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

Author

Jianing Song, Jul 13 2021

Keywords

• nonn
• hard
• more

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

Examples

			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.
		

References

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

Links

• 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's automorphisms theorem

Crossrefs

Cf. A179982.

Extensions

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