  We present the extended Kuranishi space for Kodaira surface as a non-trivial
example to Kontsevich and Barannikov's extended deformation theory. We provide
a non-trivial example of Hertling-Manin's weak Frobenius manifold. In addition,
we find that Kodaira surface is its own mirror image. Our computation is done
in the context of compact nilmanifolds. The calculation of extended deformation
and the weak Frobenius structure is based on Merkulov's perturbation method.
The approach to relating symplectic structure and complex structure is inspired
by Gualtieri's work on generalized complex structures.
