Green’s Dictionary of Slang

Botany Bay dozen n.

(Aus. Und.) a punishment of 25 lashes.

G. Thompson Slavery and Famine 9: If guilty, he is taken to a cartwheel to receive a Botany Bay dozen, which is twenty-five lashes.
[Aus]Bulletin (Sydney) 23 Aug. 24/2: Darrel [...] ordered Johnson ‘10 hours of the tube-gag’ on the morrow, and Gooch to receive a ‘dozen’ lashes [...]. By a ‘dozen’ was, of course, meant the ‘Botany Bay dozen,’ which was neither the arithmetical dozen nor the baker’s dozen, but a simple ‘twenty-five.’.