JSmooth is right on about playing the social chameleon. Unless this girl is a PUA herself, or one manipulative chick, she isn't about to invite more than one guy she's interested in. Girls don't play the numbers game for the most part, unless you did something to piss her off, or she is purposefully trying to make one of you jealous.
What this means is either:
A) She and this guy are really just friends. Maybe he even has romantic entanglements with one or more of her friends.
B) This guy likes her and she has no interest in him, or they are former romantic partners.
A true AMOG.
C) She views you as the friend and is inviting you along in that capacity, while she is pursuing AMOG as the romantic interest.
D) She really is a PUA/Manipulative Bitch.
Granted, I'm going off very little information here, but I think I'm in the general area. Regardless, if you play this situation right the above variables will have no effect on the outcome, as a true PUA has a way to deal with each individual scenario.
The one thing I would say as a critique is that you could've avoided this conundrum completely. Your mistake lies right at the beginning of this post.
"one of my targets that i've been talking too has set up a night out this friday"
WHY, OH WHY, IS SHE SETTING UP YOUR NIGHT OUT?? Dude, this is a HUGE DLV on your part! It gives her frame control and makes you seem less masculine. This could lead to huge problems!!!
Even if you do score points going out with her and her friends, you still delegated her as the leader of the interaction. As a PUA you must be the LEADER, from open to close. 24/7-365.
I know this is frustrating. I am a natural born leader, but I don't consider going around being Mr. Macho to be having a good time. I like to kick it with a woman who is more aggressive. However, this is not usually the case, and even if it is you still gotta play your part.
Girls (whether they want to admit it or not) love being led by their man. It is evolutionary psych. shit, which you need to know if you don't already. Both MM and early RSD are good for sociobiology content. RSD's Flawless Natural will give you the 411 on "Masculine Intent". Natural Tim is a fucking animal!
Bottom line is that if you played an alpha frame you wouldn't be posting this question in the first place. A women wants to be brought into your world, not the other way around. She wants you to call the shots. Though it is always a plus to be able to mix with her crowd (not only for the sake of her, but also the fact that you never know who the social chain will link to next

) you have to make the relationship about your frame, your world. She wants to experience your reality, so it better be a good one! These are the traits of a high value male.
Now, I'm not saying you need to be the guy who is so self-absorbed everything has to be about him and you don't like going out with her crew or some pussy behavior like that. As I said before there is a lot of value in being able to charm her social group. The reason I'm concerned is because from how I'm reading your post this is your first date, or whatever you want to call it. You guys haven't had sex, there isn't any attachment. It is imperative you should be the one in charge right now.
So, on Friday be prepared to be the leader! That will truly be the best way to deal with AMOG as well. Just remember MASCULINE INTENT. If he can't match your thunder then you'll be laying the hammer down, boyyee!