From Latin 'classis' (citizen division by wealth) — the top group, 'classici,' gave us 'classic' meaning first-rate.
A group of students taught together, a lesson or session of instruction, or a division of society based on social or economic status.
From Latin 'classis,' which originally meant 'a summoning, a calling together,' from the archaic verb 'calāre' (to call, to summon), from PIE *kelh₁- (to call, to shout). The Roman king Servius Tullius (6th century BCE) divided Roman citizens into six 'classēs' based on wealth for purposes of taxation and military service. The wealthiest were the 'classici' — later the source of the word 'classic' (first-rate, belonging to the highest class). The educational sense of a group of students taught together emerged in the 16th century.
The word 'classic' comes directly from 'class' — Latin 'classicus' meant 'belonging to the highest class' of Roman citizens, the wealthiest taxpayers. When a Roman literary critic called a writer 'classicus,' he was ranking that author among the elite. So calling something 'a classic' is still, 2,500 years later