Census of actions of finite groups on Riemann surfaces of genus 4 Exported on: Mon Aug 14 14:29:11 2023 Created on: Wed Jul 19 08:23:32 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 ---------------------------------------------------------------------------------------- O4.1 (4; -) <1, 1> 1 1 1 : 1 O4.2 (2; 2, 2) <2, 1> 16 16 1 : C2 O4.3 (1; 2^6) <2, 1> 4 4 1 : C2 O4.4 (0; 2^10) <2, 1> 1 1 1 : C2 O4.5 (2; -) <3, 1> 80 40 1 : C3 O4.6 (1; 3, 3, 3) <3, 1> 18 9 1 : C3 O4.7 (0; 3^6) <3, 1> 22 11 2 : C3 O4.8 (1; 2, 2, 2) <4, 2> 96 16 1 : C2 x C2 O4.9 (1; 4, 4) <4, 1> 32 16 1 : C4 O4.10 (0; 2^7) <4, 2> 546 91 2 : C2 x C2 O4.11 (0; 2^4, 4^2) <4, 1> 2 1 1 : C4 O4.12 (0; 2, 4^4) <4, 1> 8 4 1 : C4 O4.13 (0; 5, 5, 5, 5) <5, 1> 52 13 3 : C5 O4.14 (1; 2, 2) <6, 1> 96 16 1 : S3 O4.15 (1; 2, 2) <6, 2> 32 16 1 : C6 O4.16 (0; 2^6) <6, 1> 240 40 1 : S3 O4.17 (0; 2^2, 3^3) <6, 1> 24 4 1 : S3 O4.18 (0; 2^2, 3^3) <6, 2> 2 1 1 : C6 O4.19 (0; 2^3, 3, 6) <6, 2> 2 1 1 : C6 O4.20 (0; 3, 3, 6, 6) <6, 2> 6 3 2 : C6 O4.21 (0; 2, 6, 6, 6) <6, 2> 2 1 1 : C6 O4.22 (0; 2^4, 4) <8, 3> 176 22 2 : D8 O4.23 (0; 2, 4, 4, 4) <8, 4> 24 1 1 : Q8 O4.24 (0; 2, 2, 8, 8) <8, 1> 4 1 1 : C8 O4.25 (0; 3, 3, 3, 3) <9, 2> 432 9 2 : C3 x C3 O4.26 (0; 9, 9, 9) <9, 1> 18 3 1 : C9 O4.27 (0; 2, 2, 5, 5) <10, 1> 80 4 2 : D10 O4.28 (0; 2, 2, 5, 5) <10, 2> 4 1 1 : C10 O4.29 (0; 5, 10, 10) <10, 2> 12 3 2 : C10 O4.30 (1; 2) <12, 3> 96 4 1 : A4 O4.31 (0; 2^5) <12, 4> 960 80 1 : D12 O4.32 (0; 2, 3, 3, 3) <12, 3> 96 4 1 : A4 O4.33 (0; 2, 2, 3, 6) <12, 4> 24 2 1 : D12 O4.34 (0; 2, 2, 3, 6) <12, 5> 12 1 1 : C6 x C2 O4.35 (0; 6, 6, 6) <12, 5> 12 1 1 : C6 x C2 O4.36 (0; 4, 6, 12) <12, 2> 4 1 1 : C12 O4.37 (0; 3, 12, 12) <12, 2> 4 1 1 : C12 O4.38 (0; 3, 5, 15) <15, 1> 8 1 1 : C15 O4.39 (0; 2, 2, 2, 8) <16, 7> 96 3 1 : D16 O4.40 (0; 4, 4, 8) <16, 9> 32 1 1 : Q16 O4.41 (0; 2, 16, 16) <16, 1> 8 1 1 : C16 O4.42 (0; 2, 2, 3, 3) <18, 3> 48 4 2 : C3 x S3 O4.43 (0; 2, 2, 3, 3) <18, 4> 432 1 1 : (C3 x C3) : C2 O4.44 (0; 3, 6, 6) <18, 3> 24 2 2 : C3 x S3 O4.45 (0; 3, 6, 6) <18, 5> 48 1 1 : C6 x C3 O4.46 (0; 2, 9, 18) <18, 2> 6 1 1 : C18 O4.47 (0; 2, 2, 2, 5) <20, 4> 120 3 1 : D20 O4.48 (0; 4, 4, 5) <20, 1> 40 1 1 : C5 : C4 O4.49 (0; 4, 4, 5) <20, 3> 40 2 1 : C5 : C4 O4.50 (0; 2, 10, 10) <20, 5> 24 1 1 : C10 x C2 O4.51 (0; 2, 2, 2, 4) <24, 12> 96 4 1 : S4 O4.52 (0; 3, 4, 6) <24, 3> 24 1 1 : SL(2,3) O4.53 (0; 2, 6, 12) <24, 10> 16 1 1 : C3 x D8 O4.54 (0; 2, 4, 16) <32, 19> 64 1 1 : QD32 O4.55 (0; 2, 2, 2, 3) <36, 10> 216 3 1 : S3 x S3 O4.56 (0; 3, 4, 4) <36, 9> 144 1 1 : (C3 x C3) : C4 O4.57 (0; 3, 3, 6) <36, 11> 144 1 1 : C3 x A4 O4.58 (0; 2, 6, 6) <36, 10> 72 1 1 : S3 x S3 O4.59 (0; 2, 6, 6) <36, 12> 48 2 1 : C6 x S3 O4.60 (0; 2, 4, 10) <40, 8> 80 1 1 : (C10 x C2) : C2 O4.61 (0; 2, 5, 5) <60, 5> 120 1 1 : A5 O4.62 (0; 2, 4, 6) <72, 40> 144 1 1 : (S3 x S3) : C2 O4.63 (0; 2, 3, 12) <72, 42> 48 1 1 : C3 x S4 O4.64 (0; 2, 4, 5) <120, 34> 120 1 1 : S5