= Solution
Under the intended convention that the finite group is nontrivial, take \b[$\mathbb{CP}^2$]. It is <simply connected> by its <CW complex> structure. The <Lefschetz fixed-point theorem> says that a continuous self-map of a compact triangulable space with nonzero rational <Lefschetz number> has a fixed point.
For any continuous $f:\mathbb{CP}^2\to\mathbb{CP}^2$, write $f^*x=dx$ for the integral degree-two generator, with $d\in\mathbb Z$. Preservation of the <cup product> gives $f^*(x^2)=d^2x^2$. Only degrees zero, two and four contribute to the rational <Lefschetz number>, so
$$
L(f)=1+d+d^2=\left(d+\frac12\right)^2+\frac34>0.
$$
Consequently every such map has a fixed point. In a <free group action>, each nonidentity group element must act by a fixed-point-free homeomorphism. This is impossible here, so no nontrivial <finite group> can act freely. This is the <fixed-point property of even-dimensional complex projective space> for complex dimension two. \b[If the trivial group is included, the literal request has no example], since the trivial group acts freely on every space.
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