Computing characters of $\alpha$-projective representations Given a finite group $G$, a finite cyclic group $A$ (viewed as a subgroup of $\mathbb{C}^{\times}$, i.e. generated by a $|A|$-th root of unity), and a 2-cocycle $\alpha\in Z^{2}(G,A)$. Recall that an $\alpha$-projective representation of $G$ is a map $\rho:G\to GL(V)$ such that $\rho(g)\rho(h)=\alpha(g,h)\rho(gh)$ for all $g,h\in G$.

Question:
  Is it possible to use GAP (and HAP) to compute the characters of the irreducible $\alpha$-projective representations.

Initially I had thought to compute a central extension $1\to A\to C\to G\to 1$, examine the characters of the linear representations of $C$, and then infer the $\alpha$-projective characters of $G$, but I haven't had any luck.
There is some evidence to suggest that it is possible to do this in GAP, see for instance:
Projective characters with corresponding factor set
 A: Yes, the irreducible $\alpha$-projective representations may be obtained as you describe.
Given $\alpha \in Z^2(G,A)$, there is an associated central extension $1 \to A \to C \to G \to 1$ defined by $\alpha$. Irreducible $\alpha$-projective representations of $G$ lift to irreducible representations of $C$ by   definition of $C$. As $A$ is central, it acts on every irreducible representation of $C$ by scalars. Hence for $\chi$ an irreducible character, there exists $n \in \mathbb Z$ such that $\chi(a) = a^n\chi(1)$ for $a\in A$. Such $\chi$ is $\alpha^n$-projective by construction. The central extension $C$ only depends up to isomorphism on the cohomology class $[\alpha] \in H^2(G,A)$. Taking the least $m > 0$ such that $[\alpha^m]=1$ (which divides $|A|$), we obtain that $\chi$ is $\alpha$-projective if and only if there is $k \equiv 1 \mod m$ such that $\chi(a) = a^{k}\chi(1)$ for all $a \in A$.
I am not sure if you will still be interested 5 years later, but if you are, hopefully this helps.
