Census of actions of finite groups on Riemann surfaces of genus 3 Exported on: Mon Aug 14 14:22:27 2023 Created on: Wed Jul 19 08:22:44 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 ---------------------------------------------------------------------------------------- O3.1 (3; -) <1, 1> 1 1 1 : 1 O3.2 (2; -) <2, 1> 15 15 1 : C2 O3.3 (1; 2, 2, 2, 2) <2, 1> 4 4 1 : C2 O3.4 (0; 2^8) <2, 1> 1 1 1 : C2 O3.5 (1; 3, 3) <3, 1> 18 9 1 : C3 O3.6 (0; 3^5) <3, 1> 10 5 1 : C3 O3.7 (1; 2, 2) <4, 1> 12 6 1 : C4 O3.8 (1; 2, 2) <4, 2> 36 6 1 : C2 x C2 O3.9 (0; 2^6) <4, 2> 180 30 2 : C2 x C2 O3.10 (0; 2^3, 4^2) <4, 1> 2 1 1 : C4 O3.11 (0; 4, 4, 4, 4) <4, 1> 8 4 2 : C4 O3.12 (1; 3) <6, 1> 18 3 1 : S3 O3.13 (0; 2^4, 3) <6, 1> 54 9 1 : S3 O3.14 (0; 2, 3, 3, 6) <6, 2> 2 1 1 : C6 O3.15 (0; 2, 2, 6, 6) <6, 2> 2 1 1 : C6 O3.16 (0; 7, 7, 7) <7, 1> 30 5 2 : C7 O3.17 (1; 2) <8, 3> 24 3 1 : D8 O3.18 (1; 2) <8, 4> 24 1 1 : Q8 O3.19 (0; 2^5) <8, 3> 240 30 1 : D8 O3.20 (0; 2^5) <8, 5> 1680 10 1 : C2 x C2 x C2 O3.21 (0; 2, 2, 4, 4) <8, 2> 32 4 3 : C4 x C2 O3.22 (0; 2, 2, 4, 4) <8, 3> 16 2 1 : D8 O3.23 (0; 4, 8, 8) <8, 1> 8 2 2 : C8 O3.24 (0; 3, 9, 9) <9, 1> 12 2 1 : C9 O3.25 (0; 2, 2, 3, 3) <12, 3> 72 3 1 : A4 O3.26 (0; 2, 2, 2, 6) <12, 4> 36 3 1 : D12 O3.27 (0; 4, 4, 6) <12, 1> 12 1 1 : C3 : C4 O3.28 (0; 3, 4, 12) <12, 2> 4 1 1 : C12 O3.29 (0; 2, 12, 12) <12, 2> 4 1 1 : C12 O3.30 (0; 2, 7, 14) <14, 2> 6 1 1 : C14 O3.31 (0; 2, 2, 2, 4) <16, 11> 192 3 1 : C2 x D8 O3.32 (0; 2, 2, 2, 4) <16, 13> 48 1 1 : (C4 x C2) : C2 O3.33 (0; 4, 4, 4) <16, 2> 96 1 1 : C4 x C4 O3.34 (0; 4, 4, 4) <16, 4> 96 3 1 : C4 : C4 O3.35 (0; 2, 8, 8) <16, 5> 16 1 1 : C8 x C2 O3.36 (0; 2, 8, 8) <16, 6> 16 1 1 : C8 : C2 O3.37 (0; 3, 3, 7) <21, 1> 84 2 1 : C7 : C3 O3.38 (0; 2, 2, 2, 3) <24, 12> 216 9 1 : S4 O3.39 (0; 3, 4, 4) <24, 12> 24 1 1 : S4 O3.40 (0; 3, 3, 6) <24, 3> 24 1 1 : SL(2,3) O3.41 (0; 2, 6, 6) <24, 13> 24 1 1 : C2 x A4 O3.42 (0; 2, 4, 12) <24, 5> 24 1 1 : C4 x S3 O3.43 (0; 2, 4, 8) <32, 9> 64 1 1 : (C8 x C2) : C2 O3.44 (0; 2, 4, 8) <32, 11> 32 1 1 : (C4 x C4) : C2 O3.45 (0; 3, 3, 4) <48, 3> 384 1 1 : (C4 x C4) : C3 O3.46 (0; 2, 4, 6) <48, 48> 48 1 1 : C2 x S4 O3.47 (0; 2, 3, 12) <48, 33> 48 1 1 : SL(2,3) : C2 O3.48 (0; 2, 3, 8) <96, 64> 192 1 1 : ((C4 x C4) : C3) : C2 O3.49 (0; 2, 3, 7) <168, 42> 336 1 1 : PSL(3,2)