A binary matrix is a matrix consisting entirely of $0$s and $1$s. Consider the following transformations that can be performed on a binary matrix:

• Swap any two rows
• Swap any two columns
• Flip all elements in a single row ($1$s become $0$s, $0$s become $1$s)
• Flip all elements in a single column

Two binary matrices $A$ and $B$ will be considered equivalent if there is a sequence of such transformations that when applied to $A$ yields $B$. For example, the following two matrices are equivalent:

$A=\left(\begin{array}{ccc}1& 0& 1\\ 0& 0& 1\\ 0& 0& 0\end{array}\right)B=\left(\begin{array}{ccc}0& 0& 0\\ 1& 0& 0\\ 0& 0& 1\end{array}\right)$

via the sequence of two transformations "Flip all elements in column 3" followed by "Swap rows 1 and 2".

Define $c(n)$ to be the maximum number of $n\times n$ binary matrices that can be found such that no two are equivalent. For example, $c(3)=3$. You are also given that $c(5)=39$ and $c(8)=656108$.

Find $c(20)$, and give your answer modulo $1001001011$.