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From what I know (not that I know much about the Carthaginians, or the Classical period for that matter), the Carthaginian 'Sacred Band' was a group of soldiers dedicated to Ba'al that fought exclusively on the right side of the phalanx; said group was destroyed in a battle against Syracuse, and the name was dropped, though similar elite units continued to exist. AFAIK, there is no connection to the Theban Sacred Band.
I beat back their first attack with ease. Properly employed, E's can be very deadly, deadlier even than P's and Z's, though they're not as lethal as Paula Abdul or Right Said Fred.
~ Miaowara Tomokato, Samurai Cat Goes to the Movies
I believe it was because it remembered the Greeks of the Theban sacred band?
I read it on a Fantar's article time ago
The Sacred Band of Carthage also had to be made up of purely Carthaginian citizens, I believe. Cos most of Carthage's army was usually mercenaries.