Are you wanting to frag because it is getting too large? If you are just wanting to get some more pcs. to sell or trade here is an excerpt from an article by Richard Durso.
Upon closer inspection I could see it was no Aiptasia… it was a mini-Elegance!!I was amazed that this coral had dropped off a daughter colony without me noticing it. This process must have taken a significant amount of time. How could it have done that without showing some sign of stress? I quickly cleaned off the rest of the glass to see if I could locate any other daughter colonies, and I was able to locate three more, all of them in the back of the tank behind the rock work.
I noticed that in several locations the Elegance coral's outer oral disc was expanded beyond what is normal...........
This oral disc, which is hyper-extended, starts to secrete a calcium skeleton separate from the skeleton of the rest of the colony. Apparently, this skeleton continues to gain mass, and its weight stretches the flesh of the coral that is holding it to the parent colony. Eventually, this weight is great enough to tear it away from the parent and a new daughter colony is created.
Google this
Asexual Reproduction of Catalaphyllia jardinei
(Elegance coral)
for the full article.