Green’s Dictionary of Slang

(Aus.) the vent in the back of a coat, seen as a badge of ostentation; thus a tail-coat, which had such a vent and was seen as ‘upper-class’ .

1912		Sport (Adelaide) 24 Aug. 14/1: They Say [...] That Din, with his new ‘Sac and Bonnet,’ with a nobby up the back, [...] is cutting flash.
[1913		Sport (Adelaide) 8 Mar. 12/3: They Say [...] That Jack P won’t talk to the Mob now because he wears a split up the back].
1913		Sport (Adelaide) 15 Feb. 11/1: They Say [...] That J.P. is very cut up about the beauty show; cut up the extent of a 12 inch nobby in the back of his Sunday coat.
1913		Sport (Adelaide) 14 June 7/2: Dew D was re-admitted as a member, providing he leaves off his corsets, flash socks, little bow and sews up his nobby .
1913		Sport (Adelaide) 19 July 9/3: They Say [...] That Bill P., the boy who reckons he would not wear a nobby has come to light with three nobbies and a pug’s hat. Give over, Bill, the boys will be chasing you.