  It is known that the group non-membership problem is in QMA relative to any
group oracle and in ${\rm SPP}\cap{\rm BQP}$ relative to group oracles for
solvable groups. We consider a modified version of the group non-membership
problem where the order of the group is also given as an additional input. We
show that the problem is in AWPP relative to any group oracle. To show the
result, we use the idea of the postselected quantum computing.
