  Asteroseismology of solar-like oscillations in giant stars allow the
derivation of their masses and radii. For members of open clusters this allows
an age estimate of the cluster which should be identical to the age estimate
from the colour-magnitude diagram, but independent of the uncertainties that
are present for that type of analysis. Thus, a more precise and accurate age
estimate can be obtained. We aim to measure asteroseismic properties of
oscillating giant members of the open cluster NGC 6866 and utilise these for a
cluster age estimate. Model comparisons allow constraints on the stellar
physics, and here we investigate the efficiency of convective-core overshoot
and effects of rotation during the main-sequence, which has a significant
influence on the age for these relatively massive giants. We identify six giant
members of NGC 6866 and derive asteroseismic measurements for five of them.
This constrains the convective-core overshoot and enables a more precise and
accurate age estimate than previously possible. Asteroseismology establishes
the helium-core burning evolutionary phase for the giants, which have a mean
mass of 2.8 $M_{\odot}$. Their radii are significantly smaller than predicted
by current 1D stellar models unless the amount of convective-core overshoot on
the main sequence is reduced to $\alpha_{ov} \leq 0.1 H_p$ in the
step-overshoot description. Our measurements also suggest that rotation has
affected the evolution of the stars in NGC 6866 in a way that is consistent
with 3D simulations but not with current 1D stellar models. The cluster age is
estimated to be 0.43 $\pm$ 0.05 Gyr, significantly younger and more precise
than most previous estimates. We derive a precise cluster age while
constraining convective-core overshooting and effects of rotation in the
models. We uncover potential biases for automated age estimates of helium-core
burning stars.
