We had a student who didn't realise they had to put commas between elements in cycle notation, so wrote something like (12)(34567891011121314).
The last bracketed group was interpreted as a single element 34567891011121314, making the permutation group absolutely enormous. Since several of the routines involving running over every element in the group, the browser ground to a halt.
I think that throwing an error if a large element, maybe bigger than 1000, would be alright, in the absence of any clever code to deal with sparsely-defined elements.