Currently the database contains all groups G acting as automorphisms of curves X from genus 2 up to genus 15 so that the quotient space X/G is the Riemann sphere (X/G has genus 0). There are 31768 distinct refined passports in the database. The number of distinct generating vectors is 334866.

Distribution by genus

Genus 2 3 4 5 6 7 8 9 10 11
distinct families 19 40 54 70 74 103 88 194 174 163
distinct refined passports 37 176 215 627 409 969 436 3461 2039 2079
distinct generating vectors 38 191 289 792 901 2219 2080 6186 14422 14605
unique groups 18 35 43 61 58 80 62 148 116 110
maximum group order 48 168 120 192 150 504 336 320 432 240
Genus 12 13 14 15
distinct families 160 302 176 280
distinct refined passports 1506 11728 1421 6665
distinct generating vectors 17507 58043 43480 174113
unique groups 95 196 95 167
maximum group order 120 360 1092 504

Distribution by dimension

Dimension 0 1 2 3 4 5 6 7 8 9
distinct generating vectors 5985 9178 15854 45314 19202 74969 34397 8661 13427 48538
Dimension 10 11 12 13 14 15 16 17 18 19
distinct generating vectors 59092 51 42 52 44 53 0 1 0 1
Dimension 20 21 22 23 24 25 26 27 28 29
distinct generating vectors 0 1 0 1 0 1 0 1 0 1