Should I prostrate with a group who, on Friday, read aloud in unison and with one melody, and prostrate at the verse of prostration?

The ruling on reciting the Qur'an with one voice has been previously explained. The prostration of recitation (Sajdat al-Tilawah) is a recommended supererogatory act for whoever recites a verse of prostration or listens to it, not an obligatory one. This is based on the saying of Umar ibn al-Khattab: "O people, we have not been commanded to prostrate, so whoever prostrates has done well, and whoever does not prostrate commits no sin." This is sunnah for the reciter and for the listener who sat down with the intention to listen. You may prostrate with them if you sat down to listen, but if you do not prostrate, there is no sin or blame upon you. It is preferable not to sit with them if they are engaged in an unlawful act.