Is it permissible to perform congregational prayer in the kitchen of shared student housing without the administration's permission, due to the unavailability of another place that accommodates the worshippers?

If the kitchen floor is clean, or if prayer rugs can be used, then there is no harm in praying in the kitchen when a mosque is unavailable, and the manager's permission is not required. It is preferable to negotiate with the dormitory manager to designate a hall for prayer, so that the call to prayer (Adhan) and prayers can be established there, for the Prophet, peace and blessings be upon him, said: "There are no three in a village or desert in whom prayer is not established except that Satan has overcome them."