The calculation of the number of groups of order
$$2^2\cdot 3^2\cdot 5^2\cdot 7^2\cdot 11^2$$
(result $81883$) takes already two hours with GAP. So, the calculation of the number of groups of order
$$2^2\cdot 3^2\cdot 5^2\cdot 7^2\cdot 11^2\cdot 13^2$$
probably is already very time-consuming.
Any ideas how I can get the number more efficiently ?