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.