Currently the database contains all groups $G$ acting as automorphisms of curves $X/\C$ of genus 2 to 15 such that $X/G$ has genus 0, as well as genus 2 through 4 with quotient genus greater than 0. There are 31768 distinct refined passports in the database. The number of distinct generating vectors is 334866. Here are some further statistics.
Browse automorphisms of higher genus curves
A random refined passport from the database.