When attempting to copy a group, I select the CTRL to copy but the original Group moves to the new position, but it does not copy the Group.
Are you referring to copying with the Move tool? Are you using SketchUp 2019 as indicated in your profile?
If you are using 2021.1, there was a change in the way the modifier keys work. Tap and release CTRL to activate Move/Copy.
See the Release Notes for other new features.
And this video:
Also if you are using 2021, please update your profile.
I am on 2021 Pro. I figured out the tap ctrl. Thanks for following up