The adjective each is always followed by a singular noun: each person; each book. When the adjective follows a plural subject, the verb agrees with the subject: They each dress in different styles.
Is each singular or plural?
They are always singular, though. “Each” is often followed by a prepositional phrase ending in a plural word (“Each of the students”), which confuses the verb choice. Each, too, is always singular and requires a singular verb. Example: Everyone has gone.
What do we use after each?
Each can be used after the noun (or pronoun) it describes. The parents gave their children some pocket money. To avoid problems, they each received the same amount.
Is the word class a singular noun or a plural noun? This question cannot be answered with Yes or No. Use the singular if you see the class as a group of students. Use the plural if you see the class as single students.