What is the function of the controller in a software-defined network?

Multicast replication at the hardware level is a function of data plane devices (switches/routers), which are commanded by the controller, not performed by the controller itself.

Fragmenting and reassembling packets are functions performed by network devices (e.g., routers) at the data plane, typically related to handling different MTUs.

The SDN controller is the central component of the control plane, responsible for making all routing and forwarding decisions by collecting network information and then instructing data plane devices on how to handle traffic.

Forwarding packets is primarily the role of the data plane devices (switches and routers), which execute the forwarding instructions provided by the SDN controller.