100 people with high turnover is getting too big for people to think they can know everybody. I saw this when I was in college with a local organization that had lots of college-age members (though there were others too and some graduates did stick around). More recently, I've seen this in some workplaces -- you can't maintain that startup culture of everybody knowing everybody else, having lunch together, going out for beer, etc when you grow from 20 to 100.
What I've seen naturally arise in these settings, and you might try to create intentionally, is smaller groups within the larger group. The person who won't bother going to the party with 100 people he barely knows might well go to a pub event with 15 people, many of whom he already knows. Look for clusters of interests -- "outside" (non-academic) interests in particular -- that cross class cohorts (so you get a mix of "ages" within the department) and help them pursue those interests together. This could be a board-gaming day, a group outing to a sporting event, dinner and the hot new SF movie, a high-end pot-luck for people who like to cook, a LAN party, a hike, or lots of other things.
Note that since these are social, not academic, activities, you might get people wanting to bring other folks along too. While that's not your focus, tolerate it anyway -- if you want to build social coherence and people have partners with shared interests, excluding partners means you increase the chance that your member will pass -- the opposite of what you want. So long as gatherings don't become pairs events, where single people feel excluded, there's little harm here and quite a bit to be gained.
Don't start up a bunch of different things at once; try to identify one thing that enough people are interested in to make an activity viable, do that, and reinforce it. (You hope that your board-gaming day isn't a one-off; if the people enjoyed themselves, help them organize another. And another.) Then look for another affinity group and try to bring that one together. Then after some time has passed, tackle a third. I recommend this so that you don't overwhelm people and push them to make choices -- "gee, I like board games and fine dining but I can't do both outings right now so I'll join the dinner group" -- and then the gaming group falls off his radar. Let people ramp up.
Because you are not sorting people into buckets, some people will be interested in multiple groups. (And some in none, but you can't please everybody.) People who participate in more than one group bring cross-fertilization. I've had people show up at my board-gaming days who, it turns out, are also interested in cooking and might be interested in my occasional pot-lucks -- but they didn't know I did that and I didn't previously know to invite them.
Finally, this shouldn't really be as centralized and "top-down" as I'm making it sound here. The best way to bring groups together is for somebody who's already interested in a particular activity to ask around for others who share that interest. You don't want a department admin trying to play match-maker or sending out official surveys of interests; that sounds artificial. Social cohesion works when it feels organic, and that comes from the people doing the "cohesing".