Teaser 2802: That’s the ticket!

From The Sunday Times, 5th June 2016 [link]

Alan, Betty and Charlie each chose a different set of six numbers (from 1 to 49) for their lottery ticket. In each case the product of the six numbers was a perfect square and also each set of six numbers used each of the digits 0 to 9 exactly once.

Alan won the lottery by getting all six numbers correct. Betty and Charlie also got prizes because they each had at least three numbers correct.

What were Alan’s six numbers?