The fingerprint of a complex Hadamard matrix $H$ of order $N$ is the following ordered set [126], [37] $$\Phi(H) = \Big\{\big\{\left(v_i(d), m_i(d)\right) : i\in I(d)\big\}_d : d\in\{2,..., \lfloor n/2 \rfloor\}\Big\}$$ where $I(d)$ is an index set for every $2\leqslant d\leqslant \lfloor n/2\rfloor$, and $v_i(d)$ and $m_i(d)$ are the possible values of the moduli of the $d\times d$ minors and their multiplicities, respectively.
For example $\Phi($$F_2\otimes F_2 \otimes F_2$$)=$ $$ =\Big\{\big\{(0,336),(2,448)\big\}_2,\big\{(0,1344),(4,1792)\big\}_3, \big\{(0,1428),(8,3136),(16,336)\big\}_4 \Big\}. $$
See also Haagerup-set and rectangular rank profile.