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%I #18 Dec 05 2024 21:49:13
%S 48,168,120,192,150,504,336,320,432,240,120,360,1092,504,720,1344,168,
%T 720,228,480,1008,192,216,720,750,624,1296,672,264,720,372,1536,1320,
%U 544,672,1728,444,912,936,960,410,1512,516,1320,2160,384,408
%N Maximum possible order of the automorphism group of a compact Riemann surface of genus n.
%C By Hurwitz's automorphisms theorem, a(n) <= 84*(n-1). The values n such that a(n) = 84*(n-1) are listed in A179982.
%C Breuer's book erroneously gives a(33) = 768. (See errata.) - _Eric M. Schmidt_, Jul 29 2021
%D Thomas Breuer, Characters and automorphism groups of compact Riemann surfaces, Cambridge University Press, 2000.
%H Thomas Breuer, <a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/genus/doc/errata.pdf">Errata et addenda for Characters and automorphism groups of Compact Riemann surfaces</a>.
%H Marston Conder, <a href="https://www.math.auckland.ac.nz/~conder/MaximumGroupOrdersByGenus-orientable.txt">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</a>.
%H Jen Paulhus, <a href="https://paulhus.math.grinnell.edu/monodromy.html">Branching data for curves up to genus 48</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hurwitz%27s_automorphisms_theorem">Hurwitz's automorphisms theorem</a>
%e 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.
%Y Cf. A179982.
%K nonn,hard,more
%O 2,1
%A _Jianing Song_, Jul 13 2021
%E a(12)-a(48) from _Eric M. Schmidt_, Jul 29 2021