I did a bit of a dive into the SCORM documentation, which can be found here.
Adapt officially supports SCORM 1.2 and there is no attribute for class or group. I noticed in the technical documentation, found in the SCORM_1.2_RunTimeEnv.pdf file on page 29, that in the example of the attribute student_id they had included information of the year group of a student, so perhaps it's possible to add information through there and parse the received string in Adapt in a presentable way that could be shown in a classroom. However, I would assume that your current LMS platform has this configured in a certain way already.
Matt Leathes is the SCORM expert in the Adapt core team so can probably provide a better answer.