Census of actions of finite groups on Riemann surfaces of genus 6 Exported on: Mon Aug 14 14:30:51 2023 Created on: Wed Jul 19 08:39:52 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 ---------------------------------------------------------------------------------------- O6.1 (6; -) <1, 1> 1 1 1 : 1 O6.2 (3; 2, 2) <2, 1> 64 64 1 : C2 O6.3 (2; 2^6) <2, 1> 16 16 1 : C2 O6.4 (1; 2^10) <2, 1> 4 4 1 : C2 O6.5 (0; 2^14) <2, 1> 1 1 1 : C2 O6.6 (2; 3, 3) <3, 1> 162 81 1 : C3 O6.7 (1; 3^5) <3, 1> 90 45 1 : C3 O6.8 (0; 3^8) <3, 1> 86 43 2 : C3 O6.9 (1; 2^5) <4, 2> 960 160 1 : C2 x C2 O6.10 (1; 2, 2, 4, 4) <4, 1> 32 16 1 : C4 O6.11 (0; 2^9) <4, 2> 4920 820 3 : C2 x C2 O6.12 (0; 2^6, 4^2) <4, 1> 2 1 1 : C4 O6.13 (0; 2^3, 4^4) <4, 1> 8 4 1 : C4 O6.14 (0; 4^6) <4, 1> 32 16 2 : C4 O6.15 (2; -) <5, 1> 624 156 1 : C5 O6.16 (0; 5^5) <5, 1> 204 51 3 : C5 O6.17 (1; 2, 2, 3) <6, 1> 216 36 1 : S3 O6.18 (1; 6, 6) <6, 2> 72 36 1 : C6 O6.19 (0; 2^6, 3) <6, 1> 486 81 1 : S3 O6.20 (0; 2^2, 3^4) <6, 1> 48 8 1 : S3 O6.21 (0; 2^2, 3^4) <6, 2> 6 3 1 : C6 O6.22 (0; 2^3, 3^2, 6) <6, 2> 2 1 1 : C6 O6.23 (0; 2^4, 6^2) <6, 2> 2 1 1 : C6 O6.24 (0; 3^3, 6^2) <6, 2> 10 5 2 : C6 O6.25 (0; 2, 3, 6^3) <6, 2> 6 3 1 : C6 O6.26 (0; 7, 7, 7, 7) <7, 1> 186 31 4 : C7 O6.27 (0; 2^5, 4) <8, 3> 720 90 2 : D8 O6.28 (0; 2^2, 4^3) <8, 3> 32 4 1 : D8 O6.29 (0; 2^2, 4^3) <8, 4> 24 1 1 : Q8 O6.30 (0; 2^3, 8^2) <8, 1> 4 1 1 : C8 O6.31 (0; 4, 4, 8, 8) <8, 1> 16 4 2 : C8 O6.32 (0; 3, 3, 9, 9) <9, 1> 24 4 2 : C9 O6.33 (1; 2, 2) <10, 1> 480 24 1 : D10 O6.34 (1; 2, 2) <10, 2> 96 24 1 : C10 O6.35 (0; 2^6) <10, 1> 3120 156 1 : D10 O6.36 (0; 2, 5, 5, 10) <10, 2> 12 3 2 : C10 O6.37 (0; 2^3, 3^2) <12, 3> 216 9 1 : A4 O6.38 (0; 2^3, 3^2) <12, 4> 72 6 1 : D12 O6.39 (0; 2^3, 3^2) <12, 5> 12 1 1 : C6 x C2 O6.40 (0; 3, 3, 4, 4) <12, 1> 24 2 1 : C3 : C4 O6.41 (0; 3, 3, 4, 4) <12, 2> 4 1 1 : C12 O6.42 (0; 2^4, 6) <12, 4> 504 42 2 : D12 O6.43 (0; 2, 4, 4, 6) <12, 1> 12 1 1 : C3 : C4 O6.44 (0; 2, 3, 6, 6) <12, 5> 12 1 1 : C6 x C2 O6.45 (0; 2, 3, 4, 12) <12, 2> 4 1 1 : C12 O6.46 (0; 2, 2, 12, 12) <12, 2> 4 1 1 : C12 O6.47 (0; 13, 13, 13) <13, 1> 132 11 3 : C13 O6.48 (0; 2, 2, 7, 7) <14, 1> 252 6 2 : D14 O6.49 (0; 2, 2, 7, 7) <14, 2> 6 1 1 : C14 O6.50 (0; 7, 14, 14) <14, 2> 30 5 3 : C14 O6.51 (0; 5, 15, 15) <15, 1> 24 3 2 : C15 O6.52 (0; 2, 2, 4, 8) <16, 7> 64 2 1 : D16 O6.53 (0; 2, 2, 4, 8) <16, 8> 32 2 1 : QD16 O6.54 (0; 4, 16, 16) <16, 1> 16 2 1 : C16 O6.55 (0; 2, 2, 3, 9) <18, 1> 108 2 1 : D18 O6.56 (0; 3, 18, 18) <18, 2> 12 2 1 : C18 O6.57 (0; 2^5) <20, 4> 4800 120 1 : D20 O6.58 (0; 2, 2, 4, 4) <20, 3> 240 12 1 : C5 : C4 O6.59 (0; 4, 5, 20) <20, 2> 8 1 1 : C20 O6.60 (0; 3, 7, 21) <21, 2> 12 1 1 : C21 O6.61 (0; 2, 2, 3, 4) <24, 6> 48 1 1 : D24 O6.62 (0; 2, 2, 3, 4) <24, 8> 48 2 1 : (C6 x C2) : C2 O6.63 (0; 2, 2, 3, 4) <24, 12> 144 6 1 : S4 O6.64 (0; 4, 6, 6) <24, 3> 24 1 1 : SL(2,3) O6.65 (0; 4, 6, 6) <24, 10> 16 1 1 : C3 x D8 O6.66 (0; 3, 8, 8) <24, 1> 24 1 1 : C3 : C8 O6.67 (0; 2, 2, 2, 12) <24, 6> 144 3 1 : D24 O6.68 (0; 4, 4, 12) <24, 4> 48 1 1 : C3 : Q8 O6.69 (0; 2, 24, 24) <24, 2> 8 1 1 : C24 O6.70 (0; 5, 5, 5) <25, 2> 480 1 1 : C5 x C5 O6.71 (0; 2, 13, 26) <26, 2> 12 1 1 : C26 O6.72 (0; 2, 2, 2, 7) <28, 3> 252 3 1 : D28 O6.73 (0; 4, 4, 7) <28, 1> 84 1 1 : C7 : C4 O6.74 (0; 2, 14, 14) <28, 4> 36 1 1 : C14 x C2 O6.75 (0; 2, 10, 15) <30, 1> 24 1 1 : C5 x S3 O6.76 (0; 2, 9, 9) <36, 3> 72 1 1 : (C2 x C2) : C9 O6.77 (0; 3, 3, 13) <39, 1> 312 2 1 : C13 : C3 O6.78 (0; 2, 6, 8) <48, 15> 96 1 1 : (C3 x D8) : C2 O6.79 (0; 2, 6, 8) <48, 29> 48 1 1 : GL(2,3) O6.80 (0; 2, 4, 24) <48, 6> 96 1 1 : C24 : C2 O6.81 (0; 2, 5, 10) <50, 3> 80 1 1 : C5 x D10 O6.82 (0; 2, 4, 14) <56, 7> 168 1 1 : (C14 x C2) : C2 O6.83 (0; 2, 2, 2, 3) <60, 5> 1080 9 1 : A5 O6.84 (0; 2, 4, 9) <72, 15> 216 1 1 : ((C2 x C2) : C9) : C2 O6.85 (0; 3, 3, 5) <75, 2> 1200 1 1 : (C5 x C5) : C3 O6.86 (0; 2, 4, 6) <120, 34> 120 1 1 : S5 O6.87 (0; 2, 3, 10) <150, 5> 600 1 1 : ((C5 x C5) : C3) : C2