The independent permissions (surely by group) which offer more access takes precedence in each independent case. - the group just groups the permissions and has no hierarchy.
What matters is if you have permission not if you don't have permission. So all you need is permission from one group regardless of what the other groups say.
To put it in an example, if I have permission to add a file but not a folder from Group A but in group B I have permission to add a folder but not a file, then I have permission to add both files and folders. The permissions combine and not subtract.
I hope that helps.
If you were to lay the permissions of each group (as a layer per group) over top of each other, that's what your user would have as permissions. As indicated in previous answers, group permissions are inclusive or each, not exclusive.