Without more context of your problem, I can't really give a definite answer. Most clustering algorithms will work though, the problem is how "good" are your results. I'm quoting the word "good" because you'll need some sort of metric to measure that (generally inter-cluster and intra-cluster distance).
Here's the advice given to me when I was taught on how to decide on an algorithm for data mining: Try the simplest algorithms first - quite often these are overlooked but perform quite well (Naive Bayes for supervised learning is a classic example).
To start you off, try something like K-means which is a simple and popular method, you can find more info here http://en.wikipedia.org/wiki/K-means_clustering (if you look at the Software section you can also find a list of implementations that you could try).
The second part of the criteria is to be able to output the other people in the group based on a target person. This is doable in all clustering algorithms since you'll have X subsets of people, you simply need to find the subset which the target person is in and then iterate that subset and print all the people within out.