  Let $R(z,q)$ be the two-variable generating function of Dyson's rank
function. In a recent joint work with Frank Garvan, we investigated the
transformation of the elements of the $p$-dissection of $R(\zeta_p,q)$, where
$\zeta_p$ is a primitive $p$-th root of unity, under special congruence
subgroups of $SL_2(\mathbb{Z})$, leading us to interesting symmetry
observations. In this work, we derive analogous transformation results for the
two-variable crank generating function $C(z,q)$ in terms of generalized eta
products. We consider the action of the group $\Gamma_0(p)$ on the elements of
the $p$-dissection of $C(z,q)$, leading us to new symmetries for the crank
function. As an application, we give a new proof of the crank theorem predicted
by Dyson in 1944 and resolved by Andrews and Garvan in 1988. Furthermore, we
present identities expressing the elements of the crank dissection in terms of
generalized eta products for primes $p=11,13,17$ and $19$.
