have expressed here, with making sure that this does not lead to bad impressions or less connection. Your professor may tell you not to worry, or may have suggestions for you. You can also use active means of communicating your location to lab-mates, e.g., putting a note at your desk to tell people where you are and making sure that you are available electronically (e.g., via IM) if somebody wants to find you. Finally, make sure that you do participate in laboratory informal social culture when you aren't trying to focus, e.g., eating lunch with people, joining some of those research conversations, etc.
In short: figure out what actions you need to do to be productive, then make sure you communicate actively with both your professor and labmates in order to keep those actions from interfering with other aspects of your participation in the lab.