Is it permissible for a wife to secretly attend Quran memorization classes, even though her husband allows her to go out for other errands but dislikes her attending these particular classes?

Your husband is in great danger due to this act, and your duty is to advise him, instill in him the fear of Allah, and remind him of the Hereafter, using every effective means. As for your going out, it is not permissible except with his permission, unless he falls short in teaching you your religion, in which case you may go out to learn it.