Googles definition of class says "course of instruction". Would that mean a class could be something taught to a single person over a period of time?
Typically, a class, or a course, is taught to a number of students together. The words class and course can be applied to one-on-one instruction, but such cases are marginal; they are not what one first thinks of when one hears these words. The words are most likely to be applied to one-on-one instruction in the contexts in which the similarities between such instruction and the instruction in groups are more relevant than the differences. For example, a student who says 'I am taking four classes this term', may be including in that number a ‘reading course’ or an ‘independent study project’ that he is taking alone—this is because the one-on-one character of that class is irrelevant to the point of the communication (which is about his workload or the total academic credit earned).