Few different cases:
* you can't "take" a group-owned object, you have to set it for sale and buy it back - you need to have a specific group-permission in order to set deeded items for sale, so use the group window to see who has it assigned
* return/delete (if you don't own the object, they both do exactly the same thing) - requires return permission on the land where the object used to be (or an estate manage could do it sim/estate-wide), or auto-return was set on the parcel with the wrong group.
What happens to the object depends on the permissions: if it was transfer it'll be returned to the person it belonged to before it was deeded, if it was no transfer then it was deleted. I *think* full permission always get deleted on return/delete as well when group-owned but not 100% sure
* it's not actually gone but had "Allow everyone to move" checked and someone moved it
* Other misc things like it's still where it's supposed to be but the land was raised to cover it up (land owner or estate manager), another prim is covering it up, etc.
You can check the estate owners and anyone with return/delete/set group owned objects for sale permissions in the group, but there's no way for you to determine who did it other than narrow it down to who could have and ask them.
If you didn't change anything on your sim since yesterday you can always request a rollback of your private sim. Make sure you know what that actually means before just requesting one: anything that happened on your sim since the time you roll back to is undone. If you parcelled your sim since yesterday it'll be parcelled to the way it was before, if a parcel changed owners it'll revert to the previous owner, if you rezzed something it'll vanish from the sim (and not come back to your inventory), if you picked anything up you'll end with it double, etc.
Hope that helped

.