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As noted in the list of Sandrocottus species the first four species identified and named were
The given year identifies when the name was first applied, the species of course having been then identified as distinct, and the name is of the authority who made the identification and (usually) coined the name according to Binomial Nomenclature of Biological Classification.
It is quite common for the modern Binomial Names for species to be derived from Latin and/or Greek roots, and this was adhered to even more strictly in the early 19th century than it is now. It is almost certain that the Genus name Sandracottus was chosen to honour Chandragupta; was there a beetle motif associated with Chandragupta perhaps, that Illiger might have been aware of?