Central-extension conjecture for rational quotients of finite solvable groups

Let $G$ be a finite solvable group. Central-extension rationality conjecture. There exists a central extension

$$1\longrightarrow Z\longrightarrow G^c\longrightarrow G\longrightarrow 1$$

with a faithful representation $V$ of $G^c$ such that $V/G^c$ is rational. This would reduce rationality questions for quotients by finite solvable groups to suitable central extensions; the supplied text gives no resolution.