word request - Opposite of private tutoring lessons

You hire a tutor to get one-on-one tutoring. I was looking for lessons that students take with a tutor and I found private tutoring lessons. I have two questions:

1. Can I use a private tutoring class to refer to a small group of students who hired a tutor? What if there is just one student and a tutor. Can I use class here, too? For example,

I have a [class] with my tutor at 4. I'm going to my [class].

2. What's the opposite of private tutoring? Public teaching? For example,

I hate [public* classes]. [Public teaching] doesn't work. I prefer [private** classes].

*Classes with a lot of students in them; often associated with weak education.

**While you get one-on-one education with a tutor; often associated with a better quality than that of a public school.

Do the words I put within brackets sound natural in the sentences?

Answer

Classes are regularly scheduled, and have more than one student.

I take French class at school. Those are public classes.

Classes don't have to be at a public school, though.

My wife and I are taking a dance class offered by our church. We have lessons once a week.

In American English, tutoring usually refers to individual lessons in addition to those you are getting from a group elsewhere.

I am not very good at French, so I also see a tutor once a week. Also, because I am so good at biology, I have a tutor who is helping me prepare for the biology AP exam.

The distinction between public and private has to do with who pays, not who is allowed to be there. In the U.S. public schools are free to attend and are paid for by the state. Private schools are paid for entirely by those attending.

At the college/university level, public schools are subsidized by the government, but students have to provide some of the tuition themselves. Private colleges and universities are not subsidized, and are therefore much more expensive to attend.

A tutor could be private (unafiliated with my school) or could be provided by my school. If it really matters which type you have, you may have to specify it:

I am not very good at French, so I also see a tutor provided by my school. Also, because I am so good at biology, I hired a private tutor who is helping me prepare for the biology AP exam.

If you are doing some kind of individual study that isn't in addition to a group class, you might just call it lessons.

I am going to stop editing this answer now, because I have to go pick my daughter up from her piano lesson.