What is the group for the following presentation?

Question

This group has four generators $a, b, c$ and $d$. Generators satisfy the following relations:

1. $a$ commutes with $b$ and $c$ commutes with $d$.
2. $a^2=b^2=1$ and $c^{m_1}=d^{m_2}=1$ for some integers $m_1,m_2\geq3$.
3. $(ac)^{n_1}=(ad)^{n_2}=(bc)^{n_3}=(bd)^{n_4}=1$. Here $n_i\geq3$.