Census of actions of finite groups on Riemann surfaces of genus 2 Exported on: Mon Aug 14 14:16:40 2023 Created on: Wed Jul 19 08:22:17 CEST 2023 Creator: rhsolver(Magma), ver: 7.1 (20230719.c) (c) 2023 Jan Karabas, Matej Bel University. The catalogue may be used only if you refer to the original source. BibTeX entry: ---------------------------------------------------------------------------------------- @misc{jk23-1, author = {Karab\'a\v s, J\'an}, title = {Actions of finite groups on {R}iemann surfaces of higher genera}, year = {2023}, howpublished = {\url{https://www.savbb.sk/~karabas/science/discactions.html}} } ---------------------------------------------------------------------------------------- See also https://www.savbb.sk/~karabas/science/discactions.html for more information. ======================================================================================== ---------------------------------------------------------------------------------------- Code Signature SMG-ID epi autg ~top ---------------------------------------------------------------------------------------- O2.1 (2; -) <1, 1> 1 1 1 : 1 O2.2 (1; 2, 2) <2, 1> 4 4 1 : C2 O2.3 (0; 2^6) <2, 1> 1 1 1 : C2 O2.4 (0; 3, 3, 3, 3) <3, 1> 6 3 1 : C3 O2.5 (0; 2^5) <4, 2> 60 10 1 : C2 x C2 O2.6 (0; 2, 2, 4, 4) <4, 1> 2 1 1 : C4 O2.7 (0; 5, 5, 5) <5, 1> 12 3 1 : C5 O2.8 (0; 2, 2, 3, 3) <6, 1> 12 2 1 : S3 O2.9 (0; 2, 2, 3, 3) <6, 2> 2 1 1 : C6 O2.10 (0; 3, 6, 6) <6, 2> 2 1 1 : C6 O2.11 (0; 2, 2, 2, 4) <8, 3> 24 3 1 : D8 O2.12 (0; 4, 4, 4) <8, 4> 24 1 1 : Q8 O2.13 (0; 2, 8, 8) <8, 1> 4 1 1 : C8 O2.14 (0; 2, 5, 10) <10, 2> 4 1 1 : C10 O2.15 (0; 2, 2, 2, 3) <12, 4> 36 3 1 : D12 O2.16 (0; 3, 4, 4) <12, 1> 12 1 1 : C3 : C4 O2.17 (0; 2, 6, 6) <12, 5> 12 1 1 : C6 x C2 O2.18 (0; 2, 4, 8) <16, 8> 16 1 1 : QD16 O2.19 (0; 3, 3, 4) <24, 3> 24 1 1 : SL(2,3) O2.20 (0; 2, 4, 6) <24, 8> 24 1 1 : (C6 x C2) : C2 O2.21 (0; 2, 3, 8) <48, 29> 48 1 1 : GL(2,3)