  We analyze aspects of extant examples of 2d extremal chiral (super)conformal
field theories with $c\leq 24$. These are theories whose only operators with
dimension smaller or equal to $c/24$ are the vacuum and its (super)Virasoro
descendents. The prototypical example is the monster CFT, whose famous genus
zero property is intimately tied to the Rademacher summability of its twined
partition functions, a property which also distinguishes the functions of
Mathieu and umbral moonshine. However, there are now several additional known
examples of extremal CFTs, all of which have at least $\mathcal N=1$
supersymmetry and global symmetry groups connected to sporadic simple groups.
We investigate the extent to which such a property, which distinguishes the
monster moonshine module from other $c=24$ chiral CFTs, holds for the other
known extremal theories. We find that in most cases, the special Rademacher
summability property present for monstrous and umbral moonshine does not hold
for the other extremal CFTs, with the exception of the Conway module and two
$c=12, ~\mathcal N=4$ superconformal theories with $M_{11}$ and $M_{22}$
symmetry. This suggests that the connection between extremal CFT, sporadic
groups, and mock modular forms transcends strict Rademacher summability
criteria.
