The topic of kol isha is a very complicated issue that has a vast literature. The answer given in this forum is by definition general, and for specific halachic advice, one should consult one's local orthodox rabbi. Having made that disclaimer, we will attempt to offer some basic guidelines in response to your question.
Although some have suggested that because individual voices in group singing are not readily discernible there may be room for leniency of women singing in a group in the presence of men, this position is generally not accepted by most authorities (see, e.g. Hatzneh Haleches, Rav Elyakim Elensohn (page 83)). Rav Yechiel Weinberg, in a celebrated responsa (Seridei Eish 2:
, permitted mixed singing of zemiros and shirei kodesh at kiruv organization events. Athough he recognized that this was a relatively novel position at the time, under the circumstances, he felt that there existed strong reasons to rule leniently. The singing was a vital part of the religious experience trying to be created, and by prohibiting this type of singing, the women attending these events might have been distanced, rather than brought closer to religion. I know of some heads of seminaries here in Israel that have applied the leniency of the Seridei Eish to the educational context of girls singing zemiros in front of men participating at the Shabbos meals. Whether this leniency could properly be extended even to a more private setting of women singing zemiros in the presence of men outside of an educational context is questionable.
The source for the prohibition of kol isha is found in a pasuk in Shir HaShirim (2:140, and is cited in the Talmud Bavli at Berachos 24a, and the Yerushalmi Challah 2:1. It is quoted in the Rambam, Hil. Issurei Biah 21:1, the Piskei HaRosh in Berachos 3:37, and the Shulchan Aruch in Even HaEzer at 21:1. Most authorities assume the prohibition is Rabbinic in nature (Sedei Chemed).