Any Class created in Brainscape is "public" by default. In practice, most Classes aren't really discoverable until they contain a substantial amount of content (since they wouldn't show up very high in Search results), but users could still find them using a specific search query or by finding your user Profile screen. The more you and your students use Brainscape, the more discoverable your Class will become.
You can change this setting by navigating to the Learners tab for a particular Class, and finding the option to "Make Private". Making a Class private will prevent any existing users from seeing the content (without an invite), and will remove it from Search results (within 7-10 days).
Please note that private Classes require a Brainscape Pro account for every user in the Class. To inquire about a bulk purchase of Brainscape Pro accounts at a huge discount, please contact us about an Enterprise license.
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