  It is well-known that the value of the Frobenius-Schur indicator $|G|^{-1}
\sum_{g\in G} \chi(g^2)=\pm1$ of a real irreducible representation of a finite
group $G$ determines which of the two types of real representations it belongs
to, i.e. whether it is strictly real or quaternionic. We study the extension to
the case when a homomorphism $\varphi:G\to \mathbb{Z}/2\mathbb{Z}$ gives the
group algebra $\mathbb{C}[G]$ the structure of a superalgebra. Namely, we
construct of a super version of the Frobenius-Schur indicator whose value for a
real irreducible super representation is an eighth root of unity,
distinguishing which of the eight types of irreducible real super
representations described in [Wall1964] it belongs to. We also discuss its
significance in the context of two-dimensional finite-group gauge theories on
pin$^-$ surfaces.
