I am right in thinking, am I not, that a group of order 1722 can have only one Sylow 7-subgroup? Or have I missed something?
It's just that the next bit tells me to use a counting argument to show that if it has more than one then it can have only one Sylow 41-subgroup. It seems like the second question is supposed to be theoretical but I just wanted to make sure. :o(
Any comments welcome, although I don't expect I'm going to be snowed under with responses.