  Hyperstructures are a natural extension of regular algebraic structures in
which one of the operations, known as the hyperoperation, is multivalued; a
hyperfield is such an extension on a field. M. Krasner (1962) proved that the
quotient $\mathbb{F}_p/G$, where $G$ is a subgroup of units in $\mathbb{F}_p$
is a hyperfield. The characteristic of a field may be explicitly determined
from the order of the field, but there are no existing generalizations for
determining the characteristic of a hyperfield of the form $\mathbb{F}_p/G$. We
show that for odd primes $p$, there exists an explicit form for the
characteristic of the hyperfield $\mathbb{F}_p/G$ and $|G|=1,2,3,4$. Finally,
we prove a general form of the characteristic for hyperfields where $|G|$ is
prime.
