I'm interested in knowing what percentage of math phds actually succeed in landing a tenure track academic job?
Also, does a phd from AMS Group 1 guarantees you an academic job in top universities? If not what other factors come in to role to play?
No. No one single factor guarantees you an academic job in a top university. Whether or not you land such a job is a combination of many things. These include,
If you want such a job, here's what I recommend. Choose an area that you're passionate about, go to the best school (most challenging and "highest rated") that you can get into, and work with an adviser with a strong publication record. At each step along the way, surround yourself with (and learn as much as you can from) the most successful people possible.
You can find a partial answer to your question about percentage by reading the annual Survey of the Mathematical Sciences (by the American Math Society):
An additional parameter to consider is fashion: some research fields are deemed sexy and some aren't (and that assessment changes with time unpredictably!), and your chances of finding a position depend on the current perception of your field by the senior faculty.
I understood in the Netherlands somewhere around 5% ends up in a research position. This also includes people who after their PhD leave academia, so the percentage for those willing to continue is a bit higher. Ofcourse, as others already said, these general statistics do not say what your chances are, but it does illustrate that it is hard to find a position. In the Netherlands, it is important to get, apart from a good publication record, into a prestigious grants system (Venice, Vidi, Vici system). The first step is essentially a prestigious postdocs, the second leads to assistant professorship (fixed position), and the final one to full professorship. Getting into such a winning streak is important, successful projects make it easier to get new ones, I.e. the successful become more successful.
As I said in the comments: The success rate of the population will tell you little about YOUR chances of success. You are better off focusing on ways to improve YOUR chances.
To answer the second part of the question, most hiring committees at top universities for tenure track jobs primarily considered your publication record, your ability to secure funding, and your fit to the department. The fit to the department is tricky. It generally includes either research area or ability to teach a class, but may also include departmental politics. Sometimes an applicant can be such a poor communicator (often discovered during the interview) or be a known pain in the ass that this can influence the decision, but generally the decision is based on publications, money and fit. I would venture to say that more often than not the rankings do not chance based on the interviews/campus visits.