Welcome to Apple Support Communities. I understand that you joined a Group FaceTime call but you were unable to enable your camera during the call. I know what a great feature Group FaceTime is to use; I'd like to provide some information. Based on what you've described, it's possible that you're using a device that doesn't support Group FaceTime on video, but will for audio:
Use Group FaceTime on your iPhone, iPad, and iPod touchTo use Group FaceTime video calls, you need an iPhone 6s or later, iPad Pro or later, iPad Air 2, or iPad Mini 4 with iOS 12.1. Earlier models of iPhone, iPad, and iPod touch that support iOS 12.1 can join Group FaceTime calls as audio participants.
If you think your device meets the requirements for using video with Group FaceTime, can you let me know which model device you're using and the iOS version you have installed?
Best Regards.