Class years are almost always mentioned alongside alumni names—see names of people for guidelines in that context.
When mentioned in the context of a specific class, treat the phrase as a capitalized proper noun.
At Reunion 2016, members of the Class of ’41 (the oldest in attendance) met members of the Class of ’11 (the youngest).
Class years are often abbreviated to the last two digits preceded by an apostrophe; but if there is a potential for confusion about the century, fully spell out the year. In formal settings, such as the announcement of a Convocation ceremony, the full class year can be spelled out.
As the 2019 Convocation speaker, Bill Nye '77 will inspire the Cornell Class of 2019 to be curious, informed, hopeful agents of change.