At first glance, this denarius looks exactly like the last Domitian (RIC 3) that I posted a couple of days ago. There is one significant difference. Take a look at the reverse on this coin below, and the reverse on RIC 3 that I referred to above. On the in the photo below you will see the same triangular frame as RIC 3, but below the frame you will see a strange shape. It is a Lituus, a device like a crooked wand, used in augury.
As is true with RIC 3, this coin was issued very early in Domitian's reign as Augustus. As such, the portrait on this coin has the same interesting nose as RIC 3. As for cataloguing, this variation does not appear in the major references. I think it makes sense to therefore call it RIC 3 Var (Variant).
Note also that this type of reverse was also issued for Domitian's brother Titus. On the Titus denarii the variants with and without Lituus also exist.
Domitian. AR denarius
(16.88 mm 3.02 g,). Rome mint, struck A.D. 81.
Obv: IMP CAESAR DOMITIANVS AVG, laureate head right
Rev: TR P COS VII, draped throne, back decorated with grain ears Lituus beneath
RIC 3 Var;; RSC 554a.
Ex: Akropolis Ancient Coins