A346293 Maximum possible order of the automorphism group of a compact Riemann surface of genus n.

48, 168, 120, 192, 150, 504, 336, 320, 432, 240, 120, 360, 1092, 504, 720, 1344, 168, 720, 228, 480, 1008, 192, 216, 720, 750, 624, 1296, 672, 264, 720, 372, 1536, 1320, 544, 672, 1728, 444, 912, 936, 960, 410, 1512, 516, 1320, 2160, 384, 408

Offset

2,1

Comments

By Hurwitz's automorphisms theorem, a(n) <= 84*(n-1). The values n such that a(n) = 84*(n-1) are listed in A179982.

Breuer's book erroneously gives a(33) = 768. (See errata.) - Eric M. Schmidt, Jul 29 2021

References

Thomas Breuer, Characters and automorphism groups of compact Riemann surfaces, Cambridge University Press, 2000.

Links

Table of n, a(n) for n=2..48.

Thomas Breuer, Errata et addenda for Characters and automorphism groups of Compact Riemann surfaces.

Marston Conder, Two lists of the largest orders of a group of automorphisms of a compact Riemann surface of given genus g, for g between 2 and 301.

Jen Paulhus, Branching data for curves up to genus 48.

Wikipedia, Hurwitz Group

Wikipedia, Hurwitz's automorphisms theorem

Example

The Bolza surface is a compact Riemann surface of genus 2 whose automorphism group is of the highest possible order (order 48, isomorphic to GL(2,3)), so a(2) = 48.

Crossrefs

Cf. A179982.

Sequence in context: A044761 A248456 A370126 * A244178 A131683 A066134

Adjacent sequences: A346290 A346291 A346292 * A346294 A346295 A346296

Keyword

nonn,hard,more

Author

Jianing Song, Jul 13 2021

Extensions

a(12)-a(48) from Eric M. Schmidt, Jul 29 2021

Status

approved