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