Discrete as in you'll never take a derivative of anything, so the parent pun comment is meaningless. At least in the subset of group theory I studied, no continuous functions were used which are the only objects that derivatives are defined on.
In other news, (bad) pun threads have come to hacker news. I guess it was always a matter of time.
It so happens that SO(3), being a Lie group, has a well-defined space of derivatives: its associated Lie algebra so(3) [notice lower case]. In fact, the generators of the group fundamentally arise from the derivatives of rotations around the identity.
