3. Let $\left\{a_{n}\right\}$ be an arithmetic sequence with the sum of the first $n$ terms denoted as $S_{n}$. If $S_{6}=26, a_{7}=2$, then the maximum value of $n S_{n}$ is $\qquad$

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3. 338 .
$$
\begin{array}{l}
\text { Given } S_{6}=26, a_{7}=2 \\
\Rightarrow a_{1}=6, d=-\frac{2}{3} \\
\Rightarrow S_{n}=-\frac{1}{3} n^{2}+\frac{19}{3} n \\
\Rightarrow n S_{n}=-\frac{1}{3} n^{3}+\frac{19}{3} n^{2} . \\
\text { Let } f(x)=-\frac{1}{3} x^{3}+\frac{19}{3} x^{2}(x \in \mathbf{R}) .
\end{array}
$$

Then $f^{\prime}(x)=-x^{2}+\frac{38}{3} x$.
By $f^{\prime}(x)=0 \Rightarrow x=0$ or $\frac{38}{3}$.
Thus, $f(n)\left(n \in \mathbf{Z}_{+}\right)$ is increasing in the interval $[1,12]$ and decreasing in the interval $[13,+\infty)$.
Notice that, $f(12)=336, f(13)=338$. Therefore, the maximum value is 338.