It is not allowed / permitted to smoke in class.
Smoking is not permitted in class. / You are not allowed to smoke in class.
The teacher lets us to talk during lessons.
The teacher lets us talk during lessons.
They allow using the dictionary during the exam.
They allow you to use a dictionary during the exam.
This enables to make multiple copies.
This enables multiple copies to be made.
It is not permitted walking on the grass.
Walking on the grass is not permitted. / Don’t walk on the grass.
Our parents let us go to bed late.
The teacher allowed / permitted us to use a calculator during the exam.
This app enables / permits / allows you to order a taxi.
This app lets you order a taxi.
They were allowed / permitted to go home early.
All these verbs have the same meaning, though let is the least formal and permit the most formal. enable cannot be used when giving permission but only in the sense of facilitating.
They all require a personal object (e.g. to allow someone / you / her to do something).
let is less formal, requires the infinitive without to, and is not used in the passive form.