Is it permissible to create a group on "Facebook" for reciting the entire Qur'an with the intention of victory for Syria, and another for performing prayers in an unspecified number for the same purpose?

Reciting the Quran and doing good deeds to relieve distress is a legitimate act, and advising one another to do so is good, falling under cooperation in righteousness and piety. However, what is called a collective "khatmah" (completion of the Quran) does not result in the reward of a full khatmah for each individual; rather, each person only receives the reward for what they have read. It is more appropriate for you to remind one another to supplicate and seek refuge in Allah and to increase good deeds secretly to achieve sincerity.