Let \(N=\langle z\rangle\) be a cyclic group of order 2 , and \(H\) be the non-
cyclic group of order 4 with elements \(\\{1, a, b, c\\}\). Given that the
factor set
\begin{tabular}{c|cccc}
\(f\) & 1 & \(a\) & \(b\) & \(a b\) \\
\hline 1 & 1 & 1 & 1 & 1 \\
\(a\) & 1 & 1 & \(z\) & \(z\) \\
\(b\) & 1 & 1 & \(z\) & \(z\) \\
\(a b\) & 1 & 1 & 1 & 1
\end{tabular}
is a central factor set, construct the central extension \(G\). Is \(G\)
isomorphic to \(D(4)\) ?
