  We provide full characterisation of the Schatten properties of $[M_b,T]$, the
commutator of Calder\'{o}n--Zygmund singular integral $T$ with symbol $b$
$(M_bf(x):=b(x)f(x))$ on stratified Lie groups $\mathbb{G}$. We show that, when
$p$ is larger than the homogeneous dimension $\mathbb{Q}$ of $\mathbb{G}$, the
Schatten $\mathcal{L}_p$ norm of the commutator is equivalent to the Besov
semi-norm $B_{p}^{\frac{\mathbb{Q}}{p}}$ of the function $b$; but when $p\leq
\mathbb{Q}$, the commutator belongs to $\mathcal{L}_p$ if and only if $b$ is a
constant. For the endpoint case at the critical index $p=\mathbb{Q}$, we
further show that the Schatten $\mathcal{L}_{\mathbb{Q},\infty}$ norm of the
commutator is equivalent to the Sobolev norm $W^{1,\mathbb{Q}}$ of $b$. Our
method at the endpoint case differs from existing methods of Fourier transforms
or trace formula for Euclidean spaces or Heisenberg groups, respectively, and
hence can be applied to various settings beyond.
