20.113 (2022)

Let $H(q, c) = \langle a, b, c, d \mid [b, a] = [d, c]$, of exponent $q$, nilpotent of class $c \rangle$.
$\qquad$ a) Is it true that the Schur multiplier $M(H(8, 12))$ has exponent 32?
$\qquad$ b) Is it true that the Schur multiplier $M(H(7, 13))$ has exponent 49?
The difficulty is that these groups are too big to compute using current versions of the $p$-Quotient Algorithm, which use 32 bit arithmetic. So to tackle these groups it would help to have a version of the $p$-Quotient Algorithm using 64 bit arithmetic.