Class years are almost always mentioned alongside alumni names—see names of people for guidelines in that context and punctuation section for apostrophe guidelines.
When mentioned in the context of a specific class, treat the phrase as a capitalized proper noun.
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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 may 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.