In my 1st year Mathematics BSc course, dihedral groups seems to include rotations and reflections, which suggests that groups can have more than one operation. But definitions of groups I've seen seem to suggest (not totally clearly) that groups have exactly one operation. 

If that's right, what's the single operation associated with dihedral groups? I would guess it's reflection, since rotations can be retrieved from compositions of reflections, but not the reverse.