  Let $A_1$ be any spectrum in a class of finite spectra whose mod $2$
cohomology is isomorphic to a free module of rank one over the subalgebra
$\mathcal{A}(1)$ of the Steenrod algebra. Let $E_{C}$ be the second Morava-$E$
theory associated to a universal deformation of the formal completion of the
supersingular elliptic curve $(C) : y^{2}+y = x^{3}$ defined over
$\mathbb{F}_{4}$ and $G_{24}$ a maximal finite subgroup of automorphism group
$\mathbb{S}_{C}$ of the formal completion of $C$. In this paper, we compute the
homotopy groups of $E_{C}^{hG_{24}}\wedge A_1$ by means of the homotopy fixed
point spectral sequence.
