how do you select multiple layers and move them all together?

I have a photoshop file with about 20 layers. I am trying to grab three of them that need to stay together and move them. They all have alpha channels, so when I select the layers, then try to grab & move using my mouse, I end up selecting the background layer and causing it to move. I'm unable to move the three layers I want to move together using my mouse. I tried putting them in a Group folder but that didn't help; when I try to grab & move with my mouse, it ends up selecting and moving the background layer. I can move by keyboard (Shift-V), but the image is 9960 x 5599, so moving the three layers that way is too slow.