I'm Eurofleet CC (just around 16months now).
Seems to me that it's pretty sociable most of the time. There is usually someone who'll want to go out and most of the times it'll be a general invite to everyone, unless a couple of crew have particularly "clicked" and want to keep it to themselves. Don't be put-off by initial statements. I joined a crew recently who all spent all day saying there was no way they were going out that night. Result: a wonderful (and partially memorable) VLN (very late night) for all of us.
Of course you have to bear in mind things like hours, local restrictions, pick-ups, previous sectors etc. Fairly often, you as FC will be joined by CC who may already have worked sectors earlier in the day, or vice-versa. Also of course, on 75/76 you may take CC into a nightstop, but then you and they will be operating different flights the next day as we can sometimes go out on a Boeing and back on an Airbus.
Best for me so far was our Captain who we met waiting for the bus out to the aircraft who's first words were: "Right, Preflight Briefing: pizza and a glass of wine tonight everyone(?)" We never did work out if it was a question, or an instruction!
It isn't always an FC/CC divide. Very often I've ended-up stepping-out with just the Captain or just the FO.
Sometimes you'll arrive at a nightstop hotel and find a note from crew who are already there, as they will be aware that there is another crew arriving. Often the note will let you know where they have gone, and will ask you to join them if you wish.
My advice to you: If you fancy a social, just ask ... there will usually be at least one taker. Just relax and be open, nothing ventured, nothing gained. And if you are desperate but it seems there are no takers, you can always make-up some spurios reason (I've had more than 1 "birthday" in the past few months
)
Anyway ... Welcome ... Enjoy ... Oh, and mine's a pint
