It is ideal
that the Obligatory Prayer be said in private, but not obligatory. What is obligatory is that it be said alone. Not to be said in a congregation style, but it may be said in the same room as other people.
1527. Each One Must Say his Obligatory prayer by himself
"As to the obligatory prayer: Each one must say his prayer alone by himself, and this is not conditional on a private place; that is, both at home and in the worshipping-place, which is a gathering-place, it is allowable for one to say his prayer; but each person must say his prayer by himself. But if they chant supplications together, in a good and effective voice, that is very good."
('Abdu'l-Bahá: Tablets of 'Abdu'l-Bahá, Vol. II, p. 464)
(Compilations, Lights of Guidance, p. 465)
Apparently passages in the writings in Persian seem to say that saying the obligatory prayer in a group, as long as silent and not led by any individual but said wholly communally is allowable. But that is pretty unclear, and I don't read Persian, so I don't know much about it.
I can't find the quote, but the Bab talks about how prayer alone in our room is the most advisable.
As a former atheist who struggles a lot with prayer, let me put this plea out to you all:
Please do not read the Long Obligatory Prayer at feast without the consent of the rest of the friends. Long devotionals for many people defeat the purpose, and become tedious, frustrating, and unspiritual. Baha'u'llah does not advise us to needlessly lengthen our prayers. If you just ask, even though it is doubtfull anyone will object, you let those who struggle with prayer (I am not the only one) prepare ourselves and work at getting into a longer focus.
I enjoy people who can really do devotionals well and fall into prayer well, so I never object, but I need warning! I can enjoy long prayer when done by people who enjoy it, but sometimes it is excessive. Do not associate being "good at" devotionals or prayer with being spiritual or, "being bad" at those things with needing healing. The Holy Spirit interacts with each of us in different ways, and Baha'u'llah has made it clear there is no need to impose one type of religiosity on all Baha'is.
Be considerate in prayer!