Symmetric genus of groups of order 2 to 127 ........................................... The symmetric genus of a finite group G is the smallest genus of all the compact Riemann surfaces on which G acts faithfully as a group of automorphisms (as defined by Tom Tucker in the 1980s). The list below gives the symmetric genus of every finite group of order 2 to 127 inclusive, together with the signature types for the action(s) of the group on compact Riemann surfaces of the corresponding genus. The notation "Order n # k" stands for the kth group of order n in the "Small Groups Database" available in GAP and MAGMA. This list was created with the help of the MAGMA system, in November 2009. Marston Conder June 2013 ........................................................................... Groups of order 2 Total number of groups = 1 Order 2 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2];{-}), (0;+;[-];{(1)}), (1;-;[-];{-}) ] ........................................................................... Groups of order 3 Total number of groups = 1 Order 3 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[3,3];{-}) ] ........................................................................... Groups of order 4 Total number of groups = 2 Order 4 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[4,4];{-}), (1;-;[2];{-}) ] Order 4 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,2];{-}), (0;+;[-];{(2,2)}), (0;+;[2];{(1)}) ] ........................................................................... Groups of order 5 Total number of groups = 1 Order 5 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[5,5];{-}) ] ........................................................................... Groups of order 6 Total number of groups = 2 Order 6 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,3];{-}), (0;+;[-];{(3,3)}) ] Order 6 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[6,6];{-}), (0;+;[3];{(1)}), (1;-;[3];{-}) ] ........................................................................... Groups of order 7 Total number of groups = 1 Order 7 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[7,7];{-}) ] ........................................................................... Groups of order 8 Total number of groups = 5 Order 8 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[8,8];{-}), (1;-;[4];{-}) ] Order 8 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[4];{(1)}) ] Order 8 # 3 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,4];{-}), (0;+;[-];{(4,4)}), (0;+;[2];{(2)}) ] Order 8 # 4 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 8 # 5 : Symmetric genus 0 Symmetric genus actions [ (0;+;[-];{(2,2,2)}) ] ........................................................................... Groups of order 9 Total number of groups = 2 Order 9 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[9,9];{-}) ] Order 9 # 2 : Symmetric genus 1 Symmetric genus actions [ (0;+;[3,3,3];{-}), (1;+;[-];{-}) ] ........................................................................... Groups of order 10 Total number of groups = 2 Order 10 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,5];{-}), (0;+;[-];{(5,5)}) ] Order 10 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[10,10];{-}), (0;+;[5];{(1)}), (1;-;[5];{-}) ] ........................................................................... Groups of order 11 Total number of groups = 1 Order 11 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[11,11];{-}) ] ........................................................................... Groups of order 12 Total number of groups = 5 Order 12 # 1 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 12 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[12,12];{-}), (1;-;[6];{-}) ] Order 12 # 3 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,3,3];{-}) ] Order 12 # 4 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,6];{-}), (0;+;[-];{(6,6)}), (0;+;[-];{(2,2,3)}), (0;+;[2];{(3)}) ] Order 12 # 5 : Symmetric genus 0 Symmetric genus actions [ (0;+;[6];{(1)}) ] ........................................................................... Groups of order 13 Total number of groups = 1 Order 13 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[13,13];{-}) ] ........................................................................... Groups of order 14 Total number of groups = 2 Order 14 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,7];{-}), (0;+;[-];{(7,7)}) ] Order 14 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[14,14];{-}), (0;+;[7];{(1)}), (1;-;[7];{-}) ] ........................................................................... Groups of order 15 Total number of groups = 1 Order 15 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[15,15];{-}) ] ........................................................................... Groups of order 16 Total number of groups = 14 Order 16 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[16,16];{-}), (1;-;[8];{-}) ] Order 16 # 2 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] Order 16 # 3 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,4,4];{-}), (0;+;[4];{(2)}), (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 16 # 4 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 16 # 5 : Symmetric genus 0 Symmetric genus actions [ (0;+;[8];{(1)}) ] Order 16 # 6 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 16 # 7 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,8];{-}), (0;+;[-];{(8,8)}), (0;+;[2];{(4)}) ] Order 16 # 8 : Symmetric genus 1 Symmetric genus actions [ (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 16 # 9 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 16 # 10 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 16 # 11 : Symmetric genus 0 Symmetric genus actions [ (0;+;[-];{(2,2,4)}) ] Order 16 # 12 : Symmetric genus 5 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 16 # 13 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}), (0;+;[-];{(1),(1)}) ] Order 16 # 14 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,2,2,2)}) ] ........................................................................... Groups of order 17 Total number of groups = 1 Order 17 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[17,17];{-}) ] ........................................................................... Groups of order 18 Total number of groups = 5 Order 18 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,9];{-}), (0;+;[-];{(9,9)}) ] Order 18 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[18,18];{-}), (0;+;[9];{(1)}), (1;-;[9];{-}) ] Order 18 # 3 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,3,6];{-}), (0;+;[3];{(3)}), (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 18 # 4 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2,2,2];{-}), (0;+;[-];{(3,3,3)}) ] Order 18 # 5 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] ........................................................................... Groups of order 19 Total number of groups = 1 Order 19 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[19,19];{-}) ] ........................................................................... Groups of order 20 Total number of groups = 5 Order 20 # 1 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 20 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[20,20];{-}), (1;-;[10];{-}) ] Order 20 # 3 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,4,4];{-}) ] Order 20 # 4 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,10];{-}), (0;+;[-];{(10,10)}), (0;+;[-];{(2,2,5)}), (0;+;[2];{(5)}) ] Order 20 # 5 : Symmetric genus 0 Symmetric genus actions [ (0;+;[10];{(1)}) ] ........................................................................... Groups of order 21 Total number of groups = 2 Order 21 # 1 : Symmetric genus 1 Symmetric genus actions [ (0;+;[3,3,3];{-}) ] Order 21 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[21,21];{-}) ] ........................................................................... Groups of order 22 Total number of groups = 2 Order 22 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,11];{-}), (0;+;[-];{(11,11)}) ] Order 22 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[22,22];{-}), (0;+;[11];{(1)}), (1;-;[11];{-}) ] ........................................................................... Groups of order 23 Total number of groups = 1 Order 23 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[23,23];{-}) ] ........................................................................... Groups of order 24 Total number of groups = 15 Order 24 # 1 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 24 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[24,24];{-}), (1;-;[12];{-}) ] Order 24 # 3 : Symmetric genus 2 Symmetric genus actions [ (0;+;[3,3,4];{-}) ] Order 24 # 4 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 24 # 5 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 24 # 6 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,12];{-}), (0;+;[-];{(12,12)}), (0;+;[2];{(6)}) ] Order 24 # 7 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 24 # 8 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}), (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 24 # 9 : Symmetric genus 0 Symmetric genus actions [ (0;+;[12];{(1)}) ] Order 24 # 10 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 24 # 11 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 24 # 12 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,3,4];{-}), (0;+;[-];{(2,3,3)}) ] Order 24 # 13 : Symmetric genus 0 Symmetric genus actions [ (0;+;[3];{(2)}) ] Order 24 # 14 : Symmetric genus 0 Symmetric genus actions [ (0;+;[-];{(2,2,6)}) ] Order 24 # 15 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] ........................................................................... Groups of order 25 Total number of groups = 2 Order 25 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[25,25];{-}) ] Order 25 # 2 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] ........................................................................... Groups of order 26 Total number of groups = 2 Order 26 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,13];{-}), (0;+;[-];{(13,13)}) ] Order 26 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[26,26];{-}), (0;+;[13];{(1)}), (1;-;[13];{-}) ] ........................................................................... Groups of order 27 Total number of groups = 5 Order 27 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[27,27];{-}) ] Order 27 # 2 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] Order 27 # 3 : Symmetric genus 1 Symmetric genus actions [ (0;+;[3,3,3];{-}) ] Order 27 # 4 : Symmetric genus 7 Symmetric genus actions [ (0;+;[3,9,9];{-}) ] Order 27 # 5 : Symmetric genus 10 Symmetric genus actions [ (0;+;[3,3,3,3];{-}) ] ........................................................................... Groups of order 28 Total number of groups = 4 Order 28 # 1 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 28 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[28,28];{-}), (1;-;[14];{-}) ] Order 28 # 3 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,14];{-}), (0;+;[-];{(14,14)}), (0;+;[-];{(2,2,7)}), (0;+;[2];{(7)}) ] Order 28 # 4 : Symmetric genus 0 Symmetric genus actions [ (0;+;[14];{(1)}) ] ........................................................................... Groups of order 29 Total number of groups = 1 Order 29 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[29,29];{-}) ] ........................................................................... Groups of order 30 Total number of groups = 4 Order 30 # 1 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 30 # 2 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 30 # 3 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,15];{-}), (0;+;[-];{(15,15)}) ] Order 30 # 4 : Symmetric genus 0 Symmetric genus actions [ (0;+;[30,30];{-}), (0;+;[15];{(1)}), (1;-;[15];{-}) ] ........................................................................... Groups of order 31 Total number of groups = 1 Order 31 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[31,31];{-}) ] ........................................................................... Groups of order 32 Total number of groups = 51 Order 32 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[32,32];{-}), (1;-;[16];{-}) ] Order 32 # 2 : Symmetric genus 5 Symmetric genus actions [ (0;+;[4,4,4];{-}) ] Order 32 # 3 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] Order 32 # 4 : Symmetric genus 9 Symmetric genus actions [ (0;+;[4,8,8];{-}), (1;-;[4,4];{-}), (1;+;[2];{-}), (2;-;[2];{-}) ] Order 32 # 5 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}) ] Order 32 # 6 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,4,4];{-}), (0;+;[4];{(2)}) ] Order 32 # 7 : Symmetric genus 1 Symmetric genus actions [ (1;-;[2,2];{-}) ] Order 32 # 8 : Symmetric genus 9 Symmetric genus actions [ (0;+;[4,8,8];{-}), (1;-;[4,4];{-}), (1;+;[2];{-}), (2;-;[2];{-}) ] Order 32 # 9 : Symmetric genus 1 Symmetric genus actions [ (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 32 # 10 : Symmetric genus 7 Symmetric genus actions [ (0;+;[4,4,8];{-}) ] Order 32 # 11 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}) ] Order 32 # 12 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 32 # 13 : Symmetric genus 7 Symmetric genus actions [ (0;+;[4,4,8];{-}) ] Order 32 # 14 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 32 # 15 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 32 # 16 : Symmetric genus 0 Symmetric genus actions [ (0;+;[16];{(1)}) ] Order 32 # 17 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 32 # 18 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,16];{-}), (0;+;[-];{(16,16)}), (0;+;[2];{(8)}) ] Order 32 # 19 : Symmetric genus 1 Symmetric genus actions [ (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 32 # 20 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 32 # 21 : Symmetric genus 9 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 32 # 22 : Symmetric genus 5 Symmetric genus actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}), (0;+;[-];{(1),(2)}) ] Order 32 # 23 : Symmetric genus 9 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 32 # 24 : Symmetric genus 9 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 32 # 25 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 32 # 26 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 32 # 27 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,4,4)}), (0;+;[2];{(2,2)}) ] Order 32 # 28 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}) ] Order 32 # 29 : Symmetric genus 9 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 32 # 30 : Symmetric genus 5 Symmetric genus actions [ (0;+;[2,4];{(1)}), (0;+;[-];{(1),(2)}) ] Order 32 # 31 : Symmetric genus 9 Symmetric genus actions [ (0;+;[2,2,4,4];{-}), (0;+;[2,4,2,4];{-}), (0;+;[4];{(4,4)}), (0;+;[2,4];{(2)}), (0;+;[-];{(2),(2)}) ] Order 32 # 32 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 32 # 33 : Symmetric genus 13 Symmetric genus actions [ (0;+;[2,4,4,4];{-}), (0;+;[4,4];{(2)}) ] Order 32 # 34 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2,2,2];{-}) ] Order 32 # 35 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 32 # 36 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 32 # 37 : Symmetric genus 5 Symmetric genus actions [ (0;+;[-];{(1),(2)}) ] Order 32 # 38 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 32 # 39 : Symmetric genus 0 Symmetric genus actions [ (0;+;[-];{(2,2,8)}) ] Order 32 # 40 : Symmetric genus 5 Symmetric genus actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 32 # 41 : Symmetric genus 9 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 32 # 42 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}), (0;+;[-];{(1),(1)}) ] Order 32 # 43 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2];{(2,2)}), (0;+;[2,2];{(1)}) ] Order 32 # 44 : Symmetric genus 7 Symmetric genus actions [ (0;+;[2,8];{(1)}), (0;+;[-];{(1),(4)}) ] Order 32 # 45 : Symmetric genus 9 Symmetric genus actions [ (0;+;[4];{(2,2,2)}), (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 32 # 46 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,2,2,2)}) ] Order 32 # 47 : Symmetric genus 13 Symmetric genus actions [ (0;+;[4];{(1),(1)}) ] Order 32 # 48 : Symmetric genus 5 Symmetric genus actions [ (0;+;[-];{(2,2,4,4)}) ] Order 32 # 49 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,2,2,2)}) ] Order 32 # 50 : Symmetric genus 9 Symmetric genus actions [ (0;+;[-];{(4,4,4,4)}), (0;+;[2,2,2,2,2];{-}), (0;+;[2];{(1),(1)}) ] Order 32 # 51 : Symmetric genus 5 Symmetric genus actions [ (0;+;[-];{(2,2,2,2,2)}) ] ........................................................................... Groups of order 33 Total number of groups = 1 Order 33 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[33,33];{-}) ] ........................................................................... Groups of order 34 Total number of groups = 2 Order 34 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,17];{-}), (0;+;[-];{(17,17)}) ] Order 34 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[34,34];{-}), (0;+;[17];{(1)}), (1;-;[17];{-}) ] ........................................................................... Groups of order 35 Total number of groups = 1 Order 35 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[35,35];{-}) ] ........................................................................... Groups of order 36 Total number of groups = 14 Order 36 # 1 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 36 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[36,36];{-}), (1;-;[18];{-}) ] Order 36 # 3 : Symmetric genus 6 Symmetric genus actions [ (0;+;[2,9,9];{-}) ] Order 36 # 4 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,18];{-}), (0;+;[-];{(18,18)}), (0;+;[-];{(2,2,9)}), (0;+;[2];{(9)}) ] Order 36 # 5 : Symmetric genus 0 Symmetric genus actions [ (0;+;[18];{(1)}) ] Order 36 # 6 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 36 # 7 : Symmetric genus 16 Symmetric genus actions [ (0;+;[3,3,4,4];{-}), (0;+;[3,4,3,4];{-}) ] Order 36 # 8 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] Order 36 # 9 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,4,4];{-}) ] Order 36 # 10 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,3,6)}), (0;+;[-];{(2,2,2,2)}), (0;+;[2];{(2,2)}), (0;+;[2,2];{(1)}), (1;-;[2,2];{-}) ] Order 36 # 11 : Symmetric genus 1 Symmetric genus actions [ (0;+;[3,3,3];{-}) ] Order 36 # 12 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 36 # 13 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2,2,2];{-}) ] Order 36 # 14 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] ........................................................................... Groups of order 37 Total number of groups = 1 Order 37 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[37,37];{-}) ] ........................................................................... Groups of order 38 Total number of groups = 2 Order 38 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,19];{-}), (0;+;[-];{(19,19)}) ] Order 38 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[38,38];{-}), (0;+;[19];{(1)}), (1;-;[19];{-}) ] ........................................................................... Groups of order 39 Total number of groups = 2 Order 39 # 1 : Symmetric genus 1 Symmetric genus actions [ (0;+;[3,3,3];{-}) ] Order 39 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[39,39];{-}) ] ........................................................................... Groups of order 40 Total number of groups = 14 Order 40 # 1 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 40 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[40,40];{-}), (1;-;[20];{-}) ] Order 40 # 3 : Symmetric genus 11 Symmetric genus actions [ (0;+;[4,8,8];{-}) ] Order 40 # 4 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 40 # 5 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 40 # 6 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,20];{-}), (0;+;[-];{(20,20)}), (0;+;[2];{(10)}) ] Order 40 # 7 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 40 # 8 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}), (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 40 # 9 : Symmetric genus 0 Symmetric genus actions [ (0;+;[20];{(1)}) ] Order 40 # 10 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 40 # 11 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 40 # 12 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,4,4];{-}) ] Order 40 # 13 : Symmetric genus 0 Symmetric genus actions [ (0;+;[-];{(2,2,10)}) ] Order 40 # 14 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] ........................................................................... Groups of order 41 Total number of groups = 1 Order 41 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[41,41];{-}) ] ........................................................................... Groups of order 42 Total number of groups = 6 Order 42 # 1 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,3,6];{-}) ] Order 42 # 2 : Symmetric genus 8 Symmetric genus actions [ (0;+;[3,6,6];{-}), (0;+;[3,3];{(1)}), (1;-;[3,3];{-}) ] Order 42 # 3 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 42 # 4 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 42 # 5 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,21];{-}), (0;+;[-];{(21,21)}) ] Order 42 # 6 : Symmetric genus 0 Symmetric genus actions [ (0;+;[42,42];{-}), (0;+;[21];{(1)}), (1;-;[21];{-}) ] ........................................................................... Groups of order 43 Total number of groups = 1 Order 43 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[43,43];{-}) ] ........................................................................... Groups of order 44 Total number of groups = 4 Order 44 # 1 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 44 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[44,44];{-}), (1;-;[22];{-}) ] Order 44 # 3 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,22];{-}), (0;+;[-];{(22,22)}), (0;+;[-];{(2,2,11)}), (0;+;[2];{(11)}) ] Order 44 # 4 : Symmetric genus 0 Symmetric genus actions [ (0;+;[22];{(1)}) ] ........................................................................... Groups of order 45 Total number of groups = 2 Order 45 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[45,45];{-}) ] Order 45 # 2 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] ........................................................................... Groups of order 46 Total number of groups = 2 Order 46 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,23];{-}), (0;+;[-];{(23,23)}) ] Order 46 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[46,46];{-}), (0;+;[23];{(1)}), (1;-;[23];{-}) ] ........................................................................... Groups of order 47 Total number of groups = 1 Order 47 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[47,47];{-}) ] ........................................................................... Groups of order 48 Total number of groups = 52 Order 48 # 1 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 48 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[48,48];{-}), (1;-;[24];{-}) ] Order 48 # 3 : Symmetric genus 1 Symmetric genus actions [ (0;+;[3,3,3];{-}) ] Order 48 # 4 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}) ] Order 48 # 5 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}) ] Order 48 # 6 : Symmetric genus 1 Symmetric genus actions [ (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 48 # 7 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,24];{-}), (0;+;[-];{(24,24)}), (0;+;[2];{(12)}) ] Order 48 # 8 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 48 # 9 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 48 # 10 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 48 # 11 : Symmetric genus 11 Symmetric genus actions [ (0;+;[4,4,12];{-}) ] Order 48 # 12 : Symmetric genus 11 Symmetric genus actions [ (0;+;[4,4,12];{-}) ] Order 48 # 13 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 48 # 14 : Symmetric genus 1 Symmetric genus actions [ (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 48 # 15 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}), (1;-;[2,2];{-}) ] Order 48 # 16 : Symmetric genus 12 Symmetric genus actions [ (0;+;[4,6,8];{-}) ] Order 48 # 17 : Symmetric genus 1 Symmetric genus actions [ (1;-;[2,2];{-}) ] Order 48 # 18 : Symmetric genus 13 Symmetric genus actions [ (1;-;[4,4];{-}) ] Order 48 # 19 : Symmetric genus 9 Symmetric genus actions [ (0;+;[4,4,6];{-}) ] Order 48 # 20 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] Order 48 # 21 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}) ] Order 48 # 22 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 48 # 23 : Symmetric genus 0 Symmetric genus actions [ (0;+;[24];{(1)}) ] Order 48 # 24 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 48 # 25 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 48 # 26 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}) ] Order 48 # 27 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 48 # 28 : Symmetric genus 8 Symmetric genus actions [ (0;+;[3,4,8];{-}) ] Order 48 # 29 : Symmetric genus 2 Symmetric genus actions [ (0;+;[2,3,8];{-}), (0;+;[-];{(3,3,4)}) ] Order 48 # 30 : Symmetric genus 5 Symmetric genus actions [ (0;+;[3,4,4];{-}) ] Order 48 # 31 : Symmetric genus 5 Symmetric genus actions [ (1;-;[2,3];{-}) ] Order 48 # 32 : Symmetric genus 7 Symmetric genus actions [ (0;+;[3,4,6];{-}) ] Order 48 # 33 : Symmetric genus 2 Symmetric genus actions [ (0;+;[3];{(4)}) ] Order 48 # 34 : Symmetric genus 13 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 48 # 35 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 48 # 36 : Symmetric genus 0 Symmetric genus actions [ (0;+;[-];{(2,2,12)}) ] Order 48 # 37 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}), (0;+;[-];{(1),(1)}) ] Order 48 # 38 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,2,2,2)}), (0;+;[2];{(2,2)}), (0;+;[2,2];{(1)}) ] Order 48 # 39 : Symmetric genus 9 Symmetric genus actions [ (0;+;[2,6];{(1)}), (0;+;[-];{(1),(3)}) ] Order 48 # 40 : Symmetric genus 13 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 48 # 41 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}) ] Order 48 # 42 : Symmetric genus 13 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 48 # 43 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}) ] Order 48 # 44 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 48 # 45 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 48 # 46 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,12];{(1)}) ] Order 48 # 47 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 48 # 48 : Symmetric genus 0 Symmetric genus actions [ (0;+;[-];{(2,3,4)}) ] Order 48 # 49 : Symmetric genus 3 Symmetric genus actions [ (0;+;[6];{(2)}) ] Order 48 # 50 : Symmetric genus 9 Symmetric genus actions [ (0;+;[2,2,3,3];{-}), (0;+;[2,3,2,3];{-}) ] Order 48 # 51 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,2,2,2)}) ] Order 48 # 52 : Symmetric genus 13 Symmetric genus actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] ........................................................................... Groups of order 49 Total number of groups = 2 Order 49 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[49,49];{-}) ] Order 49 # 2 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] ........................................................................... Groups of order 50 Total number of groups = 5 Order 50 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,25];{-}), (0;+;[-];{(25,25)}) ] Order 50 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[50,50];{-}), (0;+;[25];{(1)}), (1;-;[25];{-}) ] Order 50 # 3 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 50 # 4 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2,2,2];{-}) ] Order 50 # 5 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] ........................................................................... Groups of order 51 Total number of groups = 1 Order 51 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[51,51];{-}) ] ........................................................................... Groups of order 52 Total number of groups = 5 Order 52 # 1 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 52 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[52,52];{-}), (1;-;[26];{-}) ] Order 52 # 3 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,4,4];{-}) ] Order 52 # 4 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,26];{-}), (0;+;[-];{(26,26)}), (0;+;[-];{(2,2,13)}), (0;+;[2];{(13)}) ] Order 52 # 5 : Symmetric genus 0 Symmetric genus actions [ (0;+;[26];{(1)}) ] ........................................................................... Groups of order 53 Total number of groups = 1 Order 53 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[53,53];{-}) ] ........................................................................... Groups of order 54 Total number of groups = 15 Order 54 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,27];{-}), (0;+;[-];{(27,27)}) ] Order 54 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[54,54];{-}), (0;+;[27];{(1)}), (1;-;[27];{-}) ] Order 54 # 3 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 54 # 4 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 54 # 5 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,3,6];{-}), (0;+;[3];{(3)}) ] Order 54 # 6 : Symmetric genus 7 Symmetric genus actions [ (0;+;[2,6,9];{-}) ] Order 54 # 7 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2,2,2];{-}) ] Order 54 # 8 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(3,3,3)}) ] Order 54 # 9 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] Order 54 # 10 : Symmetric genus 10 Symmetric genus actions [ (0;+;[3,6,6];{-}), (0;+;[3,3];{(1)}), (1;-;[3,3];{-}) ] Order 54 # 11 : Symmetric genus 16 Symmetric genus actions [ (0;+;[3,18,18];{-}), (0;+;[3,9];{(1)}), (1;-;[3,9];{-}) ] Order 54 # 12 : Symmetric genus 10 Symmetric genus actions [ (0;+;[3,6,6];{-}), (0;+;[3,3];{(1)}), (1;-;[3,3];{-}) ] Order 54 # 13 : Symmetric genus 10 Symmetric genus actions [ (0;+;[2,2,3,3];{-}), (0;+;[2,3,2,3];{-}), (0;+;[3];{(3,3)}) ] Order 54 # 14 : Symmetric genus 10 Symmetric genus actions [ (0;+;[-];{(3,3,3,3)}) ] Order 54 # 15 : Symmetric genus 28 Symmetric genus actions [ (0;+;[3,3,6,6];{-}), (0;+;[3,6,3,6];{-}), (0;+;[3,3,3];{(1)}), (1;-;[3,3,3];{-}) ] ........................................................................... Groups of order 55 Total number of groups = 2 Order 55 # 1 : Symmetric genus 12 Symmetric genus actions [ (0;+;[5,5,5];{-}) ] Order 55 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[55,55];{-}) ] ........................................................................... Groups of order 56 Total number of groups = 13 Order 56 # 1 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 56 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[56,56];{-}), (1;-;[28];{-}) ] Order 56 # 3 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 56 # 4 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 56 # 5 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,28];{-}), (0;+;[-];{(28,28)}), (0;+;[2];{(14)}) ] Order 56 # 6 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 56 # 7 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}), (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 56 # 8 : Symmetric genus 0 Symmetric genus actions [ (0;+;[28];{(1)}) ] Order 56 # 9 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 56 # 10 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 56 # 11 : Symmetric genus 7 Symmetric genus actions [ (0;+;[2,7,7];{-}) ] Order 56 # 12 : Symmetric genus 0 Symmetric genus actions [ (0;+;[-];{(2,2,14)}) ] Order 56 # 13 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] ........................................................................... Groups of order 57 Total number of groups = 2 Order 57 # 1 : Symmetric genus 1 Symmetric genus actions [ (0;+;[3,3,3];{-}) ] Order 57 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[57,57];{-}) ] ........................................................................... Groups of order 58 Total number of groups = 2 Order 58 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,29];{-}), (0;+;[-];{(29,29)}) ] Order 58 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[58,58];{-}), (0;+;[29];{(1)}), (1;-;[29];{-}) ] ........................................................................... Groups of order 59 Total number of groups = 1 Order 59 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[59,59];{-}) ] ........................................................................... Groups of order 60 Total number of groups = 13 Order 60 # 1 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 60 # 2 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 60 # 3 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 60 # 4 : Symmetric genus 0 Symmetric genus actions [ (0;+;[60,60];{-}), (1;-;[30];{-}) ] Order 60 # 5 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,3,5];{-}) ] Order 60 # 6 : Symmetric genus 11 Symmetric genus actions [ (0;+;[2,12,12];{-}) ] Order 60 # 7 : Symmetric genus 11 Symmetric genus actions [ (0;+;[4,4,6];{-}) ] Order 60 # 8 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,2,2,2)}), (0;+;[2];{(2,2)}), (0;+;[2,2];{(1)}), (1;-;[2,2];{-}) ] Order 60 # 9 : Symmetric genus 12 Symmetric genus actions [ (0;+;[2,15,15];{-}) ] Order 60 # 10 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 60 # 11 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 60 # 12 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,30];{-}), (0;+;[-];{(30,30)}), (0;+;[-];{(2,2,15)}), (0;+;[2];{(15)}) ] Order 60 # 13 : Symmetric genus 0 Symmetric genus actions [ (0;+;[30];{(1)}) ] ........................................................................... Groups of order 61 Total number of groups = 1 Order 61 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[61,61];{-}) ] ........................................................................... Groups of order 62 Total number of groups = 2 Order 62 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,31];{-}), (0;+;[-];{(31,31)}) ] Order 62 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[62,62];{-}), (0;+;[31];{(1)}), (1;-;[31];{-}) ] ........................................................................... Groups of order 63 Total number of groups = 4 Order 63 # 1 : Symmetric genus 21 Symmetric genus actions [ (0;+;[7,9,9];{-}) ] Order 63 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[63,63];{-}) ] Order 63 # 3 : Symmetric genus 1 Symmetric genus actions [ (0;+;[3,3,3];{-}) ] Order 63 # 4 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] ........................................................................... Groups of order 64 Total number of groups = 267 Order 64 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[64,64];{-}), (1;-;[32];{-}) ] Order 64 # 2 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] Order 64 # 3 : Symmetric genus 17 Symmetric genus actions [ (1;+;[2];{-}) ] Order 64 # 4 : Symmetric genus 5 Symmetric genus actions [ (0;+;[8];{(2)}) ] Order 64 # 5 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,8,8];{-}), (1;-;[4,4];{-}), (1;+;[2];{-}), (2;-;[2];{-}) ] Order 64 # 6 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}) ] Order 64 # 7 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,8,8];{-}), (1;-;[4,4];{-}) ] Order 64 # 8 : Symmetric genus 5 Symmetric genus actions [ (0;+;[2,4,8];{-}), (0;+;[4];{(4)}) ] Order 64 # 9 : Symmetric genus 13 Symmetric genus actions [ (0;+;[4,4,8];{-}) ] Order 64 # 10 : Symmetric genus 9 Symmetric genus actions [ (0;+;[2,8,8];{-}), (0;+;[8];{(4)}), (1;-;[2,4];{-}), (1;-;[-];{(2)}) ] Order 64 # 11 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,8,8];{-}), (1;-;[4,4];{-}) ] Order 64 # 12 : Symmetric genus 1 Symmetric genus actions [ (1;-;[2,2];{-}) ] Order 64 # 13 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,8,8];{-}), (1;-;[4,4];{-}) ] Order 64 # 14 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,8,8];{-}), (1;-;[4,4];{-}) ] Order 64 # 15 : Symmetric genus 17 Symmetric genus actions [ (2;-;[2];{-}) ] Order 64 # 16 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 64 # 17 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,8,8];{-}), (1;-;[4,4];{-}), (1;+;[2];{-}), (2;-;[2];{-}) ] Order 64 # 18 : Symmetric genus 13 Symmetric genus actions [ (0;+;[4,4,8];{-}) ] Order 64 # 19 : Symmetric genus 17 Symmetric genus actions [ (2;-;[2];{-}) ] Order 64 # 20 : Symmetric genus 13 Symmetric genus actions [ (0;+;[4,4,8];{-}) ] Order 64 # 21 : Symmetric genus 13 Symmetric genus actions [ (0;+;[4,4,8];{-}) ] Order 64 # 22 : Symmetric genus 17 Symmetric genus actions [ (2;-;[2];{-}) ] Order 64 # 23 : Symmetric genus 9 Symmetric genus actions [ (0;+;[4,4,4];{-}) ] Order 64 # 24 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,8,8];{-}), (1;-;[4,4];{-}), (1;+;[2];{-}), (2;-;[2];{-}) ] Order 64 # 25 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,8,8];{-}), (1;-;[4,4];{-}), (1;+;[2];{-}), (2;-;[2];{-}) ] Order 64 # 26 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] Order 64 # 27 : Symmetric genus 17 Symmetric genus actions [ (1;+;[2];{-}), (2;-;[2];{-}) ] Order 64 # 28 : Symmetric genus 17 Symmetric genus actions [ (2;-;[2];{-}) ] Order 64 # 29 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}) ] Order 64 # 30 : Symmetric genus 7 Symmetric genus actions [ (0;+;[16];{(2)}) ] Order 64 # 31 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}) ] Order 64 # 32 : Symmetric genus 1 Symmetric genus actions [ (0;+;[4];{(2)}) ] Order 64 # 33 : Symmetric genus 13 Symmetric genus actions [ (0;+;[4,4,8];{-}) ] Order 64 # 34 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,4,4];{-}) ] Order 64 # 35 : Symmetric genus 9 Symmetric genus actions [ (0;+;[4,4,4];{-}) ] Order 64 # 36 : Symmetric genus 9 Symmetric genus actions [ (0;+;[2,8,8];{-}), (0;+;[8];{(4)}), (1;-;[2,4];{-}), (1;-;[-];{(2)}) ] Order 64 # 37 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,8,8];{-}), (1;-;[4,4];{-}) ] Order 64 # 38 : Symmetric genus 1 Symmetric genus actions [ (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 64 # 39 : Symmetric genus 15 Symmetric genus actions [ (0;+;[4,4,16];{-}) ] Order 64 # 40 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}) ] Order 64 # 41 : Symmetric genus 7 Symmetric genus actions [ (0;+;[2,4,16];{-}), (0;+;[4];{(8)}) ] Order 64 # 42 : Symmetric genus 1 Symmetric genus actions [ (1;-;[2,2];{-}) ] Order 64 # 43 : Symmetric genus 17 Symmetric genus actions [ (1;-;[4,4];{-}) ] Order 64 # 44 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 64 # 45 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 64 # 46 : Symmetric genus 17 Symmetric genus actions [ (1;-;[4,4];{-}) ] Order 64 # 47 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 64 # 48 : Symmetric genus 15 Symmetric genus actions [ (0;+;[4,4,16];{-}) ] Order 64 # 49 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 64 # 50 : Symmetric genus 0 Symmetric genus actions [ (0;+;[32];{(1)}) ] Order 64 # 51 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 64 # 52 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,32];{-}), (0;+;[-];{(32,32)}), (0;+;[2];{(16)}) ] Order 64 # 53 : Symmetric genus 1 Symmetric genus actions [ (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 64 # 54 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 64 # 55 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}) ] Order 64 # 56 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 64 # 57 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 64 # 58 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 64 # 59 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 64 # 60 : Symmetric genus 9 Symmetric genus actions [ (0;+;[4];{(2,2)}) ] Order 64 # 61 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 64 # 62 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 64 # 63 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 64 # 64 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 64 # 65 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}) ] Order 64 # 66 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 64 # 67 : Symmetric genus 9 Symmetric genus actions [ (0;+;[2,4];{(1)}), (0;+;[-];{(1),(2)}) ] Order 64 # 68 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 64 # 69 : Symmetric genus 25 Symmetric genus actions [ (0;+;[2,4,4,4];{-}), (0;+;[4,4];{(2)}) ] Order 64 # 70 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 64 # 71 : Symmetric genus 17 Symmetric genus actions [ (0;+;[2,2,4,4];{-}), (0;+;[2,4,2,4];{-}), (0;+;[4];{(4,4)}), (0;+;[2,4];{(2)}), (0;+;[-];{(2),(2)}) ] Order 64 # 72 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 64 # 73 : Symmetric genus 5 Symmetric genus actions [ (0;+;[-];{(4,4,4)}) ] Order 64 # 74 : Symmetric genus 25 Symmetric genus actions [ (0;+;[2,4,4,4];{-}), (0;+;[4,4];{(2)}) ] Order 64 # 75 : Symmetric genus 17 Symmetric genus actions [ (0;+;[2,2,4,4];{-}), (0;+;[2,4,2,4];{-}), (0;+;[4];{(4,4)}), (0;+;[2,4];{(2)}), (0;+;[-];{(2),(2)}) ] Order 64 # 76 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 64 # 77 : Symmetric genus 25 Symmetric genus actions [ (0;+;[2,4,4,4];{-}), (0;+;[4,4];{(2)}) ] Order 64 # 78 : Symmetric genus 25 Symmetric genus actions [ (0;+;[2,4,4,4];{-}), (0;+;[4,4];{(2)}) ] Order 64 # 79 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 64 # 80 : Symmetric genus 25 Symmetric genus actions [ (0;+;[2,4,4,4];{-}), (0;+;[4,4];{(2)}) ] Order 64 # 81 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 64 # 82 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 64 # 83 : Symmetric genus 21 Symmetric genus actions [ (0;+;[4,8];{(1)}) ] Order 64 # 84 : Symmetric genus 21 Symmetric genus actions [ (0;+;[4,8];{(1)}) ] Order 64 # 85 : Symmetric genus 25 Symmetric genus actions [ (0;+;[8,8];{(1)}), (1;-;[4];{(1)}) ] Order 64 # 86 : Symmetric genus 21 Symmetric genus actions [ (0;+;[4,8];{(1)}) ] Order 64 # 87 : Symmetric genus 9 Symmetric genus actions [ (0;+;[-];{(1),(2)}) ] Order 64 # 88 : Symmetric genus 13 Symmetric genus actions [ (0;+;[8];{(2,2)}) ] Order 64 # 89 : Symmetric genus 9 Symmetric genus actions [ (0;+;[-];{(1),(2)}) ] Order 64 # 90 : Symmetric genus 9 Symmetric genus actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}), (0;+;[-];{(1),(2)}) ] Order 64 # 91 : Symmetric genus 17 Symmetric genus actions [ (0;+;[2,2,4,4];{-}), (0;+;[2,4,2,4];{-}), (0;+;[4];{(4,4)}), (0;+;[2,4];{(2)}), (0;+;[4,4];{(1)}), (0;+;[-];{(2),(2)}), (1;-;[2];{(1)}) ] Order 64 # 92 : Symmetric genus 9 Symmetric genus actions [ (0;+;[-];{(1),(2)}) ] Order 64 # 93 : Symmetric genus 21 Symmetric genus actions [ (0;+;[4,8];{(1)}) ] Order 64 # 94 : Symmetric genus 9 Symmetric genus actions [ (0;+;[-];{(1),(2)}) ] Order 64 # 95 : Symmetric genus 9 Symmetric genus actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 64 # 96 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 64 # 97 : Symmetric genus 9 Symmetric genus actions [ (0;+;[2,4];{(1)}) ] Order 64 # 98 : Symmetric genus 13 Symmetric genus actions [ (0;+;[2,8];{(1)}), (0;+;[-];{(1),(4)}) ] Order 64 # 99 : Symmetric genus 9 Symmetric genus actions [ (0;+;[4];{(2,2)}) ] Order 64 # 100 : Symmetric genus 21 Symmetric genus actions [ (0;+;[4,8];{(1)}) ] Order 64 # 101 : Symmetric genus 9 Symmetric genus actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 64 # 102 : Symmetric genus 9 Symmetric genus actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 64 # 103 : Symmetric genus 21 Symmetric genus actions [ (0;+;[4,8];{(1)}) ] Order 64 # 104 : Symmetric genus 25 Symmetric genus actions [ (0;+;[8,8];{(1)}), (1;-;[4];{(1)}) ] Order 64 # 105 : Symmetric genus 21 Symmetric genus actions [ (0;+;[4,8];{(1)}) ] Order 64 # 106 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 64 # 107 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 64 # 108 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 64 # 109 : Symmetric genus 21 Symmetric genus actions [ (0;+;[4,8];{(1)}) ] Order 64 # 110 : Symmetric genus 25 Symmetric genus actions [ (0;+;[8,8];{(1)}) ] Order 64 # 111 : Symmetric genus 25 Symmetric genus actions [ (0;+;[8,8];{(1)}) ] Order 64 # 112 : Symmetric genus 25 Symmetric genus actions [ (0;+;[8,8];{(1)}), (1;-;[4];{(1)}) ] Order 64 # 113 : Symmetric genus 25 Symmetric genus actions [ (0;+;[8,8];{(1)}), (1;-;[4];{(1)}) ] Order 64 # 114 : Symmetric genus 29 Symmetric genus actions [ (0;+;[4,8];{(2)}) ] Order 64 # 115 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 64 # 116 : Symmetric genus 9 Symmetric genus actions [ (0;+;[-];{(1),(2)}) ] Order 64 # 117 : Symmetric genus 17 Symmetric genus actions [ (0;+;[-];{(2),(2)}) ] Order 64 # 118 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 64 # 119 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 64 # 120 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 64 # 121 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 64 # 122 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 64 # 123 : Symmetric genus 9 Symmetric genus actions [ (0;+;[2,4];{(1)}), (0;+;[-];{(1),(2)}) ] Order 64 # 124 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 64 # 125 : Symmetric genus 9 Symmetric genus actions [ (0;+;[2,4];{(1)}), (0;+;[-];{(1),(2)}) ] Order 64 # 126 : Symmetric genus 33 Symmetric genus actions [ (3;-;[-];{-}) ] Order 64 # 127 : Symmetric genus 33 Symmetric genus actions [ (3;-;[-];{-}) ] Order 64 # 128 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2];{(2,2)}) ] Order 64 # 129 : Symmetric genus 13 Symmetric genus actions [ (0;+;[2,8];{(1)}), (0;+;[-];{(1),(4)}) ] Order 64 # 130 : Symmetric genus 7 Symmetric genus actions [ (0;+;[-];{(4,4,8)}) ] Order 64 # 131 : Symmetric genus 9 Symmetric genus actions [ (0;+;[4];{(2,2)}) ] Order 64 # 132 : Symmetric genus 21 Symmetric genus actions [ (0;+;[4,8];{(1)}) ] Order 64 # 133 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4];{(4,4)}), (0;+;[4,4];{(1)}), (0;+;[2,4];{(2)}), (1;-;[2];{(1)}) ] Order 64 # 134 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2];{(2,2)}) ] Order 64 # 135 : Symmetric genus 9 Symmetric genus actions [ (0;+;[2,2,4,2];{-}), (0;+;[2,2,2,4];{-}), (0;+;[-];{(4,8,8)}), (0;+;[2];{(4,4)}), (0;+;[2,4];{(1)}), (0;+;[2,2];{(2)}), (0;+;[-];{(1),(2)}) ] Order 64 # 136 : Symmetric genus 9 Symmetric genus actions [ (0;+;[4];{(2,2)}) ] Order 64 # 137 : Symmetric genus 17 Symmetric genus actions [ (0;+;[2,2,4,4];{-}), (0;+;[2,4,2,4];{-}), (0;+;[4];{(4,4)}), (0;+;[4,4];{(1)}), (1;-;[2];{(1)}) ] Order 64 # 138 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,4,4)}) ] Order 64 # 139 : Symmetric genus 13 Symmetric genus actions [ (0;+;[4];{(2,4)}) ] Order 64 # 140 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}) ] Order 64 # 141 : Symmetric genus 17 Symmetric genus actions [ (0;+;[2,2,4,4];{-}), (0;+;[2,4,2,4];{-}), (0;+;[4];{(4,4)}) ] Order 64 # 142 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 64 # 143 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 64 # 144 : Symmetric genus 9 Symmetric genus actions [ (0;+;[2,4];{(1)}), (0;+;[-];{(1),(2)}) ] Order 64 # 145 : Symmetric genus 25 Symmetric genus actions [ (0;+;[2,4,4,4];{-}), (0;+;[4,4];{(2)}) ] Order 64 # 146 : Symmetric genus 9 Symmetric genus actions [ (0;+;[2,4];{(1)}) ] Order 64 # 147 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}) ] Order 64 # 148 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 64 # 149 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4];{(4,4)}), (0;+;[2,4];{(2)}) ] Order 64 # 150 : Symmetric genus 7 Symmetric genus actions [ (0;+;[-];{(4,4,8)}) ] Order 64 # 151 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4,4];{(2)}) ] Order 64 # 152 : Symmetric genus 9 Symmetric genus actions [ (0;+;[2,4];{(1)}), (0;+;[-];{(1),(2)}) ] Order 64 # 153 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}) ] Order 64 # 154 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 64 # 155 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 64 # 156 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 64 # 157 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 64 # 158 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 64 # 159 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 64 # 160 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 64 # 161 : Symmetric genus 13 Symmetric genus actions [ (0;+;[2,8];{(1)}), (0;+;[-];{(1),(4)}) ] Order 64 # 162 : Symmetric genus 13 Symmetric genus actions [ (0;+;[2,8];{(1)}), (0;+;[-];{(1),(4)}) ] Order 64 # 163 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4];{(4,4)}), (0;+;[2,4];{(2)}) ] Order 64 # 164 : Symmetric genus 21 Symmetric genus actions [ (0;+;[4,8];{(1)}) ] Order 64 # 165 : Symmetric genus 21 Symmetric genus actions [ (0;+;[4,8];{(1)}) ] Order 64 # 166 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4,4];{(2)}) ] Order 64 # 167 : Symmetric genus 17 Symmetric genus actions [ (0;+;[2,2,4,4];{-}), (0;+;[2,4,2,4];{-}), (0;+;[4];{(4,4)}) ] Order 64 # 168 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 64 # 169 : Symmetric genus 25 Symmetric genus actions [ (0;+;[2,4,4,4];{-}), (0;+;[4,4];{(2)}) ] Order 64 # 170 : Symmetric genus 25 Symmetric genus actions [ (0;+;[2,4,4,4];{-}), (0;+;[4,4];{(2)}) ] Order 64 # 171 : Symmetric genus 17 Symmetric genus actions [ (0;+;[2,2,4,4];{-}), (0;+;[2,4,2,4];{-}), (0;+;[4];{(4,4)}) ] Order 64 # 172 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 64 # 173 : Symmetric genus 17 Symmetric genus actions [ (0;+;[2,2,4,4];{-}), (0;+;[2,4,2,4];{-}), (0;+;[4];{(4,4)}) ] Order 64 # 174 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2,2,2];{-}) ] Order 64 # 175 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}) ] Order 64 # 176 : Symmetric genus 17 Symmetric genus actions [ (0;+;[2,4,2,4];{-}), (0;+;[2,2,4,4];{-}), (0;+;[2,4];{(2)}), (0;+;[-];{(2),(2)}) ] Order 64 # 177 : Symmetric genus 9 Symmetric genus actions [ (0;+;[2,2,4,2];{-}), (0;+;[2,2,2,4];{-}), (0;+;[-];{(4,8,8)}), (0;+;[2];{(4,4)}), (0;+;[2,2];{(2)}) ] Order 64 # 178 : Symmetric genus 25 Symmetric genus actions [ (0;+;[2,4,4,4];{-}), (0;+;[4,4];{(2)}) ] Order 64 # 179 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 64 # 180 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 64 # 181 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 64 # 182 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 64 # 183 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 64 # 184 : Symmetric genus 9 Symmetric genus actions [ (0;+;[-];{(1),(2)}) ] Order 64 # 185 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 64 # 186 : Symmetric genus 0 Symmetric genus actions [ (0;+;[-];{(2,2,16)}) ] Order 64 # 187 : Symmetric genus 9 Symmetric genus actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 64 # 188 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 64 # 189 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}), (0;+;[-];{(1),(1)}) ] Order 64 # 190 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2];{(2,2)}), (0;+;[2,2];{(1)}) ] Order 64 # 191 : Symmetric genus 15 Symmetric genus actions [ (0;+;[2,16];{(1)}), (0;+;[-];{(1),(8)}) ] Order 64 # 192 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 193 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4];{(2,2,2)}), (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 194 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 195 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 196 : Symmetric genus 17 Symmetric genus actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 197 : Symmetric genus 41 Symmetric genus actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 198 : Symmetric genus 17 Symmetric genus actions [ (0;+;[2];{(1),(1)}) ] Order 64 # 199 : Symmetric genus 17 Symmetric genus actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 200 : Symmetric genus 41 Symmetric genus actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 201 : Symmetric genus 17 Symmetric genus actions [ (0;+;[2];{(1),(1)}) ] Order 64 # 202 : Symmetric genus 5 Symmetric genus actions [ (0;+;[-];{(2,2,4,2)}), (0;+;[-];{(2,2,2,4)}) ] Order 64 # 203 : Symmetric genus 9 Symmetric genus actions [ (0;+;[-];{(2,2,4,4)}) ] Order 64 # 204 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 205 : Symmetric genus 17 Symmetric genus actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 206 : Symmetric genus 13 Symmetric genus actions [ (0;+;[-];{(2,4,4,4)}) ] Order 64 # 207 : Symmetric genus 21 Symmetric genus actions [ (0;+;[4];{(2,2,4)}) ] Order 64 # 208 : Symmetric genus 41 Symmetric genus actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 209 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,4];{(2,2)}), (0;+;[2,4,4];{(1)}), (0;+;[4];{(1),(2)}) ] Order 64 # 210 : Symmetric genus 17 Symmetric genus actions [ (0;+;[2];{(1),(1)}) ] Order 64 # 211 : Symmetric genus 9 Symmetric genus actions [ (0;+;[-];{(2,2,4,4)}) ] Order 64 # 212 : Symmetric genus 41 Symmetric genus actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 213 : Symmetric genus 17 Symmetric genus actions [ (0;+;[-];{(4,4,4,4)}), (0;+;[2,2,2];{(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 214 : Symmetric genus 41 Symmetric genus actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 215 : Symmetric genus 5 Symmetric genus actions [ (0;+;[-];{(2,2,4,2)}), (0;+;[-];{(2,2,2,4)}) ] Order 64 # 216 : Symmetric genus 9 Symmetric genus actions [ (0;+;[-];{(2,2,4,4)}) ] Order 64 # 217 : Symmetric genus 25 Symmetric genus actions [ (0;+;[2,2,4];{(1)}), (0;+;[-];{(4,4),(1)}), (0;+;[2];{(1),(2)}), (0;+;[4];{(1),(1)}) ] Order 64 # 218 : Symmetric genus 17 Symmetric genus actions [ (0;+;[-];{(4,4,4,4)}), (0;+;[2,2,2,2,2];{-}), (0;+;[2];{(1),(1)}) ] Order 64 # 219 : Symmetric genus 13 Symmetric genus actions [ (0;+;[-];{(2,4,4,4)}) ] Order 64 # 220 : Symmetric genus 17 Symmetric genus actions [ (0;+;[2];{(1),(1)}) ] Order 64 # 221 : Symmetric genus 17 Symmetric genus actions [ (0;+;[-];{(4,4,4,4)}), (0;+;[2,2,2];{(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 222 : Symmetric genus 41 Symmetric genus actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 223 : Symmetric genus 25 Symmetric genus actions [ (0;+;[2,2,4];{(1)}), (0;+;[-];{(4,4),(1)}), (0;+;[4];{(1),(1)}), (0;+;[2];{(1),(2)}) ] Order 64 # 224 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 225 : Symmetric genus 41 Symmetric genus actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 226 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,2,2,2)}) ] Order 64 # 227 : Symmetric genus 9 Symmetric genus actions [ (0;+;[-];{(2,2,4,4)}) ] Order 64 # 228 : Symmetric genus 17 Symmetric genus actions [ (0;+;[-];{(4,4,4,4)}), (0;+;[2];{(1),(1)}) ] Order 64 # 229 : Symmetric genus 17 Symmetric genus actions [ (0;+;[-];{(4,4,4,4)}), (0;+;[2];{(1),(1)}) ] Order 64 # 230 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 231 : Symmetric genus 17 Symmetric genus actions [ (0;+;[-];{(4,4,4,4)}), (0;+;[2,2,2];{(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 232 : Symmetric genus 17 Symmetric genus actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 233 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 234 : Symmetric genus 17 Symmetric genus actions [ (0;+;[-];{(4,4,4,4)}), (0;+;[2,2,2];{(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 235 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 236 : Symmetric genus 17 Symmetric genus actions [ (0;+;[-];{(4,4,4,4)}) ] Order 64 # 237 : Symmetric genus 33 Symmetric genus actions [ (0;+;[2,4,4];{(1)}), (0;+;[4];{(1),(2)}), (1;-;[-];{(1),(1)}) ] Order 64 # 238 : Symmetric genus 57 Symmetric genus actions [ (0;+;[4,4,4,4,4];{-}) ] Order 64 # 239 : Symmetric genus 57 Symmetric genus actions [ (0;+;[4,4,4,4,4];{-}) ] Order 64 # 240 : Symmetric genus 17 Symmetric genus actions [ (0;+;[2];{(1),(1)}) ] Order 64 # 241 : Symmetric genus 13 Symmetric genus actions [ (0;+;[-];{(2,4,4,4)}) ] Order 64 # 242 : Symmetric genus 9 Symmetric genus actions [ (0;+;[-];{(2,4,2,4)}) ] Order 64 # 243 : Symmetric genus 17 Symmetric genus actions [ (0;+;[-];{(4,4,4,4)}), (0;+;[2];{(1),(1)}) ] Order 64 # 244 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 245 : Symmetric genus 57 Symmetric genus actions [ (0;+;[4,4,4,4,4];{-}) ] Order 64 # 246 : Symmetric genus 17 Symmetric genus actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 247 : Symmetric genus 17 Symmetric genus actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 248 : Symmetric genus 17 Symmetric genus actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 249 : Symmetric genus 17 Symmetric genus actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 250 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,2,2,2)}) ] Order 64 # 251 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4];{(2,2,2)}), (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 252 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 253 : Symmetric genus 9 Symmetric genus actions [ (0;+;[-];{(2,2,4,4)}) ] Order 64 # 254 : Symmetric genus 5 Symmetric genus actions [ (0;+;[-];{(2,2,4,2)}), (0;+;[-];{(2,2,2,4)}) ] Order 64 # 255 : Symmetric genus 17 Symmetric genus actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 256 : Symmetric genus 7 Symmetric genus actions [ (0;+;[-];{(2,2,8,2)}), (0;+;[-];{(2,2,2,8)}) ] Order 64 # 257 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,2,2,2)}) ] Order 64 # 258 : Symmetric genus 9 Symmetric genus actions [ (0;+;[-];{(2,2,4,4)}), (0;+;[2];{(2,2,2)}) ] Order 64 # 259 : Symmetric genus 17 Symmetric genus actions [ (0;+;[-];{(4,4,4,4)}), (0;+;[2];{(1),(1)}) ] Order 64 # 260 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4];{(2,2,2,2)}), (0;+;[-];{(2,2,2),(1)}) ] Order 64 # 261 : Symmetric genus 9 Symmetric genus actions [ (0;+;[-];{(2,2,2,2,2)}) ] Order 64 # 262 : Symmetric genus 33 Symmetric genus actions [ (0;+;[-];{(1),(1),(1)}) ] Order 64 # 263 : Symmetric genus 13 Symmetric genus actions [ (0;+;[-];{(2,2,2,4,2)}), (0;+;[-];{(2,2,2,2,4)}), (0;+;[-];{(2,2,4,2,2)}) ] Order 64 # 264 : Symmetric genus 9 Symmetric genus actions [ (0;+;[-];{(2,2,2,2,2)}) ] Order 64 # 265 : Symmetric genus 21 Symmetric genus actions [ (0;+;[-];{(2,2,4,4,4)}) ] Order 64 # 266 : Symmetric genus 9 Symmetric genus actions [ (0;+;[-];{(2,2,2,2,2)}) ] Order 64 # 267 : Symmetric genus 17 Symmetric genus actions [ (0;+;[-];{(2,2,2,2,2,2)}) ] ........................................................................... Groups of order 65 Total number of groups = 1 Order 65 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[65,65];{-}) ] ........................................................................... Groups of order 66 Total number of groups = 4 Order 66 # 1 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 66 # 2 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 66 # 3 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,33];{-}), (0;+;[-];{(33,33)}) ] Order 66 # 4 : Symmetric genus 0 Symmetric genus actions [ (0;+;[66,66];{-}), (0;+;[33];{(1)}), (1;-;[33];{-}) ] ........................................................................... Groups of order 67 Total number of groups = 1 Order 67 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[67,67];{-}) ] ........................................................................... Groups of order 68 Total number of groups = 5 Order 68 # 1 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 68 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[68,68];{-}), (1;-;[34];{-}) ] Order 68 # 3 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,4,4];{-}) ] Order 68 # 4 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,34];{-}), (0;+;[-];{(34,34)}), (0;+;[-];{(2,2,17)}), (0;+;[2];{(17)}) ] Order 68 # 5 : Symmetric genus 0 Symmetric genus actions [ (0;+;[34];{(1)}) ] ........................................................................... Groups of order 69 Total number of groups = 1 Order 69 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[69,69];{-}) ] ........................................................................... Groups of order 70 Total number of groups = 4 Order 70 # 1 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 70 # 2 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 70 # 3 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,35];{-}), (0;+;[-];{(35,35)}) ] Order 70 # 4 : Symmetric genus 0 Symmetric genus actions [ (0;+;[70,70];{-}), (0;+;[35];{(1)}), (1;-;[35];{-}) ] ........................................................................... Groups of order 71 Total number of groups = 1 Order 71 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[71,71];{-}) ] ........................................................................... Groups of order 72 Total number of groups = 50 Order 72 # 1 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 72 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[72,72];{-}), (1;-;[36];{-}) ] Order 72 # 3 : Symmetric genus 20 Symmetric genus actions [ (0;+;[4,9,9];{-}) ] Order 72 # 4 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 72 # 5 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 72 # 6 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,36];{-}), (0;+;[-];{(36,36)}), (0;+;[2];{(18)}) ] Order 72 # 7 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 72 # 8 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}), (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 72 # 9 : Symmetric genus 0 Symmetric genus actions [ (0;+;[36];{(1)}) ] Order 72 # 10 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 72 # 11 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 72 # 12 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 72 # 13 : Symmetric genus 40 Symmetric genus actions [ (0;+;[3,3,8,8];{-}), (0;+;[3,8,3,8];{-}) ] Order 72 # 14 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] Order 72 # 15 : Symmetric genus 6 Symmetric genus actions [ (0;+;[2,4,9];{-}), (0;+;[-];{(2,9,9)}) ] Order 72 # 16 : Symmetric genus 6 Symmetric genus actions [ (0;+;[9];{(2)}) ] Order 72 # 17 : Symmetric genus 0 Symmetric genus actions [ (0;+;[-];{(2,2,18)}) ] Order 72 # 18 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 72 # 19 : Symmetric genus 16 Symmetric genus actions [ (0;+;[3,8,8];{-}), (1;-;[3,4];{-}) ] Order 72 # 20 : Symmetric genus 16 Symmetric genus actions [ (0;+;[3,4];{(1)}) ] Order 72 # 21 : Symmetric genus 1 Symmetric genus actions [ (1;-;[2,2];{-}) ] Order 72 # 22 : Symmetric genus 16 Symmetric genus actions [ (0;+;[4,6,6];{-}), (0;+;[2,3,2,4];{-}), (0;+;[2,2,3,4];{-}), (0;+;[2,2,4,3];{-}), (0;+;[-];{(3,4,3,4)}), (0;+;[3];{(4,4)}) ] Order 72 # 23 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}), (1;-;[2,2];{-}) ] Order 72 # 24 : Symmetric genus 19 Symmetric genus actions [ (1;-;[4,4];{-}) ] Order 72 # 25 : Symmetric genus 7 Symmetric genus actions [ (0;+;[3,3,6];{-}) ] Order 72 # 26 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 72 # 27 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}) ] Order 72 # 28 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 72 # 29 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 72 # 30 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}) ] Order 72 # 31 : Symmetric genus 37 Symmetric genus actions [ (0;+;[4,4,4,4];{-}) ] Order 72 # 32 : Symmetric genus 16 Symmetric genus actions [ (0;+;[4];{(3,3)}) ] Order 72 # 33 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2,2,2];{-}) ] Order 72 # 34 : Symmetric genus 37 Symmetric genus actions [ (0;+;[3,4,6,4];{-}), (0;+;[3,4,4,6];{-}), (0;+;[4,4,4,4];{-}) ] Order 72 # 35 : Symmetric genus 16 Symmetric genus actions [ (0;+;[-];{(3,3,4,4)}) ] Order 72 # 36 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] Order 72 # 37 : Symmetric genus 19 Symmetric genus actions [ (1;+;[2];{-}) ] Order 72 # 38 : Symmetric genus 19 Symmetric genus actions [ (1;+;[2];{-}) ] Order 72 # 39 : Symmetric genus 10 Symmetric genus actions [ (0;+;[2,8,8];{-}), (1;-;[2,4];{-}) ] Order 72 # 40 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,4,4)}), (0;+;[4];{(2)}) ] Order 72 # 41 : Symmetric genus 10 Symmetric genus actions [ (0;+;[4,4,4];{-}) ] Order 72 # 42 : Symmetric genus 1 Symmetric genus actions [ (0;+;[3];{(3)}) ] Order 72 # 43 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(3,3,3)}) ] Order 72 # 44 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,3,6];{-}) ] Order 72 # 45 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,4,4];{-}) ] Order 72 # 46 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,2,2,2)}), (0;+;[2];{(2,2)}), (0;+;[2,2];{(1)}) ] Order 72 # 47 : Symmetric genus 13 Symmetric genus actions [ (0;+;[3,6,6];{-}), (0;+;[3,3];{(1)}), (1;-;[3,3];{-}) ] Order 72 # 48 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 72 # 49 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2,2,2];{-}) ] Order 72 # 50 : Symmetric genus 25 Symmetric genus actions [ (0;+;[6,6];{(1)}), (0;+;[3];{(1),(1)}) ] ........................................................................... Groups of order 73 Total number of groups = 1 Order 73 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[73,73];{-}) ] ........................................................................... Groups of order 74 Total number of groups = 2 Order 74 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,37];{-}), (0;+;[-];{(37,37)}) ] Order 74 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[74,74];{-}), (0;+;[37];{(1)}), (1;-;[37];{-}) ] ........................................................................... Groups of order 75 Total number of groups = 3 Order 75 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[75,75];{-}) ] Order 75 # 2 : Symmetric genus 1 Symmetric genus actions [ (0;+;[3,3,3];{-}) ] Order 75 # 3 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] ........................................................................... Groups of order 76 Total number of groups = 4 Order 76 # 1 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 76 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[76,76];{-}), (1;-;[38];{-}) ] Order 76 # 3 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,38];{-}), (0;+;[-];{(38,38)}), (0;+;[-];{(2,2,19)}), (0;+;[2];{(19)}) ] Order 76 # 4 : Symmetric genus 0 Symmetric genus actions [ (0;+;[38];{(1)}) ] ........................................................................... Groups of order 77 Total number of groups = 1 Order 77 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[77,77];{-}) ] ........................................................................... Groups of order 78 Total number of groups = 6 Order 78 # 1 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,3,6];{-}) ] Order 78 # 2 : Symmetric genus 14 Symmetric genus actions [ (0;+;[3,6,6];{-}), (0;+;[3,3];{(1)}), (1;-;[3,3];{-}) ] Order 78 # 3 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 78 # 4 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 78 # 5 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,39];{-}), (0;+;[-];{(39,39)}) ] Order 78 # 6 : Symmetric genus 0 Symmetric genus actions [ (0;+;[78,78];{-}), (0;+;[39];{(1)}), (1;-;[39];{-}) ] ........................................................................... Groups of order 79 Total number of groups = 1 Order 79 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[79,79];{-}) ] ........................................................................... Groups of order 80 Total number of groups = 52 Order 80 # 1 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 80 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[80,80];{-}), (1;-;[40];{-}) ] Order 80 # 3 : Symmetric genus 28 Symmetric genus actions [ (0;+;[5,16,16];{-}), (1;-;[5,8];{-}) ] Order 80 # 4 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}) ] Order 80 # 5 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}) ] Order 80 # 6 : Symmetric genus 1 Symmetric genus actions [ (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 80 # 7 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,40];{-}), (0;+;[-];{(40,40)}), (0;+;[2];{(20)}) ] Order 80 # 8 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 80 # 9 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 80 # 10 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 80 # 11 : Symmetric genus 19 Symmetric genus actions [ (0;+;[4,4,20];{-}) ] Order 80 # 12 : Symmetric genus 19 Symmetric genus actions [ (0;+;[4,4,20];{-}) ] Order 80 # 13 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 80 # 14 : Symmetric genus 1 Symmetric genus actions [ (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 80 # 15 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}), (1;-;[2,2];{-}) ] Order 80 # 16 : Symmetric genus 21 Symmetric genus actions [ (0;+;[4,4];{(1)}), (1;-;[4,4];{-}) ] Order 80 # 17 : Symmetric genus 1 Symmetric genus actions [ (1;-;[2,2];{-}) ] Order 80 # 18 : Symmetric genus 21 Symmetric genus actions [ (1;-;[4,4];{-}) ] Order 80 # 19 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,4,10];{-}) ] Order 80 # 20 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] Order 80 # 21 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}) ] Order 80 # 22 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 80 # 23 : Symmetric genus 0 Symmetric genus actions [ (0;+;[40];{(1)}) ] Order 80 # 24 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 80 # 25 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 80 # 26 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}) ] Order 80 # 27 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 80 # 28 : Symmetric genus 11 Symmetric genus actions [ (0;+;[2,8,8];{-}) ] Order 80 # 29 : Symmetric genus 11 Symmetric genus actions [ (0;+;[2,8,8];{-}) ] Order 80 # 30 : Symmetric genus 11 Symmetric genus actions [ (0;+;[4,4,4];{-}) ] Order 80 # 31 : Symmetric genus 11 Symmetric genus actions [ (0;+;[4,4,4];{-}) ] Order 80 # 32 : Symmetric genus 21 Symmetric genus actions [ (0;+;[4,8,8];{-}) ] Order 80 # 33 : Symmetric genus 21 Symmetric genus actions [ (0;+;[4,8,8];{-}) ] Order 80 # 34 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,4,4];{-}) ] Order 80 # 35 : Symmetric genus 21 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 80 # 36 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 80 # 37 : Symmetric genus 0 Symmetric genus actions [ (0;+;[-];{(2,2,20)}) ] Order 80 # 38 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}), (0;+;[-];{(1),(1)}) ] Order 80 # 39 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,2,2,2)}), (0;+;[2];{(2,2)}), (0;+;[2,2];{(1)}) ] Order 80 # 40 : Symmetric genus 17 Symmetric genus actions [ (0;+;[2,10];{(1)}), (0;+;[-];{(1),(5)}) ] Order 80 # 41 : Symmetric genus 21 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 80 # 42 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}) ] Order 80 # 43 : Symmetric genus 21 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 80 # 44 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}) ] Order 80 # 45 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 80 # 46 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 80 # 47 : Symmetric genus 29 Symmetric genus actions [ (0;+;[4,20];{(1)}) ] Order 80 # 48 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 80 # 49 : Symmetric genus 5 Symmetric genus actions [ (0;+;[2,5,5];{-}) ] Order 80 # 50 : Symmetric genus 11 Symmetric genus actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 80 # 51 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,2,2,2)}) ] Order 80 # 52 : Symmetric genus 21 Symmetric genus actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] ........................................................................... Groups of order 81 Total number of groups = 15 Order 81 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[81,81];{-}) ] Order 81 # 2 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] Order 81 # 3 : Symmetric genus 19 Symmetric genus actions [ (0;+;[3,9,9];{-}) ] Order 81 # 4 : Symmetric genus 28 Symmetric genus actions [ (0;+;[9,9,9];{-}), (1;+;[3];{-}) ] Order 81 # 5 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] Order 81 # 6 : Symmetric genus 25 Symmetric genus actions [ (0;+;[3,27,27];{-}) ] Order 81 # 7 : Symmetric genus 10 Symmetric genus actions [ (0;+;[3,3,9];{-}) ] Order 81 # 8 : Symmetric genus 19 Symmetric genus actions [ (0;+;[3,9,9];{-}) ] Order 81 # 9 : Symmetric genus 1 Symmetric genus actions [ (0;+;[3,3,3];{-}) ] Order 81 # 10 : Symmetric genus 28 Symmetric genus actions [ (0;+;[9,9,9];{-}), (1;+;[3];{-}) ] Order 81 # 11 : Symmetric genus 46 Symmetric genus actions [ (0;+;[3,3,9,9];{-}), (0;+;[3,9,3,9];{-}) ] Order 81 # 12 : Symmetric genus 28 Symmetric genus actions [ (0;+;[3,3,3,3];{-}) ] Order 81 # 13 : Symmetric genus 46 Symmetric genus actions [ (0;+;[3,3,9,9];{-}), (0;+;[3,9,3,9];{-}) ] Order 81 # 14 : Symmetric genus 46 Symmetric genus actions [ (0;+;[3,9,3,9];{-}), (0;+;[3,3,9,9];{-}) ] Order 81 # 15 : Symmetric genus 55 Symmetric genus actions [ (0;+;[3,3,3,3,3];{-}) ] ........................................................................... Groups of order 82 Total number of groups = 2 Order 82 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,41];{-}), (0;+;[-];{(41,41)}) ] Order 82 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[82,82];{-}), (0;+;[41];{(1)}), (1;-;[41];{-}) ] ........................................................................... Groups of order 83 Total number of groups = 1 Order 83 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[83,83];{-}) ] ........................................................................... Groups of order 84 Total number of groups = 15 Order 84 # 1 : Symmetric genus 15 Symmetric genus actions [ (0;+;[3,4,12];{-}) ] Order 84 # 2 : Symmetric genus 22 Symmetric genus actions [ (0;+;[3,12,12];{-}), (1;-;[3,6];{-}) ] Order 84 # 3 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 84 # 4 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 84 # 5 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 84 # 6 : Symmetric genus 0 Symmetric genus actions [ (0;+;[84,84];{-}), (1;-;[42];{-}) ] Order 84 # 7 : Symmetric genus 8 Symmetric genus actions [ (0;+;[2,6,6];{-}), (0;+;[3];{(2,2)}), (0;+;[2,3];{(1)}) ] Order 84 # 8 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,2,2,2)}), (0;+;[2];{(2,2)}), (0;+;[2,2];{(1)}), (1;-;[2,2];{-}) ] Order 84 # 9 : Symmetric genus 22 Symmetric genus actions [ (0;+;[6,6,6];{-}), (0;+;[3,6];{(1)}) ] Order 84 # 10 : Symmetric genus 18 Symmetric genus actions [ (0;+;[2,21,21];{-}) ] Order 84 # 11 : Symmetric genus 1 Symmetric genus actions [ (0;+;[3,3,3];{-}) ] Order 84 # 12 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 84 # 13 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 84 # 14 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,42];{-}), (0;+;[-];{(42,42)}), (0;+;[-];{(2,2,21)}), (0;+;[2];{(21)}) ] Order 84 # 15 : Symmetric genus 0 Symmetric genus actions [ (0;+;[42];{(1)}) ] ........................................................................... Groups of order 85 Total number of groups = 1 Order 85 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[85,85];{-}) ] ........................................................................... Groups of order 86 Total number of groups = 2 Order 86 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,43];{-}), (0;+;[-];{(43,43)}) ] Order 86 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[86,86];{-}), (0;+;[43];{(1)}), (1;-;[43];{-}) ] ........................................................................... Groups of order 87 Total number of groups = 1 Order 87 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[87,87];{-}) ] ........................................................................... Groups of order 88 Total number of groups = 12 Order 88 # 1 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 88 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[88,88];{-}), (1;-;[44];{-}) ] Order 88 # 3 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 88 # 4 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 88 # 5 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,44];{-}), (0;+;[-];{(44,44)}), (0;+;[2];{(22)}) ] Order 88 # 6 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 88 # 7 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}), (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 88 # 8 : Symmetric genus 0 Symmetric genus actions [ (0;+;[44];{(1)}) ] Order 88 # 9 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 88 # 10 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 88 # 11 : Symmetric genus 0 Symmetric genus actions [ (0;+;[-];{(2,2,22)}) ] Order 88 # 12 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] ........................................................................... Groups of order 89 Total number of groups = 1 Order 89 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[89,89];{-}) ] ........................................................................... Groups of order 90 Total number of groups = 10 Order 90 # 1 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 90 # 2 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 90 # 3 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,45];{-}), (0;+;[-];{(45,45)}) ] Order 90 # 4 : Symmetric genus 0 Symmetric genus actions [ (0;+;[90,90];{-}), (0;+;[45];{(1)}), (1;-;[45];{-}) ] Order 90 # 5 : Symmetric genus 28 Symmetric genus actions [ (0;+;[6,6,15];{-}) ] Order 90 # 6 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 90 # 7 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 90 # 8 : Symmetric genus 28 Symmetric genus actions [ (0;+;[15];{(3,3)}) ] Order 90 # 9 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2,2,2];{-}) ] Order 90 # 10 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] ........................................................................... Groups of order 91 Total number of groups = 1 Order 91 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[91,91];{-}) ] ........................................................................... Groups of order 92 Total number of groups = 4 Order 92 # 1 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 92 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[92,92];{-}), (1;-;[46];{-}) ] Order 92 # 3 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,46];{-}), (0;+;[-];{(46,46)}), (0;+;[-];{(2,2,23)}), (0;+;[2];{(23)}) ] Order 92 # 4 : Symmetric genus 0 Symmetric genus actions [ (0;+;[46];{(1)}) ] ........................................................................... Groups of order 93 Total number of groups = 2 Order 93 # 1 : Symmetric genus 1 Symmetric genus actions [ (0;+;[3,3,3];{-}) ] Order 93 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[93,93];{-}) ] ........................................................................... Groups of order 94 Total number of groups = 2 Order 94 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,47];{-}), (0;+;[-];{(47,47)}) ] Order 94 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[94,94];{-}), (0;+;[47];{(1)}), (1;-;[47];{-}) ] ........................................................................... Groups of order 95 Total number of groups = 1 Order 95 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[95,95];{-}) ] ........................................................................... Groups of order 96 Total number of groups = 231 Order 96 # 1 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 96 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[96,96];{-}), (1;-;[48];{-}) ] Order 96 # 3 : Symmetric genus 5 Symmetric genus actions [ (0;+;[3,3,4];{-}) ] Order 96 # 4 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}) ] Order 96 # 5 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}) ] Order 96 # 6 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,48];{-}), (0;+;[-];{(48,48)}), (0;+;[2];{(24)}) ] Order 96 # 7 : Symmetric genus 1 Symmetric genus actions [ (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 96 # 8 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 96 # 9 : Symmetric genus 25 Symmetric genus actions [ (2;-;[2];{-}) ] Order 96 # 10 : Symmetric genus 25 Symmetric genus actions [ (2;-;[2];{-}) ] Order 96 # 11 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 96 # 12 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}) ] Order 96 # 13 : Symmetric genus 9 Symmetric genus actions [ (0;+;[2,4,12];{-}), (0;+;[4];{(6)}) ] Order 96 # 14 : Symmetric genus 25 Symmetric genus actions [ (1;-;[4,4];{-}) ] Order 96 # 15 : Symmetric genus 25 Symmetric genus actions [ (1;-;[4,4];{-}) ] Order 96 # 16 : Symmetric genus 1 Symmetric genus actions [ (1;-;[2,2];{-}) ] Order 96 # 17 : Symmetric genus 25 Symmetric genus actions [ (1;-;[4,4];{-}) ] Order 96 # 18 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 96 # 19 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 96 # 20 : Symmetric genus 25 Symmetric genus actions [ (1;-;[4,4];{-}) ] Order 96 # 21 : Symmetric genus 25 Symmetric genus actions [ (1;-;[4,4];{-}) ] Order 96 # 22 : Symmetric genus 25 Symmetric genus actions [ (1;-;[4,4];{-}) ] Order 96 # 23 : Symmetric genus 23 Symmetric genus actions [ (0;+;[4,4,24];{-}) ] Order 96 # 24 : Symmetric genus 23 Symmetric genus actions [ (0;+;[4,4,24];{-}) ] Order 96 # 25 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 96 # 26 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 96 # 27 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}) ] Order 96 # 28 : Symmetric genus 1 Symmetric genus actions [ (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 96 # 29 : Symmetric genus 25 Symmetric genus actions [ (2;-;[2];{-}) ] Order 96 # 30 : Symmetric genus 1 Symmetric genus actions [ (1;-;[2,2];{-}) ] Order 96 # 31 : Symmetric genus 25 Symmetric genus actions [ (1;-;[4,4];{-}) ] Order 96 # 32 : Symmetric genus 11 Symmetric genus actions [ (0;+;[2,4,24];{-}), (0;+;[4];{(12)}) ] Order 96 # 33 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}), (1;-;[2,2];{-}) ] Order 96 # 34 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4,4];{(1)}), (1;-;[4,4];{-}) ] Order 96 # 35 : Symmetric genus 1 Symmetric genus actions [ (1;-;[2,2];{-}) ] Order 96 # 36 : Symmetric genus 25 Symmetric genus actions [ (1;-;[4,4];{-}) ] Order 96 # 37 : Symmetric genus 25 Symmetric genus actions [ (2;-;[2];{-}) ] Order 96 # 38 : Symmetric genus 21 Symmetric genus actions [ (0;+;[4,4,12];{-}) ] Order 96 # 39 : Symmetric genus 23 Symmetric genus actions [ (0;+;[4,6,8];{-}) ] Order 96 # 40 : Symmetric genus 25 Symmetric genus actions [ (2;-;[2];{-}) ] Order 96 # 41 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,4,6];{-}) ] Order 96 # 42 : Symmetric genus 25 Symmetric genus actions [ (1;-;[4,4];{-}) ] Order 96 # 43 : Symmetric genus 25 Symmetric genus actions [ (2;-;[2];{-}) ] Order 96 # 44 : Symmetric genus 23 Symmetric genus actions [ (0;+;[4,6,8];{-}) ] Order 96 # 45 : Symmetric genus 25 Symmetric genus actions [ (1;+;[2];{-}), (2;-;[2];{-}) ] Order 96 # 46 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] Order 96 # 47 : Symmetric genus 25 Symmetric genus actions [ (1;+;[2];{-}), (2;-;[2];{-}) ] Order 96 # 48 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}) ] Order 96 # 49 : Symmetric genus 9 Symmetric genus actions [ (0;+;[12];{(2)}) ] Order 96 # 50 : Symmetric genus 11 Symmetric genus actions [ (0;+;[24];{(2)}) ] Order 96 # 51 : Symmetric genus 25 Symmetric genus actions [ (1;+;[2];{-}), (2;-;[2];{-}) ] Order 96 # 52 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}) ] Order 96 # 53 : Symmetric genus 25 Symmetric genus actions [ (2;-;[2];{-}) ] Order 96 # 54 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}) ] Order 96 # 55 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 96 # 56 : Symmetric genus 25 Symmetric genus actions [ (2;-;[2];{-}) ] Order 96 # 57 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 96 # 58 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 96 # 59 : Symmetric genus 0 Symmetric genus actions [ (0;+;[48];{(1)}) ] Order 96 # 60 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 96 # 61 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 96 # 62 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}) ] Order 96 # 63 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 96 # 64 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(3,3,3)}), (0;+;[3];{(3)}) ] Order 96 # 65 : Symmetric genus 21 Symmetric genus actions [ (0;+;[3,8,8];{-}) ] Order 96 # 66 : Symmetric genus 15 Symmetric genus actions [ (0;+;[3,4,8];{-}) ] Order 96 # 67 : Symmetric genus 9 Symmetric genus actions [ (0;+;[3,4,4];{-}) ] Order 96 # 68 : Symmetric genus 13 Symmetric genus actions [ (0;+;[3,4,6];{-}) ] Order 96 # 69 : Symmetric genus 17 Symmetric genus actions [ (0;+;[3,4,12];{-}) ] Order 96 # 70 : Symmetric genus 9 Symmetric genus actions [ (0;+;[2,6,6];{-}), (0;+;[2,3];{(1)}), (1;-;[2,3];{-}) ] Order 96 # 71 : Symmetric genus 13 Symmetric genus actions [ (0;+;[3,4,6];{-}) ] Order 96 # 72 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,3,6];{-}) ] Order 96 # 73 : Symmetric genus 21 Symmetric genus actions [ (0;+;[2,24,24];{-}), (1;-;[2,12];{-}), (1;-;[3,4];{-}) ] Order 96 # 74 : Symmetric genus 9 Symmetric genus actions [ (1;-;[2,3];{-}) ] Order 96 # 75 : Symmetric genus 49 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 96 # 76 : Symmetric genus 49 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 96 # 77 : Symmetric genus 49 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 96 # 78 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 96 # 79 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 96 # 80 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 96 # 81 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2,2,2];{-}) ] Order 96 # 82 : Symmetric genus 25 Symmetric genus actions [ (0;+;[2,2,4,4];{-}), (0;+;[2,4,2,4];{-}), (0;+;[2,4];{(2)}), (0;+;[-];{(2),(2)}) ] Order 96 # 83 : Symmetric genus 37 Symmetric genus actions [ (0;+;[2,4,4,4];{-}), (0;+;[4,4];{(2)}) ] Order 96 # 84 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,12];{(1)}) ] Order 96 # 85 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,12];{(1)}) ] Order 96 # 86 : Symmetric genus 37 Symmetric genus actions [ (0;+;[4,4];{(2)}) ] Order 96 # 87 : Symmetric genus 13 Symmetric genus actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}), (0;+;[-];{(1),(2)}) ] Order 96 # 88 : Symmetric genus 17 Symmetric genus actions [ (0;+;[-];{(1),(3)}) ] Order 96 # 89 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2];{(2,2)}) ] Order 96 # 90 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4];{(4,4)}), (0;+;[2,4];{(2)}), (0;+;[4,4];{(1)}) ] Order 96 # 91 : Symmetric genus 11 Symmetric genus actions [ (0;+;[-];{(4,4,12)}) ] Order 96 # 92 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4];{(4,4)}), (0;+;[2,4];{(2)}) ] Order 96 # 93 : Symmetric genus 21 Symmetric genus actions [ (0;+;[2,12];{(1)}), (0;+;[-];{(1),(6)}) ] Order 96 # 94 : Symmetric genus 49 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 96 # 95 : Symmetric genus 49 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 96 # 96 : Symmetric genus 49 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 96 # 97 : Symmetric genus 49 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 96 # 98 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 96 # 99 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 96 # 100 : Symmetric genus 13 Symmetric genus actions [ (0;+;[2,4];{(1)}), (0;+;[-];{(1),(2)}) ] Order 96 # 101 : Symmetric genus 13 Symmetric genus actions [ (0;+;[2,4];{(1)}), (0;+;[-];{(1),(2)}) ] Order 96 # 102 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}) ] Order 96 # 103 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 96 # 104 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 96 # 105 : Symmetric genus 37 Symmetric genus actions [ (0;+;[2,4,4,4];{-}), (0;+;[4,4];{(2)}) ] Order 96 # 106 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 96 # 107 : Symmetric genus 19 Symmetric genus actions [ (0;+;[8];{(2,2)}), (0;+;[2,8];{(1)}) ] Order 96 # 108 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 96 # 109 : Symmetric genus 13 Symmetric genus actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 96 # 110 : Symmetric genus 0 Symmetric genus actions [ (0;+;[-];{(2,2,24)}) ] Order 96 # 111 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}), (0;+;[-];{(1),(1)}) ] Order 96 # 112 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 96 # 113 : Symmetric genus 13 Symmetric genus actions [ (0;+;[-];{(1),(2)}) ] Order 96 # 114 : Symmetric genus 13 Symmetric genus actions [ (0;+;[-];{(1),(2)}) ] Order 96 # 115 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2];{(2,2)}), (0;+;[2,2];{(1)}) ] Order 96 # 116 : Symmetric genus 23 Symmetric genus actions [ (0;+;[2,24];{(1)}), (0;+;[-];{(1),(12)}) ] Order 96 # 117 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,2,2,2)}), (0;+;[2];{(2,2)}), (0;+;[2,2];{(1)}) ] Order 96 # 118 : Symmetric genus 12 Symmetric genus actions [ (0;+;[-];{(4,6,8)}) ] Order 96 # 119 : Symmetric genus 25 Symmetric genus actions [ (0;+;[-];{(4,4,4,4)}), (0;+;[4];{(4,4)}), (0;+;[4,4];{(1)}), (1;-;[2];{(1)}) ] Order 96 # 120 : Symmetric genus 13 Symmetric genus actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 96 # 121 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2];{(2,2)}) ] Order 96 # 122 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4];{(4,4)}), (1;-;[2];{(1)}) ] Order 96 # 123 : Symmetric genus 13 Symmetric genus actions [ (0;+;[2];{(4,4)}), (0;+;[2,4];{(1)}) ] Order 96 # 124 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 96 # 125 : Symmetric genus 19 Symmetric genus actions [ (0;+;[2,8];{(1)}), (0;+;[-];{(1),(4)}) ] Order 96 # 126 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}) ] Order 96 # 127 : Symmetric genus 33 Symmetric genus actions [ (0;+;[3];{(1),(1)}) ] Order 96 # 128 : Symmetric genus 35 Symmetric genus actions [ (0;+;[6,8];{(1)}) ] Order 96 # 129 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 96 # 130 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 96 # 131 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 96 # 132 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 96 # 133 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 96 # 134 : Symmetric genus 13 Symmetric genus actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 96 # 135 : Symmetric genus 13 Symmetric genus actions [ (0;+;[2,4];{(1)}) ] Order 96 # 136 : Symmetric genus 13 Symmetric genus actions [ (0;+;[2,4];{(1)}) ] Order 96 # 137 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}) ] Order 96 # 138 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}) ] Order 96 # 139 : Symmetric genus 13 Symmetric genus actions [ (0;+;[2,4];{(1)}) ] Order 96 # 140 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 96 # 141 : Symmetric genus 29 Symmetric genus actions [ (0;+;[4,6];{(1)}) ] Order 96 # 142 : Symmetric genus 29 Symmetric genus actions [ (0;+;[4,6];{(1)}) ] Order 96 # 143 : Symmetric genus 37 Symmetric genus actions [ (0;+;[4,4];{(2)}) ] Order 96 # 144 : Symmetric genus 9 Symmetric genus actions [ (0;+;[-];{(4,4,6)}) ] Order 96 # 145 : Symmetric genus 23 Symmetric genus actions [ (0;+;[-];{(3,4,4,4)}) ] Order 96 # 146 : Symmetric genus 17 Symmetric genus actions [ (0;+;[2,6];{(1)}) ] Order 96 # 147 : Symmetric genus 11 Symmetric genus actions [ (0;+;[-];{(4,4,12)}) ] Order 96 # 148 : Symmetric genus 19 Symmetric genus actions [ (0;+;[8];{(2,2)}), (0;+;[2,8];{(1)}) ] Order 96 # 149 : Symmetric genus 19 Symmetric genus actions [ (0;+;[2,8];{(1)}) ] Order 96 # 150 : Symmetric genus 31 Symmetric genus actions [ (0;+;[4,8];{(1)}) ] Order 96 # 151 : Symmetric genus 49 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 96 # 152 : Symmetric genus 49 Symmetric genus actions [ (0;+;[4,4,4,4];{-}), (3;-;[-];{-}) ] Order 96 # 153 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 96 # 154 : Symmetric genus 25 Symmetric genus actions [ (0;+;[2,2,4,4];{-}), (0;+;[2,4,2,4];{-}), (0;+;[2,4];{(2)}), (0;+;[-];{(2),(2)}) ] Order 96 # 155 : Symmetric genus 33 Symmetric genus actions [ (0;+;[3];{(1),(1)}) ] Order 96 # 156 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}) ] Order 96 # 157 : Symmetric genus 13 Symmetric genus actions [ (0;+;[2,4];{(1)}) ] Order 96 # 158 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 96 # 159 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 96 # 160 : Symmetric genus 13 Symmetric genus actions [ (0;+;[2,4];{(1)}) ] Order 96 # 161 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,12];{(1)}) ] Order 96 # 162 : Symmetric genus 13 Symmetric genus actions [ (0;+;[-];{(1),(2)}) ] Order 96 # 163 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,12];{(1)}) ] Order 96 # 164 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,12];{(1)}) ] Order 96 # 165 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 96 # 166 : Symmetric genus 49 Symmetric genus actions [ (3;-;[-];{-}) ] Order 96 # 167 : Symmetric genus 13 Symmetric genus actions [ (0;+;[-];{(1),(2)}) ] Order 96 # 168 : Symmetric genus 13 Symmetric genus actions [ (0;+;[-];{(1),(2)}) ] Order 96 # 169 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,12];{(1)}) ] Order 96 # 170 : Symmetric genus 13 Symmetric genus actions [ (0;+;[-];{(1),(2)}) ] Order 96 # 171 : Symmetric genus 25 Symmetric genus actions [ (0;+;[-];{(2),(2)}) ] Order 96 # 172 : Symmetric genus 49 Symmetric genus actions [ (3;-;[-];{-}) ] Order 96 # 173 : Symmetric genus 45 Symmetric genus actions [ (0;+;[4,12];{(2)}) ] Order 96 # 174 : Symmetric genus 25 Symmetric genus actions [ (0;+;[-];{(2),(2)}) ] Order 96 # 175 : Symmetric genus 49 Symmetric genus actions [ (3;-;[-];{-}) ] Order 96 # 176 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 96 # 177 : Symmetric genus 13 Symmetric genus actions [ (0;+;[-];{(1),(2)}) ] Order 96 # 178 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 96 # 179 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 96 # 180 : Symmetric genus 19 Symmetric genus actions [ (0;+;[-];{(1),(4)}) ] Order 96 # 181 : Symmetric genus 33 Symmetric genus actions [ (0;+;[4,12];{(1)}) ] Order 96 # 182 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 96 # 183 : Symmetric genus 13 Symmetric genus actions [ (0;+;[-];{(1),(2)}) ] Order 96 # 184 : Symmetric genus 19 Symmetric genus actions [ (0;+;[-];{(1),(4)}) ] Order 96 # 185 : Symmetric genus 21 Symmetric genus actions [ (0;+;[4,4,12];{-}) ] Order 96 # 186 : Symmetric genus 5 Symmetric genus actions [ (0;+;[4];{(3)}) ] Order 96 # 187 : Symmetric genus 5 Symmetric genus actions [ (0;+;[2];{(2,3)}) ] Order 96 # 188 : Symmetric genus 21 Symmetric genus actions [ (0;+;[3,4];{(1)}) ] Order 96 # 189 : Symmetric genus 7 Symmetric genus actions [ (0;+;[-];{(3,4,6)}) ] Order 96 # 190 : Symmetric genus 9 Symmetric genus actions [ (0;+;[6];{(3)}) ] Order 96 # 191 : Symmetric genus 21 Symmetric genus actions [ (0;+;[3,4];{(1)}) ] Order 96 # 192 : Symmetric genus 8 Symmetric genus actions [ (0;+;[-];{(3,4,8)}) ] Order 96 # 193 : Symmetric genus 2 Symmetric genus actions [ (0;+;[-];{(2,3,8)}) ] Order 96 # 194 : Symmetric genus 17 Symmetric genus actions [ (0;+;[4,4,6];{-}) ] Order 96 # 195 : Symmetric genus 5 Symmetric genus actions [ (0;+;[2,4,6];{-}), (0;+;[-];{(3,4,4)}) ] Order 96 # 196 : Symmetric genus 9 Symmetric genus actions [ (0;+;[12];{(2)}) ] Order 96 # 197 : Symmetric genus 5 Symmetric genus actions [ (0;+;[6];{(2)}) ] Order 96 # 198 : Symmetric genus 21 Symmetric genus actions [ (0;+;[4,6,6];{-}), (0;+;[3,4];{(1)}) ] Order 96 # 199 : Symmetric genus 25 Symmetric genus actions [ (1;+;[2];{-}), (2;-;[2];{-}) ] Order 96 # 200 : Symmetric genus 9 Symmetric genus actions [ (0;+;[3];{(2,2)}), (0;+;[2,3];{(1)}) ] Order 96 # 201 : Symmetric genus 9 Symmetric genus actions [ (0;+;[3];{(2,2)}) ] Order 96 # 202 : Symmetric genus 9 Symmetric genus actions [ (0;+;[2,6,6];{-}) ] Order 96 # 203 : Symmetric genus 25 Symmetric genus actions [ (0;+;[2,3,3,3];{-}) ] Order 96 # 204 : Symmetric genus 17 Symmetric genus actions [ (0;+;[2,2,3,3];{-}), (0;+;[2,3,2,3];{-}) ] Order 96 # 205 : Symmetric genus 37 Symmetric genus actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 206 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4];{(2,2,2)}), (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 207 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,2,2,2)}) ] Order 96 # 208 : Symmetric genus 13 Symmetric genus actions [ (0;+;[-];{(2,2,4,4)}) ] Order 96 # 209 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,2,2,2)}) ] Order 96 # 210 : Symmetric genus 25 Symmetric genus actions [ (0;+;[-];{(4,4,4,4)}), (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 211 : Symmetric genus 9 Symmetric genus actions [ (0;+;[-];{(2,2,6,2)}), (0;+;[-];{(2,2,2,6)}) ] Order 96 # 212 : Symmetric genus 37 Symmetric genus actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 213 : Symmetric genus 17 Symmetric genus actions [ (0;+;[-];{(2,2,12,4)}), (0;+;[-];{(2,2,4,12)}) ] Order 96 # 214 : Symmetric genus 25 Symmetric genus actions [ (0;+;[2,2,2,2,2];{-}), (0;+;[2];{(1),(1)}) ] Order 96 # 215 : Symmetric genus 13 Symmetric genus actions [ (0;+;[-];{(2,2,4,4)}) ] Order 96 # 216 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,2,2,2)}) ] Order 96 # 217 : Symmetric genus 25 Symmetric genus actions [ (0;+;[-];{(4,4,4,4)}), (0;+;[2];{(1),(1)}) ] Order 96 # 218 : Symmetric genus 37 Symmetric genus actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 219 : Symmetric genus 13 Symmetric genus actions [ (0;+;[-];{(2,2,4,4)}) ] Order 96 # 220 : Symmetric genus 25 Symmetric genus actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 221 : Symmetric genus 25 Symmetric genus actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 222 : Symmetric genus 37 Symmetric genus actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 223 : Symmetric genus 25 Symmetric genus actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 224 : Symmetric genus 25 Symmetric genus actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 225 : Symmetric genus 25 Symmetric genus actions [ (0;+;[2];{(1),(1)}) ] Order 96 # 226 : Symmetric genus 3 Symmetric genus actions [ (0;+;[-];{(2,4,6)}) ] Order 96 # 227 : Symmetric genus 9 Symmetric genus actions [ (0;+;[3,4,4];{-}), (0;+;[2,2,2,3];{-}), (0;+;[2,2,3,2];{-}), (0;+;[-];{(2,2,3,3)}), (0;+;[-];{(2,3,2,3)}), (0;+;[2];{(3,3)}) ] Order 96 # 228 : Symmetric genus 13 Symmetric genus actions [ (0;+;[-];{(1),(2)}) ] Order 96 # 229 : Symmetric genus 9 Symmetric genus actions [ (0;+;[3];{(2,2)}) ] Order 96 # 230 : Symmetric genus 13 Symmetric genus actions [ (0;+;[-];{(2,2,2,2,2)}) ] Order 96 # 231 : Symmetric genus 37 Symmetric genus actions [ (0;+;[-];{(2,2,2),(1)}) ] ........................................................................... Groups of order 97 Total number of groups = 1 Order 97 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[97,97];{-}) ] ........................................................................... Groups of order 98 Total number of groups = 5 Order 98 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,49];{-}), (0;+;[-];{(49,49)}) ] Order 98 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[98,98];{-}), (0;+;[49];{(1)}), (1;-;[49];{-}) ] Order 98 # 3 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 98 # 4 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2,2,2];{-}) ] Order 98 # 5 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] ........................................................................... Groups of order 99 Total number of groups = 2 Order 99 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[99,99];{-}) ] Order 99 # 2 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] ........................................................................... Groups of order 100 Total number of groups = 16 Order 100 # 1 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 100 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[100,100];{-}), (1;-;[50];{-}) ] Order 100 # 3 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,4,4];{-}) ] Order 100 # 4 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,50];{-}), (0;+;[-];{(50,50)}), (0;+;[-];{(2,2,25)}), (0;+;[2];{(25)}) ] Order 100 # 5 : Symmetric genus 0 Symmetric genus actions [ (0;+;[50];{(1)}) ] Order 100 # 6 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 100 # 7 : Symmetric genus 51 Symmetric genus actions [ (0;+;[4,4,4,4];{-}) ] Order 100 # 8 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] Order 100 # 9 : Symmetric genus 16 Symmetric genus actions [ (1;-;[2,5];{-}) ] Order 100 # 10 : Symmetric genus 16 Symmetric genus actions [ (0;+;[4,4,5];{-}) ] Order 100 # 11 : Symmetric genus 26 Symmetric genus actions [ (0;+;[2,4,2,4];{-}), (0;+;[2,2,4,4];{-}), (1;-;[2,2,2];{-}) ] Order 100 # 12 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,4,4];{-}) ] Order 100 # 13 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,2,2,2)}), (0;+;[2];{(2,2)}), (0;+;[2,2];{(1)}), (1;-;[2,2];{-}) ] Order 100 # 14 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 100 # 15 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2,2,2];{-}) ] Order 100 # 16 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] ........................................................................... Groups of order 101 Total number of groups = 1 Order 101 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[101,101];{-}) ] ........................................................................... Groups of order 102 Total number of groups = 4 Order 102 # 1 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 102 # 2 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 102 # 3 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,51];{-}), (0;+;[-];{(51,51)}) ] Order 102 # 4 : Symmetric genus 0 Symmetric genus actions [ (0;+;[102,102];{-}), (0;+;[51];{(1)}), (1;-;[51];{-}) ] ........................................................................... Groups of order 103 Total number of groups = 1 Order 103 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[103,103];{-}) ] ........................................................................... Groups of order 104 Total number of groups = 14 Order 104 # 1 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 104 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[104,104];{-}), (1;-;[52];{-}) ] Order 104 # 3 : Symmetric genus 27 Symmetric genus actions [ (0;+;[4,8,8];{-}) ] Order 104 # 4 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 104 # 5 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 104 # 6 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,52];{-}), (0;+;[-];{(52,52)}), (0;+;[2];{(26)}) ] Order 104 # 7 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 104 # 8 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}), (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 104 # 9 : Symmetric genus 0 Symmetric genus actions [ (0;+;[52];{(1)}) ] Order 104 # 10 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 104 # 11 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 104 # 12 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,4,4];{-}) ] Order 104 # 13 : Symmetric genus 0 Symmetric genus actions [ (0;+;[-];{(2,2,26)}) ] Order 104 # 14 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] ........................................................................... Groups of order 105 Total number of groups = 2 Order 105 # 1 : Symmetric genus 29 Symmetric genus actions [ (0;+;[3,15,15];{-}) ] Order 105 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[105,105];{-}) ] ........................................................................... Groups of order 106 Total number of groups = 2 Order 106 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,53];{-}), (0;+;[-];{(53,53)}) ] Order 106 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[106,106];{-}), (0;+;[53];{(1)}), (1;-;[53];{-}) ] ........................................................................... Groups of order 107 Total number of groups = 1 Order 107 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[107,107];{-}) ] ........................................................................... Groups of order 108 Total number of groups = 45 Order 108 # 1 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 108 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[108,108];{-}), (1;-;[54];{-}) ] Order 108 # 3 : Symmetric genus 24 Symmetric genus actions [ (0;+;[2,27,27];{-}) ] Order 108 # 4 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,54];{-}), (0;+;[-];{(54,54)}), (0;+;[-];{(2,2,27)}), (0;+;[2];{(27)}) ] Order 108 # 5 : Symmetric genus 0 Symmetric genus actions [ (0;+;[54];{(1)}) ] Order 108 # 6 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 108 # 7 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 108 # 8 : Symmetric genus 19 Symmetric genus actions [ (0;+;[3,4,12];{-}) ] Order 108 # 9 : Symmetric genus 31 Symmetric genus actions [ (0;+;[4,9,12];{-}) ] Order 108 # 10 : Symmetric genus 55 Symmetric genus actions [ (0;+;[4,4,4,4];{-}) ] Order 108 # 11 : Symmetric genus 46 Symmetric genus actions [ (0;+;[3,4,3,4];{-}), (0;+;[3,3,4,4];{-}) ] Order 108 # 12 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] Order 108 # 13 : Symmetric genus 28 Symmetric genus actions [ (0;+;[3,12,12];{-}), (1;-;[3,6];{-}) ] Order 108 # 14 : Symmetric genus 34 Symmetric genus actions [ (0;+;[3,36,36];{-}), (1;-;[3,18];{-}) ] Order 108 # 15 : Symmetric genus 10 Symmetric genus actions [ (0;+;[2,4,12];{-}), (0;+;[3,4,4];{-}), (1;-;[2,3];{-}) ] Order 108 # 16 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,2,2,2)}), (0;+;[2];{(2,2)}), (0;+;[2,2];{(1)}), (1;-;[2,2];{-}) ] Order 108 # 17 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,3,6)}) ] Order 108 # 18 : Symmetric genus 25 Symmetric genus actions [ (0;+;[3,9,9];{-}) ] Order 108 # 19 : Symmetric genus 25 Symmetric genus actions [ (0;+;[3,9,9];{-}) ] Order 108 # 20 : Symmetric genus 28 Symmetric genus actions [ (1;+;[2];{-}) ] Order 108 # 21 : Symmetric genus 34 Symmetric genus actions [ (0;+;[6,9,9];{-}) ] Order 108 # 22 : Symmetric genus 1 Symmetric genus actions [ (0;+;[3,3,3];{-}) ] Order 108 # 23 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 108 # 24 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 108 # 25 : Symmetric genus 10 Symmetric genus actions [ (0;+;[2,6,6];{-}), (0;+;[6];{(3)}), (0;+;[3];{(2,2)}), (0;+;[2,3];{(1)}) ] Order 108 # 26 : Symmetric genus 16 Symmetric genus actions [ (0;+;[2,6,18];{-}), (0;+;[6];{(9)}) ] Order 108 # 27 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2,2,2];{-}) ] Order 108 # 28 : Symmetric genus 10 Symmetric genus actions [ (0;+;[-];{(3,6,6)}), (0;+;[-];{(2,2,3,3)}), (0;+;[2];{(3,3)}) ] Order 108 # 29 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] Order 108 # 30 : Symmetric genus 28 Symmetric genus actions [ (0;+;[6,6,6];{-}), (0;+;[3,6];{(1)}) ] Order 108 # 31 : Symmetric genus 34 Symmetric genus actions [ (0;+;[3,18];{(1)}) ] Order 108 # 32 : Symmetric genus 28 Symmetric genus actions [ (0;+;[3,12,12];{-}), (1;-;[3,6];{-}) ] Order 108 # 33 : Symmetric genus 46 Symmetric genus actions [ (0;+;[3,3,4,4];{-}), (0;+;[3,4,3,4];{-}) ] Order 108 # 34 : Symmetric genus 82 Symmetric genus actions [ (0;+;[3,3,3,4,4];{-}), (0;+;[3,3,4,3,4];{-}), (0;+;[3,3,4,4,3];{-}), (0;+;[3,4,3,3,4];{-}) ] Order 108 # 35 : Symmetric genus 64 Symmetric genus actions [ (0;+;[3,3,12,12];{-}), (0;+;[3,12,3,12];{-}), (1;-;[3,3,6];{-}) ] Order 108 # 36 : Symmetric genus 10 Symmetric genus actions [ (1;-;[2,3];{-}) ] Order 108 # 37 : Symmetric genus 10 Symmetric genus actions [ (0;+;[3,4,4];{-}) ] Order 108 # 38 : Symmetric genus 10 Symmetric genus actions [ (0;+;[2,6,6];{-}), (0;+;[6];{(3)}), (0;+;[3];{(2,2)}), (0;+;[2,3];{(1)}) ] Order 108 # 39 : Symmetric genus 10 Symmetric genus actions [ (0;+;[-];{(3,6,6)}), (0;+;[-];{(2,2,3,3)}), (0;+;[2];{(3,3)}) ] Order 108 # 40 : Symmetric genus 10 Symmetric genus actions [ (0;+;[2,2,3,2];{-}), (0;+;[2,2,2,3];{-}), (0;+;[-];{(2,3,2,3)}) ] Order 108 # 41 : Symmetric genus 37 Symmetric genus actions [ (0;+;[3,3,3,3];{-}) ] Order 108 # 42 : Symmetric genus 28 Symmetric genus actions [ (0;+;[6,6,6];{-}), (0;+;[3,6];{(1)}) ] Order 108 # 43 : Symmetric genus 28 Symmetric genus actions [ (0;+;[2,2,3,6];{-}), (0;+;[2,2,6,3];{-}), (0;+;[2,3,2,6];{-}), (0;+;[3];{(6,6)}), (0;+;[6];{(3,3)}), (0;+;[2,3];{(3)}), (0;+;[3];{(2,2,3)}) ] Order 108 # 44 : Symmetric genus 28 Symmetric genus actions [ (0;+;[-];{(3,3,6,6)}), (0;+;[-];{(3,6,3,6)}), (0;+;[-];{(2,2,3,3,3)}), (0;+;[2];{(3,3,3)}) ] Order 108 # 45 : Symmetric genus 64 Symmetric genus actions [ (0;+;[3,6,6,6];{-}), (0;+;[3,3,6];{(1)}) ] ........................................................................... Groups of order 109 Total number of groups = 1 Order 109 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[109,109];{-}) ] ........................................................................... Groups of order 110 Total number of groups = 6 Order 110 # 1 : Symmetric genus 12 Symmetric genus actions [ (0;+;[2,5,10];{-}) ] Order 110 # 2 : Symmetric genus 34 Symmetric genus actions [ (0;+;[5,10,10];{-}), (0;+;[5,5];{(1)}), (1;-;[5,5];{-}) ] Order 110 # 3 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 110 # 4 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 110 # 5 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,55];{-}), (0;+;[-];{(55,55)}) ] Order 110 # 6 : Symmetric genus 0 Symmetric genus actions [ (0;+;[110,110];{-}), (0;+;[55];{(1)}), (1;-;[55];{-}) ] ........................................................................... Groups of order 111 Total number of groups = 2 Order 111 # 1 : Symmetric genus 1 Symmetric genus actions [ (0;+;[3,3,3];{-}) ] Order 111 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[111,111];{-}) ] ........................................................................... Groups of order 112 Total number of groups = 43 Order 112 # 1 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 112 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[112,112];{-}), (1;-;[56];{-}) ] Order 112 # 3 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}) ] Order 112 # 4 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}) ] Order 112 # 5 : Symmetric genus 1 Symmetric genus actions [ (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 112 # 6 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,56];{-}), (0;+;[-];{(56,56)}), (0;+;[2];{(28)}) ] Order 112 # 7 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 112 # 8 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 112 # 9 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 112 # 10 : Symmetric genus 27 Symmetric genus actions [ (0;+;[4,4,28];{-}) ] Order 112 # 11 : Symmetric genus 27 Symmetric genus actions [ (0;+;[4,4,28];{-}) ] Order 112 # 12 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 112 # 13 : Symmetric genus 1 Symmetric genus actions [ (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 112 # 14 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}), (1;-;[2,2];{-}) ] Order 112 # 15 : Symmetric genus 29 Symmetric genus actions [ (0;+;[4,4];{(1)}), (1;-;[4,4];{-}) ] Order 112 # 16 : Symmetric genus 1 Symmetric genus actions [ (1;-;[2,2];{-}) ] Order 112 # 17 : Symmetric genus 29 Symmetric genus actions [ (1;-;[4,4];{-}) ] Order 112 # 18 : Symmetric genus 25 Symmetric genus actions [ (0;+;[4,4,14];{-}) ] Order 112 # 19 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] Order 112 # 20 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}) ] Order 112 # 21 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 112 # 22 : Symmetric genus 0 Symmetric genus actions [ (0;+;[56];{(1)}) ] Order 112 # 23 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 112 # 24 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 112 # 25 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}) ] Order 112 # 26 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 112 # 27 : Symmetric genus 29 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 112 # 28 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 112 # 29 : Symmetric genus 0 Symmetric genus actions [ (0;+;[-];{(2,2,28)}) ] Order 112 # 30 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}), (0;+;[-];{(1),(1)}) ] Order 112 # 31 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,2,2,2)}), (0;+;[2];{(2,2)}), (0;+;[2,2];{(1)}) ] Order 112 # 32 : Symmetric genus 25 Symmetric genus actions [ (0;+;[2,14];{(1)}), (0;+;[-];{(1),(7)}) ] Order 112 # 33 : Symmetric genus 29 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 112 # 34 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}) ] Order 112 # 35 : Symmetric genus 29 Symmetric genus actions [ (0;+;[4,4];{(1)}) ] Order 112 # 36 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}) ] Order 112 # 37 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 112 # 38 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 112 # 39 : Symmetric genus 41 Symmetric genus actions [ (0;+;[4,28];{(1)}) ] Order 112 # 40 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 112 # 41 : Symmetric genus 7 Symmetric genus actions [ (0;+;[7];{(2)}) ] Order 112 # 42 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,2,2,2)}) ] Order 112 # 43 : Symmetric genus 29 Symmetric genus actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] ........................................................................... Groups of order 113 Total number of groups = 1 Order 113 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[113,113];{-}) ] ........................................................................... Groups of order 114 Total number of groups = 6 Order 114 # 1 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,3,6];{-}) ] Order 114 # 2 : Symmetric genus 20 Symmetric genus actions [ (0;+;[3,6,6];{-}), (0;+;[3,3];{(1)}), (1;-;[3,3];{-}) ] Order 114 # 3 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 114 # 4 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 114 # 5 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,57];{-}), (0;+;[-];{(57,57)}) ] Order 114 # 6 : Symmetric genus 0 Symmetric genus actions [ (0;+;[114,114];{-}), (0;+;[57];{(1)}), (1;-;[57];{-}) ] ........................................................................... Groups of order 115 Total number of groups = 1 Order 115 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[115,115];{-}) ] ........................................................................... Groups of order 116 Total number of groups = 5 Order 116 # 1 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 116 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[116,116];{-}), (1;-;[58];{-}) ] Order 116 # 3 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,4,4];{-}) ] Order 116 # 4 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,58];{-}), (0;+;[-];{(58,58)}), (0;+;[-];{(2,2,29)}), (0;+;[2];{(29)}) ] Order 116 # 5 : Symmetric genus 0 Symmetric genus actions [ (0;+;[58];{(1)}) ] ........................................................................... Groups of order 117 Total number of groups = 4 Order 117 # 1 : Symmetric genus 40 Symmetric genus actions [ (0;+;[9,9,9];{-}) ] Order 117 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[117,117];{-}) ] Order 117 # 3 : Symmetric genus 1 Symmetric genus actions [ (0;+;[3,3,3];{-}) ] Order 117 # 4 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] ........................................................................... Groups of order 118 Total number of groups = 2 Order 118 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,59];{-}), (0;+;[-];{(59,59)}) ] Order 118 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[118,118];{-}), (0;+;[59];{(1)}), (1;-;[59];{-}) ] ........................................................................... Groups of order 119 Total number of groups = 1 Order 119 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[119,119];{-}) ] ........................................................................... Groups of order 120 Total number of groups = 47 Order 120 # 1 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 120 # 2 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 120 # 3 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 120 # 4 : Symmetric genus 0 Symmetric genus actions [ (0;+;[120,120];{-}), (1;-;[60];{-}) ] Order 120 # 5 : Symmetric genus 14 Symmetric genus actions [ (0;+;[3,4,5];{-}) ] Order 120 # 6 : Symmetric genus 41 Symmetric genus actions [ (0;+;[4,24,24];{-}) ] Order 120 # 7 : Symmetric genus 41 Symmetric genus actions [ (0;+;[8,8,12];{-}) ] Order 120 # 8 : Symmetric genus 31 Symmetric genus actions [ (0;+;[4,4];{(1)}), (1;-;[4,4];{-}) ] Order 120 # 9 : Symmetric genus 31 Symmetric genus actions [ (0;+;[4,4];{(1)}), (1;-;[4,4];{-}) ] Order 120 # 10 : Symmetric genus 1 Symmetric genus actions [ (1;-;[2,2];{-}) ] Order 120 # 11 : Symmetric genus 30 Symmetric genus actions [ (0;+;[4,6,10];{-}), (0;+;[-];{(3,4,5,4)}) ] Order 120 # 12 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}), (1;-;[2,2];{-}) ] Order 120 # 13 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}), (1;-;[2,2];{-}) ] Order 120 # 14 : Symmetric genus 31 Symmetric genus actions [ (1;-;[4,4];{-}) ] Order 120 # 15 : Symmetric genus 34 Symmetric genus actions [ (0;+;[3,15,20];{-}) ] Order 120 # 16 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 120 # 17 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}) ] Order 120 # 18 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 120 # 19 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 120 # 20 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}) ] Order 120 # 21 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 120 # 22 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}) ] Order 120 # 23 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 120 # 24 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 120 # 25 : Symmetric genus 1 Symmetric genus actions [ (1;-;[-];{(1)}) ] Order 120 # 26 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 120 # 27 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 120 # 28 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,60];{-}), (0;+;[-];{(60,60)}), (0;+;[2];{(30)}) ] Order 120 # 29 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 120 # 30 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2];{(1)}), (1;-;[2,2];{-}), (1;-;[-];{(1)}) ] Order 120 # 31 : Symmetric genus 0 Symmetric genus actions [ (0;+;[60];{(1)}) ] Order 120 # 32 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 120 # 33 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 120 # 34 : Symmetric genus 4 Symmetric genus actions [ (0;+;[2,4,5];{-}), (0;+;[5];{(2)}) ] Order 120 # 35 : Symmetric genus 0 Symmetric genus actions [ (0;+;[-];{(2,3,5)}) ] Order 120 # 36 : Symmetric genus 11 Symmetric genus actions [ (0;+;[2,4,12];{-}) ] Order 120 # 37 : Symmetric genus 16 Symmetric genus actions [ (0;+;[-];{(1),(2)}), (1;-;[-];{(2)}) ] Order 120 # 38 : Symmetric genus 12 Symmetric genus actions [ (0;+;[2,4,15];{-}), (0;+;[-];{(2,15,15)}) ] Order 120 # 39 : Symmetric genus 16 Symmetric genus actions [ (0;+;[-];{(1),(2)}), (1;-;[-];{(2)}) ] Order 120 # 40 : Symmetric genus 20 Symmetric genus actions [ (0;+;[12];{(5)}) ] Order 120 # 41 : Symmetric genus 21 Symmetric genus actions [ (0;+;[4,4,6];{-}) ] Order 120 # 42 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(2,2,2,2)}), (0;+;[2];{(2,2)}), (0;+;[2,2];{(1)}) ] Order 120 # 43 : Symmetric genus 12 Symmetric genus actions [ (0;+;[15];{(2)}) ] Order 120 # 44 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 120 # 45 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] Order 120 # 46 : Symmetric genus 0 Symmetric genus actions [ (0;+;[-];{(2,2,30)}) ] Order 120 # 47 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}) ] ........................................................................... Groups of order 121 Total number of groups = 2 Order 121 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[121,121];{-}) ] Order 121 # 2 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] ........................................................................... Groups of order 122 Total number of groups = 2 Order 122 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,61];{-}), (0;+;[-];{(61,61)}) ] Order 122 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[122,122];{-}), (0;+;[61];{(1)}), (1;-;[61];{-}) ] ........................................................................... Groups of order 123 Total number of groups = 1 Order 123 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[123,123];{-}) ] ........................................................................... Groups of order 124 Total number of groups = 4 Order 124 # 1 : Symmetric genus 1 Symmetric genus actions [ (2;-;[-];{-}) ] Order 124 # 2 : Symmetric genus 0 Symmetric genus actions [ (0;+;[124,124];{-}), (1;-;[62];{-}) ] Order 124 # 3 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,62];{-}), (0;+;[-];{(62,62)}), (0;+;[-];{(2,2,31)}), (0;+;[2];{(31)}) ] Order 124 # 4 : Symmetric genus 0 Symmetric genus actions [ (0;+;[62];{(1)}) ] ........................................................................... Groups of order 125 Total number of groups = 5 Order 125 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[125,125];{-}) ] Order 125 # 2 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] Order 125 # 3 : Symmetric genus 26 Symmetric genus actions [ (0;+;[5,5,5];{-}) ] Order 125 # 4 : Symmetric genus 46 Symmetric genus actions [ (0;+;[5,25,25];{-}) ] Order 125 # 5 : Symmetric genus 76 Symmetric genus actions [ (0;+;[5,5,5,5];{-}) ] ........................................................................... Groups of order 126 Total number of groups = 16 Order 126 # 1 : Symmetric genus 21 Symmetric genus actions [ (0;+;[9];{(7)}) ] Order 126 # 2 : Symmetric genus 48 Symmetric genus actions [ (0;+;[7,18,18];{-}), (0;+;[7,9];{(1)}), (1;-;[7,9];{-}) ] Order 126 # 3 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 126 # 4 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 126 # 5 : Symmetric genus 0 Symmetric genus actions [ (0;+;[2,2,63];{-}), (0;+;[-];{(63,63)}) ] Order 126 # 6 : Symmetric genus 0 Symmetric genus actions [ (0;+;[126,126];{-}), (0;+;[63];{(1)}), (1;-;[63];{-}) ] Order 126 # 7 : Symmetric genus 22 Symmetric genus actions [ (0;+;[3,6,6];{-}), (0;+;[3,3];{(1)}), (1;-;[3,3];{-}) ] Order 126 # 8 : Symmetric genus 22 Symmetric genus actions [ (0;+;[3,6,6];{-}), (0;+;[3,3];{(1)}), (1;-;[3,3];{-}) ] Order 126 # 9 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,3,6];{-}) ] Order 126 # 10 : Symmetric genus 22 Symmetric genus actions [ (0;+;[3,6,6];{-}), (0;+;[3,3];{(1)}), (1;-;[3,3];{-}) ] Order 126 # 11 : Symmetric genus 40 Symmetric genus actions [ (0;+;[6,6,21];{-}) ] Order 126 # 12 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 126 # 13 : Symmetric genus 1 Symmetric genus actions [ (0;+;[-];{(1),(1)}), (1;-;[-];{(1)}), (2;-;[-];{-}) ] Order 126 # 14 : Symmetric genus 40 Symmetric genus actions [ (0;+;[21];{(3,3)}) ] Order 126 # 15 : Symmetric genus 1 Symmetric genus actions [ (0;+;[2,2,2,2];{-}) ] Order 126 # 16 : Symmetric genus 1 Symmetric genus actions [ (1;+;[-];{-}) ] ........................................................................... Groups of order 127 Total number of groups = 1 Order 127 # 1 : Symmetric genus 0 Symmetric genus actions [ (0;+;[127,127];{-}) ] ...........................................................................