Double ramification cycles on the moduli spaces of admissible covers

We derive a formula for the virtual class of the moduli space of rubber maps to $[\mathbb{P}^1/G]$ pushed forward to the moduli space of stable maps to $BG$. As an application, we show that the Gromov-Witten theory of $[\mathbb{P}^1/G]$ relative to $0$ and $\infty$ are determined by known calculations.