Is there a way to select a group and copy in Kicad Schematic Editor?

It should. If it doesn't, that's definitely a bug.

As an alternative, select with your mouse, right-click and go to "Save", which is KiCad 4's way of saying "Copy". Then use the paste icon to insert a copy of the block you selected.

-- Addendum --

It occurs to me that you might be holding SHIFT and clicking to copy an item. KiCad only supports the idea of copying a block of items. You would need to hold SHIFT and then click+drag to select and copy the items. To duplicate a single item, you need to use the SHIFT and click+drag action but only allow the selection box to cover a single item.