Maximal automorphism groups of symmetric Riemann surfaces with small genus (Q1100560)

The genus of the finite group G, of order \(| G|\), is the smallest genus g(G) of a surface into which some Cayley graph of G can be embedded. \textit{T. W. Tucker} [Trans. Am. Math. Soc. 258, 167-179 (1980; Zbl 0444.05039)] showed that \(| G| \leq 168(g(G)-1)\) and that the inequality is strict unless G is isomorphic to a quotient of the (2,3,7) group. It is also required that the element of order two and the one of order three generate a proper subgroup of G. In this case G embeds in the homeomorphism group of a Riemann surface of genus g(G). The author computes all such groups, having minimal genus, of order less than 2 million.