Curiosities above c = 24

Two-dimensional rational CFT are characterised by an integer $\mathrm{\ell }$, related to the number of zeroes of the Wronskian of the characters. For two-character RCFT’s with $\mathrm{\ell }<6$ there is a finite number of theories and most of these are classified. Recently it has been shown that for $\mathrm{\ell }\ge 6$ there are infinitely many admissible characters that could potentially describe CFT’s. In this note we examine the $\mathrm{\ell }=6$ case, whose central charges lie between 24 and 32, and propose a classification method based on cosets of meromorphic CFT’s. We illustrate the method using theories on Kervaire lattices with complete root systems. In the process we construct the first known two-character RCFT’s beyond $\mathrm{\ell }=2$.