  We show that $G$-Fano threefolds are mirror-modular.
  1. Mirror maps are inversed reversed Hauptmoduln for moonshine subgroups of
$SL_2(\mathbb{R})$.
  2. Quantum periods, shifted by an integer constant (eigenvalue of quantum
operator on primitive cohomology) are expansions of weight 2 modular forms
(theta-functions) in terms of inversed Hauptmoduln.
  3. Products of inversed Hauptmoduln with some fractional powers of shifted
quantum periods are very nice cuspforms (eta-quotients).
  The latter cuspforms also appear in work of Mason and others: they are
eta-products, related to conjugacy classes of sporadic simple groups, such as
Mathieu group $M_{24}$ and Conway's group of isometries of Leech lattice.
  This gives a strange correspondence between deformation classes of $G$-Fano
threefolds and conjugacy classes of Mathieu group $M_{24}$.
