Weird base on the ctg. plus no shoulder, just straight taper.
I would measure the bore diameter as well.
The early 1871 Mausers, up to and including 1876 version, have a groove diameter of .457/8 and a bore of .437".
The chamber would not allow a bullet larger than .446" dia. being seated in the case. The deep grooves
were originally thought needed for collecting fouling - or, the original paper patched bullets were thought
to expand to fit the oversized grooves. This worked, however in the 1884 model 71, the groove diameter was reduced to .446".

The .490" neck would admit a .458" bullet and having 15" neck wall with 1/2 thou each side for expansion - or just use a .4595" bullet
for a press fit in a fired case.

AHH - just noticed - 3 1/4" case length - cool!
A .45 3 1/4" case should work, with or without a brass ring/collar in front of the rim to take up the extra slop.

The rate of twist will dictate what bullet weight is usable or required.
The 11mm Mauser carbine I had, had a 20" twist, seems to me, however all the ammo was loaded with a 370gr. bullet.