  We propose a definition of partition quantum spaces. They are given by
universal $C^*$-algebras whose relations come from partitions of sets. We ask
for the maximal compact matrix quantum group acting on them. We show how those
fit into the setting of easy quantum groups: Our approach yields spaces these
groups are acting on. In a way, our partition quantum spaces arise as the first
$d$ columns of easy quantum groups. However, we define them as universal
$C^*$-algebras rather than as $C^*$-subalgebras of easy quantum groups. We also
investigate the minimal number $d$ needed to recover an easy quantum group as
the quantum symmetry group of a partition quantum space. In the free unitary
case, $d$ takes the values one or two.
