Cameras and lights act like real-world cameras and lights, you can't fade a camera or a light. Cameras are either on or off, like in real-life. You can keyframe the opacity of a light just like controlling the dimmer on a real-world light.
You want to remove the camera from your original group. Maybe create a higher level group, if needed for some reason, then move the camera and your original group into that as two separate layers. Keyframe or Fade In/Out the original group. Or just pull the camera out of that original group into an independent layer.
Fade media or groups that only contain media, not the actual cameras and lights.
Personally, I've never had need to put a cameras into a group.