Groups with strong symmetric genus 2 to 32
..........................................

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 all the finite groups that have strong symmetric 
genus between 2 and 32 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



...........................................................................

Small groups with strong symmetric genus 2
Group of order 8 # 4 acting with signature (0; 4,4,4)
Group of order 12 # 1 acting with signature (0; 3,4,4)
Group of order 16 # 8 acting with signature (0; 2,4,8)
Group of order 24 # 3 acting with signature (0; 3,3,4)
Group of order 24 # 8 acting with signature (0; 2,4,6)
Group of order 48 # 29 acting with signature (0; 2,3,8)
Number of different groups of strong symmetric genus 2 = 6

...........................................................................

Small groups with strong symmetric genus 3
Group of order 16 # 4 acting with signature (0; 4,4,4)
Group of order 16 # 6 acting with signature (0; 2,8,8)
Group of order 16 # 13 acting with signature (0; 2,2,2,4)
Group of order 24 # 5 acting with signature (0; 2,4,12)
Group of order 32 # 9 acting with signature (0; 2,4,8)
Group of order 32 # 11 acting with signature (0; 2,4,8)
Group of order 48 # 33 acting with signature (0; 2,3,12)
Group of order 48 # 48 acting with signature (0; 2,4,6)
Group of order 96 # 64 acting with signature (0; 2,3,8)
Group of order 168 # 42 acting with signature (0; 2,3,7)
Number of different groups of strong symmetric genus 3 = 10

...........................................................................

Small groups with strong symmetric genus 4
Group of order 16 # 9 acting with signature (0; 4,4,8)
Group of order 20 # 1 acting with signature (0; 4,4,5)
Group of order 24 # 10 acting with signature (0; 2,6,12)
Group of order 32 # 19 acting with signature (0; 2,4,16)
Group of order 36 # 10 acting with signature (0; 2,6,6)
  ... and with signature (0; 2,2,2,3)
Group of order 36 # 12 acting with signature (0; 2,6,6)
Group of order 40 # 8 acting with signature (0; 2,4,10)
Group of order 72 # 40 acting with signature (0; 2,4,6)
Group of order 72 # 42 acting with signature (0; 2,3,12)
Group of order 120 # 34 acting with signature (0; 2,4,5)
Number of different groups of strong symmetric genus 4 = 10

...........................................................................

Small groups with strong symmetric genus 5
Group of order 16 # 10 acting with signature (0; 2,2,4,4)
Group of order 16 # 14 acting with signature (0; 2,2,2,2,2)
Group of order 24 # 7 acting with signature (0; 4,4,6)
Group of order 30 # 2 acting with signature (0; 2,6,15)
Group of order 32 # 2 acting with signature (0; 4,4,4)
Group of order 32 # 5 acting with signature (0; 2,8,8)
Group of order 32 # 7 acting with signature (0; 2,8,8)
Group of order 32 # 27 acting with signature (0; 2,2,2,4)
Group of order 32 # 28 acting with signature (0; 2,2,2,4)
Group of order 32 # 43 acting with signature (0; 2,2,2,4)
Group of order 40 # 5 acting with signature (0; 2,4,20)
Group of order 48 # 14 acting with signature (0; 2,4,12)
Group of order 48 # 30 acting with signature (0; 3,4,4)
Group of order 48 # 49 acting with signature (0; 2,6,6)
Group of order 64 # 8 acting with signature (0; 2,4,8)
Group of order 64 # 32 acting with signature (0; 2,4,8)
Group of order 80 # 49 acting with signature (0; 2,5,5)
Group of order 96 # 3 acting with signature (0; 3,3,4)
Group of order 96 # 195 acting with signature (0; 2,4,6)
Group of order 120 # 35 acting with signature (0; 2,3,10)
Group of order 160 # 234 acting with signature (0; 2,4,5)
Group of order 192 # 181 acting with signature (0; 2,3,8)
Number of different groups of strong symmetric genus 5 = 22

...........................................................................

Small groups with strong symmetric genus 6
Group of order 24 # 1 acting with signature (0; 3,8,8)
Group of order 24 # 4 acting with signature (0; 4,4,12)
Group of order 28 # 1 acting with signature (0; 4,4,7)
Group of order 30 # 1 acting with signature (0; 2,10,15)
Group of order 36 # 3 acting with signature (0; 2,9,9)
Group of order 48 # 6 acting with signature (0; 2,4,24)
Group of order 48 # 15 acting with signature (0; 2,6,8)
Group of order 50 # 3 acting with signature (0; 2,5,10)
Group of order 56 # 7 acting with signature (0; 2,4,14)
Group of order 72 # 15 acting with signature (0; 2,4,9)
Group of order 150 # 5 acting with signature (0; 2,3,10)
Number of different groups of strong symmetric genus 6 = 11

...........................................................................

Small groups with strong symmetric genus 7
Group of order 16 # 12 acting with signature (0; 2,4,4,4)
Group of order 24 # 11 acting with signature (1; 2)
Group of order 27 # 4 acting with signature (0; 3,9,9)
Group of order 32 # 10 acting with signature (0; 4,4,8)
Group of order 32 # 13 acting with signature (0; 4,4,8)
Group of order 32 # 14 acting with signature (0; 4,4,8)
Group of order 32 # 17 acting with signature (0; 2,16,16)
Group of order 32 # 42 acting with signature (0; 2,2,2,8)
Group of order 36 # 6 acting with signature (0; 3,4,12)
Group of order 42 # 4 acting with signature (0; 2,6,21)
Group of order 48 # 32 acting with signature (0; 3,4,6)
Group of order 48 # 38 acting with signature (0; 2,2,2,4)
Group of order 48 # 41 acting with signature (0; 2,2,2,4)
Group of order 54 # 3 acting with signature (0; 2,6,9)
Group of order 54 # 6 acting with signature (0; 2,6,9)
Group of order 56 # 4 acting with signature (0; 2,4,28)
Group of order 56 # 11 acting with signature (0; 2,7,7)
Group of order 64 # 38 acting with signature (0; 2,4,16)
Group of order 64 # 41 acting with signature (0; 2,4,16)
Group of order 72 # 25 acting with signature (0; 3,3,6)
Group of order 144 # 127 acting with signature (0; 2,3,12)
Group of order 504 # 156 acting with signature (0; 2,3,7)
Number of different groups of strong symmetric genus 7 = 22

...........................................................................

Small groups with strong symmetric genus 8
Group of order 32 # 20 acting with signature (0; 4,4,16)
Group of order 36 # 1 acting with signature (0; 4,4,9)
Group of order 40 # 10 acting with signature (0; 2,10,20)
Group of order 42 # 2 acting with signature (0; 3,6,6)
Group of order 48 # 17 acting with signature (0; 2,8,12)
Group of order 48 # 25 acting with signature (0; 2,6,24)
Group of order 48 # 28 acting with signature (0; 3,4,8)
Group of order 60 # 8 acting with signature (0; 2,6,10)
Group of order 64 # 53 acting with signature (0; 2,4,32)
Group of order 72 # 8 acting with signature (0; 2,4,18)
Group of order 84 # 7 acting with signature (0; 2,6,6)
Group of order 336 # 208 acting with signature (0; 2,3,8)
Number of different groups of strong symmetric genus 8 = 12

...........................................................................

Small groups with strong symmetric genus 9
Group of order 24 # 15 acting with signature (0; 2,2,6,6)
Group of order 32 # 4 acting with signature (0; 4,8,8)
  ... and with signature (1; 2)
Group of order 32 # 8 acting with signature (0; 4,8,8)
  ... and with signature (1; 2)
Group of order 32 # 12 acting with signature (0; 4,8,8)
  ... and with signature (1; 2)
Group of order 32 # 22 acting with signature (0; 2,2,4,4)
Group of order 32 # 25 acting with signature (0; 2,2,4,4)
Group of order 32 # 30 acting with signature (0; 2,2,4,4)
Group of order 32 # 31 acting with signature (0; 2,2,4,4)
Group of order 32 # 40 acting with signature (0; 2,2,4,4)
Group of order 32 # 46 acting with signature (0; 2,2,2,2,2)
Group of order 32 # 49 acting with signature (0; 2,2,2,2,2)
Group of order 32 # 50 acting with signature (0; 2,2,2,2,2)
Group of order 40 # 7 acting with signature (0; 4,4,10)
Group of order 42 # 3 acting with signature (0; 2,14,21)
Group of order 48 # 4 acting with signature (0; 2,8,24)
Group of order 48 # 5 acting with signature (0; 2,8,24)
Group of order 48 # 19 acting with signature (0; 4,4,6)
Group of order 48 # 21 acting with signature (0; 2,12,12)
Group of order 48 # 31 acting with signature (0; 2,12,12)
  ... and with signature (0; 3,4,12)
Group of order 48 # 43 acting with signature (0; 2,2,2,6)
Group of order 48 # 50 acting with signature (0; 2,2,3,3)
Group of order 64 # 4 acting with signature (0; 2,8,8)
Group of order 64 # 6 acting with signature (0; 2,8,8)
Group of order 64 # 10 acting with signature (0; 2,8,8)
Group of order 64 # 12 acting with signature (0; 2,8,8)
Group of order 64 # 23 acting with signature (0; 4,4,4)
Group of order 64 # 35 acting with signature (0; 4,4,4)
Group of order 64 # 36 acting with signature (0; 2,8,8)
Group of order 64 # 73 acting with signature (0; 2,2,2,4)
Group of order 64 # 128 acting with signature (0; 2,2,2,4)
Group of order 64 # 134 acting with signature (0; 2,2,2,4)
Group of order 64 # 135 acting with signature (0; 2,2,2,4)
Group of order 64 # 138 acting with signature (0; 2,2,2,4)
Group of order 64 # 140 acting with signature (0; 2,2,2,4)
Group of order 64 # 177 acting with signature (0; 2,2,2,4)
Group of order 64 # 190 acting with signature (0; 2,2,2,4)
Group of order 72 # 5 acting with signature (0; 2,4,36)
Group of order 80 # 14 acting with signature (0; 2,4,20)
Group of order 96 # 13 acting with signature (0; 2,4,12)
Group of order 96 # 67 acting with signature (0; 3,4,4)
Group of order 96 # 70 acting with signature (0; 2,6,6)
Group of order 96 # 186 acting with signature (0; 2,4,12)
Group of order 96 # 187 acting with signature (0; 2,4,12)
Group of order 96 # 193 acting with signature (0; 2,2,2,3)
Group of order 96 # 202 acting with signature (0; 2,6,6)
Group of order 96 # 227 acting with signature (0; 3,4,4)
  ... and with signature (0; 2,2,2,3)
Group of order 128 # 75 acting with signature (0; 2,4,8)
Group of order 128 # 134 acting with signature (0; 2,4,8)
Group of order 128 # 136 acting with signature (0; 2,4,8)
Group of order 128 # 138 acting with signature (0; 2,4,8)
Group of order 160 # 199 acting with signature (0; 2,5,5)
Group of order 192 # 194 acting with signature (0; 2,3,12)
Group of order 192 # 955 acting with signature (0; 2,4,6)
Group of order 192 # 990 acting with signature (0; 2,4,6)
Group of order 320 # 1582 acting with signature (0; 2,4,5)
Number of different groups of strong symmetric genus 9 = 55

...........................................................................

Small groups with strong symmetric genus 10
Group of order 27 # 5 acting with signature (0; 3,3,3,3)
Group of order 40 # 4 acting with signature (0; 4,4,20)
Group of order 44 # 1 acting with signature (0; 4,4,11)
Group of order 48 # 26 acting with signature (0; 2,12,24)
Group of order 54 # 4 acting with signature (0; 2,9,18)
Group of order 54 # 8 acting with signature (0; 2,2,3,3)
  ... and with signature (0; 2,2,2,6)
Group of order 54 # 10 acting with signature (0; 3,6,6)
Group of order 54 # 12 acting with signature (0; 3,6,6)
Group of order 54 # 13 acting with signature (0; 2,2,3,3)
Group of order 60 # 10 acting with signature (0; 2,6,30)
Group of order 72 # 23 acting with signature (0; 2,6,12)
Group of order 72 # 28 acting with signature (0; 2,6,12)
Group of order 72 # 30 acting with signature (0; 2,6,12)
Group of order 72 # 39 acting with signature (0; 2,8,8)
Group of order 72 # 41 acting with signature (0; 4,4,4)
Group of order 72 # 43 acting with signature (0; 2,2,2,4)
Group of order 80 # 6 acting with signature (0; 2,4,40)
Group of order 81 # 7 acting with signature (0; 3,3,9)
Group of order 88 # 7 acting with signature (0; 2,4,22)
Group of order 108 # 15 acting with signature (0; 2,4,12)
  ... and with signature (0; 3,4,4)
Group of order 108 # 17 acting with signature (0; 2,6,6)
  ... and with signature (0; 2,2,2,3)
Group of order 108 # 25 acting with signature (0; 2,6,6)
Group of order 108 # 37 acting with signature (0; 3,4,4)
Group of order 108 # 38 acting with signature (0; 2,6,6)
Group of order 108 # 40 acting with signature (0; 2,2,2,3)
Group of order 144 # 122 acting with signature (0; 2,3,24)
Group of order 144 # 182 acting with signature (0; 2,4,8)
Group of order 162 # 14 acting with signature (0; 2,3,18)
Group of order 180 # 19 acting with signature (0; 2,3,15)
Group of order 216 # 87 acting with signature (0; 2,4,6)
Group of order 216 # 92 acting with signature (0; 2,3,12)
Group of order 216 # 153 acting with signature (0; 3,3,4)
Group of order 216 # 158 acting with signature (0; 2,4,6)
Group of order 324 # 160 acting with signature (0; 2,3,9)
Group of order 360 # 118 acting with signature (0; 2,4,5)
Group of order 432 # 734 acting with signature (0; 2,3,8)
Number of different groups of strong symmetric genus 10 = 36

...........................................................................

Small groups with strong symmetric genus 11
Group of order 32 # 15 acting with signature (0; 8,8,8)
Group of order 32 # 44 acting with signature (0; 2,2,4,8)
Group of order 40 # 3 acting with signature (0; 4,8,8)
Group of order 40 # 11 acting with signature (1; 2)
Group of order 48 # 11 acting with signature (0; 4,4,12)
Group of order 48 # 12 acting with signature (0; 4,4,12)
Group of order 48 # 13 acting with signature (0; 4,4,12)
Group of order 48 # 24 acting with signature (0; 2,24,24)
Group of order 48 # 37 acting with signature (0; 2,2,2,12)
Group of order 60 # 6 acting with signature (0; 2,12,12)
Group of order 60 # 7 acting with signature (0; 4,4,6)
Group of order 64 # 40 acting with signature (0; 2,8,16)
Group of order 64 # 42 acting with signature (0; 2,8,16)
Group of order 66 # 2 acting with signature (0; 2,6,33)
Group of order 80 # 28 acting with signature (0; 2,8,8)
Group of order 80 # 29 acting with signature (0; 2,8,8)
Group of order 80 # 30 acting with signature (0; 4,4,4)
Group of order 80 # 31 acting with signature (0; 4,4,4)
Group of order 80 # 39 acting with signature (0; 2,2,2,4)
Group of order 80 # 42 acting with signature (0; 2,2,2,4)
Group of order 88 # 4 acting with signature (0; 2,4,44)
Group of order 96 # 28 acting with signature (0; 2,4,24)
Group of order 96 # 32 acting with signature (0; 2,4,24)
Group of order 96 # 189 acting with signature (0; 2,6,8)
Group of order 96 # 190 acting with signature (0; 2,6,8)
Group of order 120 # 36 acting with signature (0; 2,4,12)
Group of order 160 # 82 acting with signature (0; 2,4,8)
Group of order 160 # 85 acting with signature (0; 2,4,8)
Group of order 240 # 189 acting with signature (0; 2,4,6)
Number of different groups of strong symmetric genus 11 = 29

...........................................................................

Small groups with strong symmetric genus 12
Group of order 40 # 1 acting with signature (0; 5,8,8)
Group of order 48 # 8 acting with signature (0; 4,4,24)
Group of order 48 # 16 acting with signature (0; 4,6,8)
Group of order 52 # 1 acting with signature (0; 4,4,13)
Group of order 55 # 1 acting with signature (0; 5,5,5)
Group of order 56 # 9 acting with signature (0; 2,14,28)
Group of order 60 # 9 acting with signature (0; 2,15,15)
Group of order 60 # 11 acting with signature (0; 2,10,30)
Group of order 80 # 15 acting with signature (0; 2,8,10)
Group of order 84 # 8 acting with signature (0; 2,6,14)
Group of order 96 # 7 acting with signature (0; 2,4,48)
Group of order 104 # 8 acting with signature (0; 2,4,26)
Group of order 110 # 1 acting with signature (0; 2,5,10)
Group of order 120 # 38 acting with signature (0; 2,4,15)
Number of different groups of strong symmetric genus 12 = 14

...........................................................................

Small groups with strong symmetric genus 13
Group of order 32 # 21 acting with signature (0; 2,4,4,4)
Group of order 32 # 23 acting with signature (0; 2,4,4,4)
Group of order 32 # 24 acting with signature (0; 2,4,4,4)
Group of order 32 # 29 acting with signature (0; 2,4,4,4)
Group of order 32 # 33 acting with signature (0; 2,4,4,4)
Group of order 32 # 36 acting with signature (0; 2,2,8,8)
Group of order 32 # 37 acting with signature (0; 2,2,8,8)
Group of order 32 # 38 acting with signature (0; 2,2,8,8)
Group of order 32 # 48 acting with signature (0; 2,2,2,2,4)
Group of order 48 # 22 acting with signature (1; 2)
Group of order 48 # 35 acting with signature (0; 2,2,4,4)
Group of order 48 # 51 acting with signature (0; 2,2,2,2,2)
Group of order 56 # 6 acting with signature (0; 4,4,14)
Group of order 64 # 9 acting with signature (0; 4,4,8)
Group of order 64 # 18 acting with signature (0; 4,4,8)
Group of order 64 # 20 acting with signature (0; 4,4,8)
Group of order 64 # 21 acting with signature (0; 4,4,8)
Group of order 64 # 29 acting with signature (0; 2,16,16)
Group of order 64 # 30 acting with signature (0; 2,16,16)
Group of order 64 # 31 acting with signature (0; 2,16,16)
Group of order 64 # 33 acting with signature (0; 4,4,8)
Group of order 64 # 130 acting with signature (0; 2,2,2,8)
Group of order 64 # 147 acting with signature (0; 2,2,2,8)
Group of order 64 # 150 acting with signature (0; 2,2,2,8)
Group of order 64 # 153 acting with signature (0; 2,2,2,8)
Group of order 72 # 16 acting with signature (0; 2,9,18)
Group of order 72 # 21 acting with signature (0; 2,12,12)
Group of order 72 # 27 acting with signature (0; 2,12,12)
Group of order 72 # 46 acting with signature (0; 2,2,2,6)
Group of order 72 # 47 acting with signature (0; 3,6,6)
Group of order 78 # 4 acting with signature (0; 2,6,39)
Group of order 90 # 7 acting with signature (0; 2,6,15)
Group of order 96 # 68 acting with signature (0; 3,4,6)
Group of order 96 # 71 acting with signature (0; 3,4,6)
Group of order 96 # 89 acting with signature (0; 2,2,2,4)
Group of order 96 # 102 acting with signature (0; 2,2,2,4)
Group of order 96 # 115 acting with signature (0; 2,2,2,4)
Group of order 96 # 197 acting with signature (0; 2,6,12)
Group of order 96 # 200 acting with signature (0; 2,6,12)
Group of order 96 # 226 acting with signature (0; 2,2,2,4)
Group of order 104 # 5 acting with signature (0; 2,4,52)
Group of order 112 # 13 acting with signature (0; 2,4,28)
Group of order 128 # 71 acting with signature (0; 2,4,16)
Group of order 128 # 79 acting with signature (0; 2,4,16)
Group of order 144 # 115 acting with signature (0; 2,4,12)
Group of order 144 # 183 acting with signature (0; 2,2,2,3)
Group of order 144 # 184 acting with signature (0; 3,3,6)
Group of order 144 # 190 acting with signature (0; 2,6,6)
Group of order 288 # 1024 acting with signature (0; 2,3,12)
Group of order 360 # 121 acting with signature (0; 2,3,10)
Number of different groups of strong symmetric genus 13 = 50

...........................................................................

Small groups with strong symmetric genus 14
Group of order 48 # 1 acting with signature (0; 3,16,16)
Group of order 48 # 18 acting with signature (0; 4,8,12)
Group of order 56 # 3 acting with signature (0; 4,4,28)
Group of order 60 # 3 acting with signature (0; 4,4,15)
Group of order 70 # 2 acting with signature (0; 2,10,35)
Group of order 78 # 2 acting with signature (0; 3,6,6)
Group of order 80 # 17 acting with signature (0; 2,8,20)
Group of order 84 # 12 acting with signature (0; 2,6,42)
Group of order 96 # 33 acting with signature (0; 2,6,16)
Group of order 112 # 5 acting with signature (0; 2,4,56)
Group of order 120 # 5 acting with signature (0; 3,4,5)
Group of order 120 # 30 acting with signature (0; 2,4,30)
Group of order 156 # 8 acting with signature (0; 2,6,6)
Group of order 1092 # 25 acting with signature (0; 2,3,7)
Number of different groups of strong symmetric genus 14 = 14

...........................................................................

Small groups with strong symmetric genus 15
Group of order 32 # 41 acting with signature (0; 2,4,4,8)
Group of order 48 # 9 acting with signature (0; 6,8,8)
Group of order 48 # 10 acting with signature (0; 6,8,8)
Group of order 48 # 39 acting with signature (0; 2,2,4,6)
Group of order 56 # 10 acting with signature (1; 2)
Group of order 64 # 39 acting with signature (0; 4,4,16)
Group of order 64 # 47 acting with signature (0; 4,4,16)
Group of order 64 # 48 acting with signature (0; 4,4,16)
Group of order 64 # 51 acting with signature (0; 2,32,32)
Group of order 64 # 189 acting with signature (0; 2,2,2,16)
Group of order 66 # 1 acting with signature (0; 2,22,33)
Group of order 70 # 1 acting with signature (0; 2,14,35)
Group of order 80 # 4 acting with signature (0; 2,8,40)
Group of order 80 # 5 acting with signature (0; 2,8,40)
Group of order 84 # 1 acting with signature (0; 3,4,12)
Group of order 96 # 12 acting with signature (0; 2,8,12)
Group of order 96 # 16 acting with signature (0; 2,8,12)
Group of order 96 # 66 acting with signature (0; 3,4,8)
Group of order 96 # 192 acting with signature (0; 2,8,12)
Group of order 98 # 3 acting with signature (0; 2,7,14)
Group of order 112 # 31 acting with signature (0; 2,2,2,4)
Group of order 112 # 34 acting with signature (0; 2,2,2,4)
Group of order 120 # 27 acting with signature (0; 2,4,60)
Group of order 128 # 147 acting with signature (0; 2,4,32)
Group of order 128 # 150 acting with signature (0; 2,4,32)
Group of order 144 # 109 acting with signature (0; 2,4,18)
Group of order 168 # 23 acting with signature (0; 3,3,6)
Group of order 168 # 43 acting with signature (0; 3,3,6)
Group of order 240 # 93 acting with signature (0; 2,3,20)
Group of order 294 # 7 acting with signature (0; 2,3,14)
Group of order 336 # 134 acting with signature (0; 2,3,12)
Number of different groups of strong symmetric genus 15 = 31

...........................................................................

Small groups with strong symmetric genus 16
Group of order 36 # 7 acting with signature (0; 3,3,4,4)
Group of order 48 # 27 acting with signature (0; 4,12,24)
Group of order 54 # 11 acting with signature (0; 3,18,18)
Group of order 64 # 54 acting with signature (0; 4,4,32)
Group of order 68 # 1 acting with signature (0; 4,4,17)
Group of order 72 # 10 acting with signature (0; 2,18,36)
Group of order 72 # 19 acting with signature (0; 3,8,8)
Group of order 72 # 22 acting with signature (0; 4,6,6)
  ... and with signature (0; 2,2,3,4)
Group of order 80 # 25 acting with signature (0; 2,10,40)
Group of order 96 # 61 acting with signature (0; 2,6,48)
Group of order 100 # 10 acting with signature (0; 4,4,5)
Group of order 100 # 13 acting with signature (0; 2,10,10)
  ... and with signature (0; 2,2,2,5)
Group of order 100 # 14 acting with signature (0; 2,10,10)
Group of order 108 # 16 acting with signature (0; 2,6,18)
Group of order 108 # 23 acting with signature (0; 2,6,18)
Group of order 108 # 26 acting with signature (0; 2,6,18)
Group of order 128 # 162 acting with signature (0; 2,4,64)
Group of order 136 # 8 acting with signature (0; 2,4,34)
Group of order 144 # 117 acting with signature (0; 2,6,8)
Group of order 200 # 43 acting with signature (0; 2,4,10)
Group of order 300 # 22 acting with signature (0; 2,5,5)
Group of order 600 # 145 acting with signature (0; 2,4,5)
Group of order 720 # 764 acting with signature (0; 2,3,8)
Number of different groups of strong symmetric genus 16 = 23

...........................................................................

Small groups with strong symmetric genus 17
Group of order 32 # 26 acting with signature (0; 4,4,4,4)
Group of order 32 # 32 acting with signature (0; 4,4,4,4)
Group of order 32 # 35 acting with signature (0; 4,4,4,4)
Group of order 32 # 45 acting with signature (0; 2,2,2,4,4)
Group of order 32 # 51 acting with signature (0; 2,2,2,2,2,2)
Group of order 40 # 14 acting with signature (0; 2,2,10,10)
Group of order 48 # 45 acting with signature (0; 2,2,6,6)
Group of order 64 # 3 acting with signature (1; 2)
Group of order 64 # 5 acting with signature (0; 4,8,8)
  ... and with signature (1; 2)
Group of order 64 # 7 acting with signature (0; 4,8,8)
Group of order 64 # 11 acting with signature (0; 4,8,8)
Group of order 64 # 13 acting with signature (0; 4,8,8)
Group of order 64 # 14 acting with signature (0; 4,8,8)
Group of order 64 # 17 acting with signature (0; 4,8,8)
  ... and with signature (1; 2)
Group of order 64 # 24 acting with signature (0; 4,8,8)
  ... and with signature (1; 2)
Group of order 64 # 25 acting with signature (0; 4,8,8)
  ... and with signature (1; 2)
Group of order 64 # 27 acting with signature (1; 2)
Group of order 64 # 37 acting with signature (0; 4,8,8)
Group of order 64 # 44 acting with signature (1; 2)
Group of order 64 # 60 acting with signature (0; 2,2,4,4)
Group of order 64 # 67 acting with signature (0; 2,2,4,4)
Group of order 64 # 71 acting with signature (0; 2,2,4,4)
Group of order 64 # 75 acting with signature (0; 2,2,4,4)
Group of order 64 # 90 acting with signature (0; 2,2,4,4)
Group of order 64 # 91 acting with signature (0; 2,2,4,4)
Group of order 64 # 95 acting with signature (0; 2,2,4,4)
Group of order 64 # 99 acting with signature (0; 2,2,4,4)
Group of order 64 # 101 acting with signature (0; 2,2,4,4)
Group of order 64 # 102 acting with signature (0; 2,2,4,4)
Group of order 64 # 118 acting with signature (0; 2,2,4,4)
Group of order 64 # 123 acting with signature (0; 2,2,4,4)
Group of order 64 # 131 acting with signature (0; 2,2,4,4)
Group of order 64 # 136 acting with signature (0; 2,2,4,4)
Group of order 64 # 137 acting with signature (0; 2,2,4,4)
Group of order 64 # 139 acting with signature (0; 2,2,4,4)
Group of order 64 # 141 acting with signature (0; 2,2,4,4)
Group of order 64 # 144 acting with signature (0; 2,2,4,4)
Group of order 64 # 167 acting with signature (0; 2,2,4,4)
Group of order 64 # 171 acting with signature (0; 2,2,4,4)
Group of order 64 # 173 acting with signature (0; 2,2,4,4)
Group of order 64 # 176 acting with signature (0; 2,2,4,4)
Group of order 64 # 187 acting with signature (0; 2,2,4,4)
Group of order 64 # 202 acting with signature (0; 2,2,2,2,2)
Group of order 64 # 211 acting with signature (0; 2,2,2,2,2)
Group of order 64 # 215 acting with signature (0; 2,2,2,2,2)
Group of order 64 # 216 acting with signature (0; 2,2,2,2,2)
Group of order 64 # 218 acting with signature (0; 2,2,2,2,2)
Group of order 64 # 226 acting with signature (0; 2,2,2,2,2)
Group of order 64 # 241 acting with signature (0; 2,2,2,2,2)
Group of order 64 # 250 acting with signature (0; 2,2,2,2,2)
Group of order 64 # 254 acting with signature (0; 2,2,2,2,2)
Group of order 64 # 256 acting with signature (0; 2,2,2,2,2)
Group of order 64 # 257 acting with signature (0; 2,2,2,2,2)
Group of order 72 # 7 acting with signature (0; 4,4,18)
Group of order 80 # 19 acting with signature (0; 4,4,10)
Group of order 80 # 21 acting with signature (0; 2,20,20)
Group of order 80 # 44 acting with signature (0; 2,2,2,10)
Group of order 96 # 27 acting with signature (0; 2,8,24)
Group of order 96 # 30 acting with signature (0; 2,8,24)
Group of order 96 # 41 acting with signature (0; 4,4,6)
Group of order 96 # 49 acting with signature (0; 2,12,12)
Group of order 96 # 69 acting with signature (0; 3,4,12)
Group of order 96 # 117 acting with signature (0; 2,2,2,6)
Group of order 96 # 138 acting with signature (0; 2,2,2,6)
Group of order 96 # 147 acting with signature (0; 2,2,2,6)
Group of order 96 # 194 acting with signature (0; 4,4,6)
Group of order 96 # 196 acting with signature (0; 2,12,12)
Group of order 96 # 201 acting with signature (0; 2,12,12)
Group of order 96 # 204 acting with signature (0; 2,2,3,3)
Group of order 96 # 229 acting with signature (0; 2,2,3,3)
Group of order 102 # 2 acting with signature (0; 2,6,51)
Group of order 112 # 41 acting with signature (0; 2,7,14)
Group of order 120 # 39 acting with signature (0; 2,6,15)
Group of order 128 # 2 acting with signature (0; 2,8,8)
Group of order 128 # 36 acting with signature (0; 4,4,4)
Group of order 128 # 48 acting with signature (0; 2,8,8)
Group of order 128 # 50 acting with signature (0; 2,8,8)
Group of order 128 # 77 acting with signature (0; 2,8,8)
Group of order 128 # 125 acting with signature (0; 4,4,4)
Group of order 128 # 135 acting with signature (0; 2,8,8)
Group of order 128 # 137 acting with signature (0; 2,8,8)
Group of order 128 # 141 acting with signature (0; 4,4,4)
Group of order 128 # 142 acting with signature (0; 2,8,8)
Group of order 128 # 144 acting with signature (0; 4,4,4)
Group of order 128 # 327 acting with signature (0; 2,2,2,4)
Group of order 128 # 330 acting with signature (0; 2,2,2,4)
Group of order 128 # 453 acting with signature (0; 2,2,2,4)
Group of order 128 # 738 acting with signature (0; 2,2,2,4)
Group of order 128 # 740 acting with signature (0; 2,2,2,4)
Group of order 128 # 743 acting with signature (0; 2,2,2,4)
Group of order 128 # 753 acting with signature (0; 2,2,2,4)
Group of order 128 # 916 acting with signature (0; 2,2,2,4)
Group of order 128 # 922 acting with signature (0; 2,2,2,4)
Group of order 128 # 928 acting with signature (0; 2,2,2,4)
Group of order 128 # 932 acting with signature (0; 2,2,2,4)
Group of order 128 # 938 acting with signature (0; 2,2,2,4)
Group of order 128 # 982 acting with signature (0; 2,2,2,4)
Group of order 128 # 995 acting with signature (0; 2,2,2,4)
Group of order 136 # 5 acting with signature (0; 2,4,68)
Group of order 144 # 14 acting with signature (0; 2,4,36)
Group of order 160 # 13 acting with signature (0; 2,4,20)
Group of order 160 # 235 acting with signature (0; 2,5,10)
Group of order 192 # 33 acting with signature (0; 2,4,12)
Group of order 192 # 185 acting with signature (0; 3,4,4)
Group of order 192 # 201 acting with signature (0; 2,6,6)
Group of order 192 # 956 acting with signature (0; 2,2,2,3)
Group of order 192 # 972 acting with signature (0; 2,4,12)
Group of order 192 # 988 acting with signature (0; 2,4,12)
Group of order 192 # 1000 acting with signature (0; 2,6,6)
Group of order 192 # 1002 acting with signature (0; 2,6,6)
Group of order 192 # 1008 acting with signature (0; 2,6,6)
Group of order 192 # 1491 acting with signature (0; 3,4,4)
Group of order 192 # 1493 acting with signature (0; 3,4,4)
Group of order 192 # 1494 acting with signature (0; 2,2,2,3)
Group of order 192 # 1495 acting with signature (0; 3,4,4)
Group of order 192 # 1538 acting with signature (0; 2,2,2,3)
Group of order 240 # 90 acting with signature (0; 2,5,6)
Group of order 256 # 382 acting with signature (0; 2,4,8)
Group of order 256 # 390 acting with signature (0; 2,4,8)
Group of order 256 # 396 acting with signature (0; 2,4,8)
Group of order 256 # 515 acting with signature (0; 2,4,8)
Group of order 336 # 209 acting with signature (0; 2,3,14)
Group of order 384 # 4 acting with signature (0; 3,3,4)
Group of order 384 # 5602 acting with signature (0; 2,4,6)
Group of order 384 # 5604 acting with signature (0; 2,4,6)
Group of order 384 # 5657 acting with signature (0; 2,4,6)
Group of order 384 # 5677 acting with signature (0; 2,4,6)
Group of order 768 # 1085341 acting with signature (0; 2,3,8)
Group of order 1344 # 814 acting with signature (0; 2,3,7)
Number of different groups of strong symmetric genus 17 = 129

...........................................................................

Small groups with strong symmetric genus 18
Group of order 56 # 1 acting with signature (0; 7,8,8)
Group of order 60 # 1 acting with signature (0; 3,20,20)
Group of order 72 # 4 acting with signature (0; 4,4,36)
Group of order 76 # 1 acting with signature (0; 4,4,19)
Group of order 78 # 3 acting with signature (0; 2,26,39)
Group of order 80 # 26 acting with signature (0; 2,20,40)
Group of order 84 # 10 acting with signature (0; 2,21,21)
Group of order 84 # 13 acting with signature (0; 2,14,42)
Group of order 90 # 1 acting with signature (0; 2,10,45)
Group of order 96 # 35 acting with signature (0; 2,12,16)
Group of order 112 # 14 acting with signature (0; 2,8,14)
Group of order 120 # 12 acting with signature (0; 2,6,20)
Group of order 136 # 12 acting with signature (0; 2,8,8)
Group of order 144 # 7 acting with signature (0; 2,4,72)
Group of order 152 # 7 acting with signature (0; 2,4,38)
Group of order 168 # 46 acting with signature (0; 2,4,21)
Number of different groups of strong symmetric genus 18 = 16

...........................................................................

Small groups with strong symmetric genus 19
Group of order 48 # 40 acting with signature (0; 2,4,4,4)
Group of order 48 # 47 acting with signature (0; 2,2,6,12)
Group of order 54 # 14 acting with signature (0; 2,2,2,2,3)
Group of order 60 # 2 acting with signature (0; 4,12,15)
Group of order 64 # 43 acting with signature (0; 4,8,16)
Group of order 64 # 46 acting with signature (0; 4,8,16)
Group of order 72 # 11 acting with signature (1; 2)
Group of order 72 # 12 acting with signature (0; 3,8,24)
Group of order 72 # 20 acting with signature (0; 4,6,12)
Group of order 72 # 29 acting with signature (0; 4,6,12)
Group of order 72 # 32 acting with signature (0; 2,2,4,4)
Group of order 72 # 35 acting with signature (0; 2,2,4,4)
Group of order 72 # 37 acting with signature (1; 2)
Group of order 72 # 38 acting with signature (1; 2)
Group of order 80 # 11 acting with signature (0; 4,4,20)
Group of order 80 # 12 acting with signature (0; 4,4,20)
Group of order 80 # 13 acting with signature (0; 4,4,20)
Group of order 80 # 24 acting with signature (0; 2,40,40)
Group of order 80 # 38 acting with signature (0; 2,2,2,20)
Group of order 81 # 3 acting with signature (0; 3,9,9)
Group of order 81 # 8 acting with signature (0; 3,9,9)
Group of order 90 # 6 acting with signature (0; 2,15,30)
Group of order 96 # 52 acting with signature (0; 2,12,24)
Group of order 96 # 54 acting with signature (0; 2,12,24)
Group of order 96 # 121 acting with signature (0; 2,2,2,8)
Group of order 96 # 126 acting with signature (0; 2,2,2,8)
Group of order 108 # 8 acting with signature (0; 3,4,12)
Group of order 108 # 28 acting with signature (0; 2,2,2,6)
Group of order 108 # 36 acting with signature (0; 2,12,12)
  ... and with signature (0; 3,4,12)
Group of order 108 # 39 acting with signature (0; 2,2,2,6)
Group of order 114 # 4 acting with signature (0; 2,6,57)
Group of order 126 # 13 acting with signature (0; 2,6,21)
Group of order 126 # 13 acting with signature (0; 2,6,21)
Group of order 144 # 41 acting with signature (0; 2,2,2,4)
Group of order 144 # 44 acting with signature (0; 2,2,2,4)
Group of order 144 # 120 acting with signature (0; 4,4,4)
Group of order 144 # 128 acting with signature (0; 3,4,6)
Group of order 144 # 130 acting with signature (0; 2,8,8)
Group of order 144 # 131 acting with signature (0; 2,8,8)
Group of order 144 # 132 acting with signature (0; 4,4,4)
Group of order 144 # 133 acting with signature (0; 4,4,4)
Group of order 144 # 172 acting with signature (0; 2,2,2,4)
Group of order 144 # 175 acting with signature (0; 2,2,2,4)
Group of order 144 # 185 acting with signature (0; 2,8,8)
Group of order 144 # 186 acting with signature (0; 2,2,2,4)
Group of order 144 # 188 acting with signature (0; 2,6,12)
Group of order 144 # 189 acting with signature (0; 2,2,2,4)
Group of order 152 # 4 acting with signature (0; 2,4,76)
Group of order 160 # 28 acting with signature (0; 2,4,40)
Group of order 160 # 32 acting with signature (0; 2,4,40)
Group of order 162 # 5 acting with signature (0; 2,6,9)
Group of order 162 # 10 acting with signature (0; 2,6,9)
Group of order 162 # 11 acting with signature (0; 2,6,9)
Group of order 162 # 13 acting with signature (0; 2,6,9)
Group of order 216 # 42 acting with signature (0; 3,3,6)
Group of order 216 # 100 acting with signature (0; 2,4,12)
Group of order 216 # 156 acting with signature (0; 2,4,12)
Group of order 288 # 397 acting with signature (0; 2,3,24)
Group of order 288 # 430 acting with signature (0; 2,4,8)
Group of order 288 # 433 acting with signature (0; 2,4,8)
Group of order 288 # 841 acting with signature (0; 2,4,8)
Group of order 432 # 269 acting with signature (0; 2,3,12)
Group of order 720 # 766 acting with signature (0; 2,4,5)
Number of different groups of strong symmetric genus 19 = 63

...........................................................................

Small groups with strong symmetric genus 20
Group of order 72 # 3 acting with signature (0; 4,9,9)
Group of order 80 # 8 acting with signature (0; 4,4,40)
Group of order 84 # 5 acting with signature (0; 4,4,21)
Group of order 88 # 9 acting with signature (0; 2,22,44)
Group of order 90 # 2 acting with signature (0; 2,18,45)
Group of order 96 # 62 acting with signature (0; 2,12,48)
Group of order 112 # 16 acting with signature (0; 2,8,28)
Group of order 114 # 2 acting with signature (0; 3,6,6)
Group of order 120 # 13 acting with signature (0; 2,10,12)
Group of order 120 # 18 acting with signature (0; 2,6,60)
Group of order 132 # 5 acting with signature (0; 2,6,22)
Group of order 144 # 32 acting with signature (0; 2,8,9)
Group of order 160 # 7 acting with signature (0; 2,4,80)
Group of order 168 # 38 acting with signature (0; 2,4,42)
Group of order 228 # 7 acting with signature (0; 2,6,6)
Number of different groups of strong symmetric genus 20 = 15

...........................................................................

Small groups with strong symmetric genus 21
Group of order 32 # 47 acting with signature (0; 2,2,4,4,4)
Group of order 48 # 42 acting with signature (0; 2,4,4,6)
Group of order 48 # 44 acting with signature (0; 2,2,12,12)
Group of order 63 # 1 acting with signature (0; 7,9,9)
Group of order 64 # 15 acting with signature (0; 8,8,8)
Group of order 64 # 16 acting with signature (0; 8,8,8)
Group of order 64 # 19 acting with signature (0; 8,8,8)
Group of order 64 # 22 acting with signature (0; 8,8,8)
Group of order 64 # 28 acting with signature (0; 4,16,16)
Group of order 64 # 45 acting with signature (0; 4,16,16)
Group of order 64 # 97 acting with signature (0; 2,2,4,8)
Group of order 64 # 98 acting with signature (0; 2,2,4,8)
Group of order 64 # 124 acting with signature (0; 2,2,4,8)
Group of order 64 # 125 acting with signature (0; 2,2,4,8)
Group of order 64 # 129 acting with signature (0; 2,2,4,8)
Group of order 64 # 133 acting with signature (0; 2,2,4,8)
Group of order 64 # 146 acting with signature (0; 2,2,4,8)
Group of order 64 # 149 acting with signature (0; 2,2,4,8)
Group of order 64 # 152 acting with signature (0; 2,2,4,8)
Group of order 64 # 161 acting with signature (0; 2,2,4,8)
Group of order 64 # 162 acting with signature (0; 2,2,4,8)
Group of order 64 # 163 acting with signature (0; 2,2,4,8)
Group of order 80 # 22 acting with signature (1; 2)
Group of order 80 # 32 acting with signature (0; 4,8,8)
Group of order 80 # 33 acting with signature (0; 4,8,8)
Group of order 80 # 36 acting with signature (0; 2,2,4,4)
Group of order 80 # 50 acting with signature (0; 2,2,4,4)
Group of order 80 # 51 acting with signature (0; 2,2,2,2,2)
Group of order 88 # 6 acting with signature (0; 4,4,22)
Group of order 96 # 4 acting with signature (0; 2,16,48)
Group of order 96 # 5 acting with signature (0; 2,16,48)
Group of order 96 # 38 acting with signature (0; 4,4,12)
Group of order 96 # 48 acting with signature (0; 2,24,24)
Group of order 96 # 50 acting with signature (0; 2,24,24)
Group of order 96 # 65 acting with signature (0; 3,8,8)
Group of order 96 # 73 acting with signature (0; 2,24,24)
Group of order 96 # 74 acting with signature (0; 2,24,24)
Group of order 96 # 91 acting with signature (0; 2,2,2,12)
Group of order 96 # 137 acting with signature (0; 2,2,2,12)
Group of order 96 # 144 acting with signature (0; 2,2,2,12)
Group of order 96 # 156 acting with signature (0; 2,2,2,12)
Group of order 96 # 185 acting with signature (0; 4,4,12)
Group of order 96 # 198 acting with signature (0; 4,6,6)
Group of order 100 # 9 acting with signature (0; 2,20,20)
Group of order 112 # 3 acting with signature (0; 2,8,56)
Group of order 112 # 4 acting with signature (0; 2,8,56)
Group of order 120 # 40 acting with signature (0; 2,12,12)
Group of order 120 # 41 acting with signature (0; 4,4,6)
Group of order 120 # 42 acting with signature (0; 2,2,2,6)
Group of order 128 # 63 acting with signature (0; 2,8,16)
Group of order 128 # 65 acting with signature (0; 2,8,16)
Group of order 128 # 67 acting with signature (0; 2,8,16)
Group of order 128 # 68 acting with signature (0; 2,8,16)
Group of order 128 # 73 acting with signature (0; 2,8,16)
Group of order 128 # 81 acting with signature (0; 2,8,16)
Group of order 128 # 92 acting with signature (0; 2,8,16)
Group of order 128 # 93 acting with signature (0; 2,8,16)
Group of order 160 # 78 acting with signature (0; 2,8,8)
Group of order 160 # 81 acting with signature (0; 4,4,4)
Group of order 160 # 86 acting with signature (0; 4,4,4)
Group of order 160 # 88 acting with signature (0; 2,8,8)
Group of order 160 # 103 acting with signature (0; 2,2,2,4)
Group of order 160 # 116 acting with signature (0; 2,2,2,4)
Group of order 160 # 129 acting with signature (0; 2,2,2,4)
Group of order 168 # 35 acting with signature (0; 2,4,84)
Group of order 176 # 13 acting with signature (0; 2,4,44)
Group of order 192 # 4 acting with signature (0; 3,3,8)
Group of order 192 # 29 acting with signature (0; 2,4,24)
Group of order 192 # 34 acting with signature (0; 2,4,24)
Group of order 192 # 944 acting with signature (0; 2,6,8)
Group of order 192 # 960 acting with signature (0; 2,4,24)
Group of order 192 # 961 acting with signature (0; 2,4,24)
Group of order 192 # 963 acting with signature (0; 2,4,24)
Group of order 192 # 964 acting with signature (0; 2,4,24)
Group of order 192 # 974 acting with signature (0; 2,6,8)
Group of order 192 # 980 acting with signature (0; 2,6,8)
Group of order 200 # 41 acting with signature (0; 2,4,20)
Group of order 240 # 91 acting with signature (0; 2,4,12)
  ... and with signature (0; 3,4,4)
Group of order 240 # 96 acting with signature (0; 2,4,12)
Group of order 240 # 190 acting with signature (0; 2,2,2,3)
Group of order 320 # 202 acting with signature (0; 2,4,8)
Group of order 320 # 206 acting with signature (0; 2,4,8)
Group of order 320 # 1635 acting with signature (0; 2,4,8)
Group of order 384 # 568 acting with signature (0; 2,3,16)
Group of order 384 # 570 acting with signature (0; 2,3,16)
Group of order 480 # 951 acting with signature (0; 2,4,6)
Number of different groups of strong symmetric genus 21 = 86

...........................................................................

Small groups with strong symmetric genus 22
Group of order 72 # 24 acting with signature (0; 4,12,12)
Group of order 72 # 26 acting with signature (0; 4,12,12)
Group of order 80 # 16 acting with signature (0; 4,8,10)
Group of order 84 # 2 acting with signature (0; 3,12,12)
Group of order 84 # 9 acting with signature (0; 6,6,6)
Group of order 88 # 3 acting with signature (0; 4,4,44)
Group of order 92 # 1 acting with signature (0; 4,4,23)
Group of order 108 # 24 acting with signature (0; 2,18,18)
Group of order 110 # 4 acting with signature (0; 2,10,55)
Group of order 126 # 1 acting with signature (0; 2,9,18)
Group of order 126 # 7 acting with signature (0; 3,6,6)
Group of order 126 # 8 acting with signature (0; 3,6,6)
Group of order 126 # 10 acting with signature (0; 3,6,6)
Group of order 126 # 1 acting with signature (0; 2,9,18)
Group of order 126 # 7 acting with signature (0; 3,6,6)
Group of order 126 # 8 acting with signature (0; 3,6,6)
Group of order 126 # 10 acting with signature (0; 3,6,6)
Group of order 132 # 7 acting with signature (0; 2,6,66)
Group of order 144 # 57 acting with signature (0; 2,6,24)
Group of order 144 # 72 acting with signature (0; 2,6,24)
Group of order 144 # 80 acting with signature (0; 2,6,24)
Group of order 144 # 118 acting with signature (0; 2,8,12)
Group of order 168 # 9 acting with signature (0; 2,6,12)
Group of order 168 # 11 acting with signature (0; 2,6,12)
Group of order 176 # 5 acting with signature (0; 2,4,88)
Group of order 184 # 7 acting with signature (0; 2,4,46)
Group of order 252 # 26 acting with signature (0; 2,6,6)
Group of order 252 # 27 acting with signature (0; 3,3,6)
Group of order 252 # 30 acting with signature (0; 2,6,6)
Group of order 504 # 157 acting with signature (0; 3,3,4)
Group of order 504 # 160 acting with signature (0; 2,3,12)
Group of order 1008 # 881 acting with signature (0; 2,3,8)
Number of different groups of strong symmetric genus 22 = 32

...........................................................................

Small groups with strong symmetric genus 23
Group of order 48 # 34 acting with signature (0; 2,4,4,12)
Group of order 64 # 49 acting with signature (0; 8,8,16)
Group of order 64 # 191 acting with signature (0; 2,2,4,16)
Group of order 88 # 10 acting with signature (1; 2)
Group of order 96 # 23 acting with signature (0; 4,4,24)
Group of order 96 # 24 acting with signature (0; 4,4,24)
Group of order 96 # 25 acting with signature (0; 4,4,24)
Group of order 96 # 39 acting with signature (0; 4,6,8)
Group of order 96 # 44 acting with signature (0; 4,6,8)
Group of order 96 # 60 acting with signature (0; 2,48,48)
Group of order 96 # 111 acting with signature (0; 2,2,2,24)
Group of order 96 # 118 acting with signature (0; 2,2,2,24)
Group of order 96 # 123 acting with signature (0; 2,2,2,24)
Group of order 96 # 188 acting with signature (0; 4,6,8)
Group of order 120 # 10 acting with signature (0; 2,12,20)
Group of order 128 # 149 acting with signature (0; 2,8,32)
Group of order 128 # 151 acting with signature (0; 2,8,32)
Group of order 138 # 2 acting with signature (0; 2,6,69)
Group of order 176 # 31 acting with signature (0; 2,2,2,4)
Group of order 176 # 34 acting with signature (0; 2,2,2,4)
Group of order 184 # 4 acting with signature (0; 2,4,92)
Group of order 192 # 68 acting with signature (0; 2,4,48)
Group of order 192 # 77 acting with signature (0; 2,4,48)
Number of different groups of strong symmetric genus 23 = 23

...........................................................................

Small groups with strong symmetric genus 24
Group of order 72 # 1 acting with signature (0; 8,8,9)
Group of order 80 # 18 acting with signature (0; 4,8,20)
Group of order 96 # 8 acting with signature (0; 4,4,48)
Group of order 100 # 1 acting with signature (0; 4,4,25)
Group of order 102 # 1 acting with signature (0; 2,34,51)
Group of order 104 # 10 acting with signature (0; 2,26,52)
Group of order 108 # 3 acting with signature (0; 2,27,27)
Group of order 112 # 24 acting with signature (0; 2,14,56)
Group of order 120 # 20 acting with signature (0; 2,12,30)
Group of order 120 # 23 acting with signature (0; 2,10,60)
Group of order 120 # 37 acting with signature (0; 2,15,20)
Group of order 140 # 7 acting with signature (0; 2,10,14)
Group of order 144 # 16 acting with signature (0; 2,8,18)
Group of order 156 # 11 acting with signature (0; 2,6,26)
Group of order 192 # 8 acting with signature (0; 2,4,96)
Group of order 200 # 8 acting with signature (0; 2,4,50)
Group of order 216 # 21 acting with signature (0; 2,4,27)
Number of different groups of strong symmetric genus 24 = 17

...........................................................................

Small groups with strong symmetric genus 25
Group of order 48 # 46 acting with signature (1; 2,2)
Group of order 56 # 13 acting with signature (0; 2,2,14,14)
Group of order 64 # 56 acting with signature (0; 2,4,4,4)
Group of order 64 # 58 acting with signature (0; 2,4,4,4)
Group of order 64 # 61 acting with signature (0; 2,4,4,4)
Group of order 64 # 62 acting with signature (0; 2,4,4,4)
Group of order 64 # 66 acting with signature (0; 2,4,4,4)
Group of order 64 # 69 acting with signature (0; 2,4,4,4)
Group of order 64 # 74 acting with signature (0; 2,4,4,4)
Group of order 64 # 77 acting with signature (0; 2,4,4,4)
Group of order 64 # 78 acting with signature (0; 2,4,4,4)
Group of order 64 # 80 acting with signature (0; 2,4,4,4)
Group of order 64 # 87 acting with signature (0; 2,2,8,8)
Group of order 64 # 88 acting with signature (0; 2,2,8,8)
Group of order 64 # 89 acting with signature (0; 2,2,8,8)
Group of order 64 # 92 acting with signature (0; 2,2,8,8)
Group of order 64 # 94 acting with signature (0; 2,2,8,8)
Group of order 64 # 115 acting with signature (0; 2,2,8,8)
Group of order 64 # 116 acting with signature (0; 2,2,8,8)
Group of order 64 # 117 acting with signature (0; 2,2,8,8)
Group of order 64 # 119 acting with signature (0; 2,4,4,4)
Group of order 64 # 121 acting with signature (0; 2,4,4,4)
Group of order 64 # 142 acting with signature (0; 2,4,4,4)
Group of order 64 # 145 acting with signature (0; 2,4,4,4)
Group of order 64 # 155 acting with signature (0; 2,4,4,4)
Group of order 64 # 157 acting with signature (0; 2,4,4,4)
Group of order 64 # 159 acting with signature (0; 2,4,4,4)
Group of order 64 # 169 acting with signature (0; 2,4,4,4)
Group of order 64 # 170 acting with signature (0; 2,4,4,4)
Group of order 64 # 178 acting with signature (0; 2,4,4,4)
Group of order 64 # 203 acting with signature (0; 2,2,2,2,4)
Group of order 64 # 206 acting with signature (0; 2,2,2,2,4)
Group of order 64 # 213 acting with signature (0; 2,2,2,2,4)
Group of order 64 # 219 acting with signature (0; 2,2,2,2,4)
Group of order 64 # 221 acting with signature (0; 2,2,2,2,4)
Group of order 64 # 227 acting with signature (0; 2,2,2,2,4)
Group of order 64 # 228 acting with signature (0; 2,2,2,2,4)
Group of order 64 # 229 acting with signature (0; 2,2,2,2,4)
Group of order 64 # 231 acting with signature (0; 2,2,2,2,4)
Group of order 64 # 234 acting with signature (0; 2,2,2,2,4)
Group of order 64 # 236 acting with signature (0; 2,2,2,2,4)
Group of order 64 # 242 acting with signature (0; 2,2,2,2,4)
Group of order 64 # 243 acting with signature (0; 2,2,2,2,4)
Group of order 64 # 253 acting with signature (0; 2,2,2,2,4)
Group of order 64 # 258 acting with signature (0; 2,2,2,2,4)
Group of order 72 # 48 acting with signature (0; 2,2,6,6)
Group of order 81 # 6 acting with signature (0; 3,27,27)
Group of order 96 # 45 acting with signature (1; 2)
Group of order 96 # 47 acting with signature (1; 2)
Group of order 96 # 51 acting with signature (1; 2)
Group of order 96 # 55 acting with signature (1; 2)
Group of order 96 # 80 acting with signature (0; 2,2,4,4)
Group of order 96 # 82 acting with signature (0; 2,2,4,4)
Group of order 96 # 87 acting with signature (0; 2,2,4,4)
Group of order 96 # 100 acting with signature (0; 2,2,4,4)
Group of order 96 # 101 acting with signature (0; 2,2,4,4)
Group of order 96 # 109 acting with signature (0; 2,2,4,4)
Group of order 96 # 134 acting with signature (0; 2,2,4,4)
Group of order 96 # 154 acting with signature (0; 2,2,4,4)
Group of order 96 # 199 acting with signature (1; 2)
Group of order 96 # 203 acting with signature (0; 2,3,3,3)
Group of order 96 # 207 acting with signature (0; 2,2,2,2,2)
Group of order 96 # 209 acting with signature (0; 2,2,2,2,2)
Group of order 96 # 211 acting with signature (0; 2,2,2,2,2)
Group of order 96 # 214 acting with signature (0; 2,2,2,2,2)
Group of order 96 # 216 acting with signature (0; 2,2,2,2,2)
Group of order 104 # 7 acting with signature (0; 4,4,26)
Group of order 108 # 18 acting with signature (0; 3,9,9)
Group of order 108 # 19 acting with signature (0; 3,9,9)
Group of order 110 # 3 acting with signature (0; 2,22,55)
Group of order 112 # 18 acting with signature (0; 4,4,14)
Group of order 112 # 20 acting with signature (0; 2,28,28)
Group of order 112 # 36 acting with signature (0; 2,2,2,14)
Group of order 120 # 17 acting with signature (0; 2,12,60)
Group of order 120 # 43 acting with signature (0; 2,15,30)
Group of order 128 # 16 acting with signature (0; 4,4,8)
Group of order 128 # 21 acting with signature (0; 4,4,8)
Group of order 128 # 26 acting with signature (0; 4,4,8)
Group of order 128 # 29 acting with signature (0; 4,4,8)
Group of order 128 # 46 acting with signature (0; 2,16,16)
Group of order 128 # 47 acting with signature (0; 2,16,16)
Group of order 128 # 52 acting with signature (0; 2,16,16)
Group of order 128 # 53 acting with signature (0; 2,16,16)
Group of order 128 # 61 acting with signature (0; 2,16,16)
Group of order 128 # 62 acting with signature (0; 2,16,16)
Group of order 128 # 76 acting with signature (0; 4,4,8)
Group of order 128 # 83 acting with signature (0; 4,4,8)
Group of order 128 # 84 acting with signature (0; 4,4,8)
Group of order 128 # 87 acting with signature (0; 2,16,16)
Group of order 128 # 89 acting with signature (0; 2,16,16)
Group of order 128 # 91 acting with signature (0; 2,16,16)
Group of order 128 # 122 acting with signature (0; 4,4,8)
Group of order 128 # 123 acting with signature (0; 4,4,8)
Group of order 128 # 139 acting with signature (0; 4,4,8)
Group of order 128 # 146 acting with signature (0; 4,4,8)
Group of order 128 # 332 acting with signature (0; 2,2,2,8)
Group of order 128 # 351 acting with signature (0; 2,2,2,8)
Group of order 128 # 353 acting with signature (0; 2,2,2,8)
Group of order 128 # 356 acting with signature (0; 2,2,2,8)
Group of order 128 # 357 acting with signature (0; 2,2,2,8)
Group of order 128 # 387 acting with signature (0; 2,2,2,8)
Group of order 128 # 388 acting with signature (0; 2,2,2,8)
Group of order 128 # 399 acting with signature (0; 2,2,2,8)
Group of order 128 # 419 acting with signature (0; 2,2,2,8)
Group of order 128 # 731 acting with signature (0; 2,2,2,8)
Group of order 128 # 734 acting with signature (0; 2,2,2,8)
Group of order 128 # 742 acting with signature (0; 2,2,2,8)
Group of order 128 # 749 acting with signature (0; 2,2,2,8)
Group of order 128 # 750 acting with signature (0; 2,2,2,8)
Group of order 128 # 924 acting with signature (0; 2,2,2,8)
Group of order 128 # 931 acting with signature (0; 2,2,2,8)
Group of order 128 # 934 acting with signature (0; 2,2,2,8)
Group of order 128 # 936 acting with signature (0; 2,2,2,8)
Group of order 128 # 945 acting with signature (0; 2,2,2,8)
Group of order 144 # 65 acting with signature (0; 2,12,12)
Group of order 144 # 79 acting with signature (0; 2,12,12)
Group of order 144 # 123 acting with signature (0; 3,4,12)
Group of order 144 # 125 acting with signature (0; 2,2,3,3)
Group of order 144 # 129 acting with signature (0; 3,4,12)
Group of order 144 # 144 acting with signature (0; 2,2,2,6)
Group of order 144 # 151 acting with signature (0; 2,2,2,6)
Group of order 144 # 153 acting with signature (0; 2,2,2,6)
Group of order 144 # 154 acting with signature (0; 2,2,2,6)
Group of order 144 # 156 acting with signature (0; 3,6,6)
Group of order 150 # 2 acting with signature (0; 2,6,75)
Group of order 162 # 7 acting with signature (0; 2,6,27)
Group of order 162 # 9 acting with signature (0; 2,6,27)
Group of order 168 # 48 acting with signature (0; 2,6,21)
Group of order 192 # 189 acting with signature (0; 3,4,6)
Group of order 192 # 195 acting with signature (0; 3,4,6)
Group of order 192 # 197 acting with signature (0; 3,4,6)
Group of order 192 # 198 acting with signature (0; 3,4,6)
Group of order 192 # 230 acting with signature (0; 2,2,2,4)
Group of order 192 # 271 acting with signature (0; 2,2,2,4)
Group of order 192 # 291 acting with signature (0; 2,2,2,4)
Group of order 192 # 300 acting with signature (0; 2,2,2,4)
Group of order 192 # 306 acting with signature (0; 2,2,2,4)
Group of order 192 # 312 acting with signature (0; 2,2,2,4)
Group of order 192 # 402 acting with signature (0; 2,2,2,4)
Group of order 192 # 467 acting with signature (0; 2,2,2,4)
Group of order 192 # 1003 acting with signature (0; 2,6,12)
Group of order 192 # 1470 acting with signature (0; 2,2,2,4)
Group of order 192 # 1472 acting with signature (0; 2,2,2,4)
Group of order 192 # 1478 acting with signature (0; 2,2,2,4)
Group of order 200 # 5 acting with signature (0; 2,4,100)
Group of order 208 # 14 acting with signature (0; 2,4,52)
Group of order 216 # 96 acting with signature (0; 2,6,9)
Group of order 216 # 97 acting with signature (0; 2,6,9)
Group of order 224 # 12 acting with signature (0; 2,4,28)
Group of order 256 # 64 acting with signature (0; 2,4,16)
Group of order 256 # 384 acting with signature (0; 2,4,16)
Group of order 256 # 386 acting with signature (0; 2,4,16)
Group of order 256 # 394 acting with signature (0; 2,4,16)
Group of order 256 # 503 acting with signature (0; 2,4,16)
Group of order 256 # 507 acting with signature (0; 2,4,16)
Group of order 256 # 511 acting with signature (0; 2,4,16)
Group of order 288 # 230 acting with signature (0; 3,3,6)
Group of order 288 # 386 acting with signature (0; 2,4,12)
Group of order 288 # 847 acting with signature (0; 2,2,2,3)
Group of order 288 # 859 acting with signature (0; 3,3,6)
Group of order 288 # 923 acting with signature (0; 2,6,6)
Group of order 288 # 1025 acting with signature (0; 2,6,6)
Group of order 320 # 1636 acting with signature (0; 2,4,10)
Group of order 360 # 122 acting with signature (0; 2,3,30)
Group of order 384 # 608 acting with signature (0; 2,3,24)
Group of order 576 # 1997 acting with signature (0; 2,3,12)
Group of order 576 # 8270 acting with signature (0; 2,3,12)
Number of different groups of strong symmetric genus 25 = 167

...........................................................................

Small groups with strong symmetric genus 26
Group of order 84 # 3 acting with signature (0; 3,28,28)
Group of order 96 # 34 acting with signature (0; 4,6,16)
Group of order 100 # 6 acting with signature (0; 4,5,20)
Group of order 100 # 11 acting with signature (0; 2,2,4,4)
Group of order 104 # 4 acting with signature (0; 4,4,52)
Group of order 108 # 1 acting with signature (0; 4,4,27)
Group of order 112 # 25 acting with signature (0; 2,28,56)
Group of order 120 # 25 acting with signature (0; 2,20,30)
Group of order 125 # 3 acting with signature (0; 5,5,5)
Group of order 125 # 3 acting with signature (0; 5,5,5)
Group of order 130 # 2 acting with signature (0; 2,10,65)
Group of order 144 # 18 acting with signature (0; 2,8,36)
Group of order 150 # 7 acting with signature (0; 3,6,6)
Group of order 150 # 11 acting with signature (0; 2,10,15)
Group of order 156 # 15 acting with signature (0; 2,6,78)
Group of order 168 # 16 acting with signature (0; 2,6,28)
Group of order 200 # 40 acting with signature (0; 2,8,8)
Group of order 200 # 44 acting with signature (0; 4,4,4)
Group of order 208 # 6 acting with signature (0; 2,4,104)
Group of order 216 # 8 acting with signature (0; 2,4,54)
Group of order 250 # 5 acting with signature (0; 2,5,10)
Group of order 300 # 23 acting with signature (0; 3,4,4)
Group of order 300 # 25 acting with signature (0; 2,2,2,3)
Group of order 300 # 27 acting with signature (0; 2,6,6)
Group of order 375 # 2 acting with signature (0; 3,3,5)
Group of order 600 # 150 acting with signature (0; 3,3,4)
Group of order 660 # 13 acting with signature (0; 2,3,11)
Group of order 750 # 5 acting with signature (0; 2,3,10)
Number of different groups of strong symmetric genus 26 = 28

...........................................................................

Small groups with strong symmetric genus 27
Group of order 80 # 9 acting with signature (0; 8,8,10)
Group of order 80 # 10 acting with signature (0; 8,8,10)
Group of order 80 # 40 acting with signature (0; 2,2,4,10)
Group of order 84 # 4 acting with signature (0; 4,12,21)
Group of order 96 # 14 acting with signature (0; 4,8,12)
Group of order 96 # 15 acting with signature (0; 4,8,12)
Group of order 96 # 17 acting with signature (0; 4,8,12)
Group of order 96 # 42 acting with signature (0; 4,8,12)
Group of order 96 # 191 acting with signature (0; 4,8,12)
Group of order 104 # 3 acting with signature (0; 4,8,8)
Group of order 104 # 11 acting with signature (1; 2)
Group of order 112 # 10 acting with signature (0; 4,4,28)
Group of order 112 # 11 acting with signature (0; 4,4,28)
Group of order 112 # 12 acting with signature (0; 4,4,28)
Group of order 112 # 23 acting with signature (0; 2,56,56)
Group of order 112 # 30 acting with signature (0; 2,2,2,28)
Group of order 114 # 3 acting with signature (0; 2,38,57)
Group of order 120 # 22 acting with signature (0; 2,20,60)
Group of order 126 # 3 acting with signature (0; 2,14,63)
Group of order 126 # 3 acting with signature (0; 2,14,63)
Group of order 144 # 5 acting with signature (0; 2,8,72)
Group of order 144 # 6 acting with signature (0; 2,8,72)
Group of order 144 # 36 acting with signature (0; 2,9,36)
Group of order 156 # 1 acting with signature (0; 3,4,12)
Group of order 156 # 7 acting with signature (0; 2,12,12)
  ... and with signature (0; 3,4,12)
Group of order 156 # 9 acting with signature (0; 2,12,12)
Group of order 156 # 10 acting with signature (0; 4,4,6)
Group of order 160 # 12 acting with signature (0; 2,8,20)
Group of order 160 # 16 acting with signature (0; 2,8,20)
Group of order 208 # 28 acting with signature (0; 2,8,8)
Group of order 208 # 29 acting with signature (0; 2,8,8)
Group of order 208 # 30 acting with signature (0; 4,4,4)
Group of order 208 # 31 acting with signature (0; 4,4,4)
Group of order 208 # 39 acting with signature (0; 2,2,2,4)
Group of order 208 # 42 acting with signature (0; 2,2,2,4)
Group of order 216 # 5 acting with signature (0; 2,4,108)
Group of order 224 # 27 acting with signature (0; 2,4,56)
Group of order 224 # 31 acting with signature (0; 2,4,56)
Group of order 240 # 197 acting with signature (0; 2,4,30)
Group of order 312 # 26 acting with signature (0; 3,3,6)
Group of order 312 # 46 acting with signature (0; 2,4,12)
Group of order 416 # 82 acting with signature (0; 2,4,8)
Group of order 416 # 85 acting with signature (0; 2,4,8)
Group of order 624 # 150 acting with signature (0; 2,3,12)
Number of different groups of strong symmetric genus 27 = 44

...........................................................................

Small groups with strong symmetric genus 28
Group of order 54 # 15 acting with signature (0; 3,3,6,6)
Group of order 80 # 1 acting with signature (0; 5,16,16)
Group of order 80 # 3 acting with signature (0; 5,16,16)
Group of order 80 # 27 acting with signature (0; 4,20,40)
Group of order 81 # 4 acting with signature (0; 9,9,9)
  ... and with signature (1; 3)
Group of order 81 # 10 acting with signature (0; 9,9,9)
  ... and with signature (1; 3)
Group of order 81 # 12 acting with signature (0; 3,3,3,3)
Group of order 90 # 5 acting with signature (0; 6,6,15)
Group of order 108 # 13 acting with signature (0; 3,12,12)
Group of order 108 # 20 acting with signature (1; 2)
Group of order 108 # 30 acting with signature (0; 6,6,6)
Group of order 108 # 32 acting with signature (0; 3,12,12)
Group of order 108 # 42 acting with signature (0; 6,6,6)
Group of order 108 # 43 acting with signature (0; 2,2,3,6)
Group of order 112 # 7 acting with signature (0; 4,4,56)
Group of order 116 # 1 acting with signature (0; 4,4,29)
Group of order 120 # 32 acting with signature (0; 2,30,60)
Group of order 126 # 4 acting with signature (0; 2,18,63)
Group of order 126 # 12 acting with signature (0; 2,21,42)
Group of order 126 # 4 acting with signature (0; 2,18,63)
Group of order 126 # 12 acting with signature (0; 2,21,42)
Group of order 140 # 8 acting with signature (0; 2,10,70)
Group of order 144 # 60 acting with signature (0; 2,12,24)
Group of order 144 # 71 acting with signature (0; 2,12,24)
Group of order 144 # 82 acting with signature (0; 2,12,24)
Group of order 144 # 121 acting with signature (0; 3,4,24)
Group of order 160 # 33 acting with signature (0; 2,10,16)
Group of order 162 # 3 acting with signature (0; 2,9,18)
Group of order 162 # 4 acting with signature (0; 2,9,18)
Group of order 162 # 6 acting with signature (0; 2,9,18)
Group of order 162 # 12 acting with signature (0; 2,9,18)
Group of order 162 # 17 acting with signature (0; 2,2,2,6)
Group of order 162 # 19 acting with signature (0; 2,2,2,6)
  ... and with signature (0; 2,2,3,3)
Group of order 162 # 20 acting with signature (0; 2,2,2,6)
Group of order 162 # 21 acting with signature (0; 2,2,2,6)
  ... and with signature (0; 2,2,3,3)
Group of order 162 # 22 acting with signature (0; 2,2,2,6)
Group of order 162 # 30 acting with signature (0; 3,6,6)
Group of order 162 # 34 acting with signature (0; 3,6,6)
Group of order 162 # 35 acting with signature (0; 3,6,6)
Group of order 162 # 40 acting with signature (0; 2,2,3,3)
Group of order 162 # 41 acting with signature (0; 2,2,3,3)
Group of order 168 # 26 acting with signature (0; 2,6,84)
Group of order 180 # 26 acting with signature (0; 2,6,30)
Group of order 180 # 29 acting with signature (0; 2,6,30)
Group of order 180 # 34 acting with signature (0; 2,6,30)
Group of order 216 # 37 acting with signature (0; 2,6,12)
Group of order 216 # 51 acting with signature (0; 2,6,12)
Group of order 216 # 60 acting with signature (0; 2,6,12)
Group of order 216 # 86 acting with signature (0; 2,8,8)
Group of order 216 # 88 acting with signature (0; 4,4,4)
Group of order 216 # 93 acting with signature (0; 2,2,2,4)
Group of order 216 # 94 acting with signature (0; 2,2,2,4)
Group of order 216 # 122 acting with signature (0; 2,6,12)
Group of order 216 # 157 acting with signature (0; 2,6,12)
Group of order 216 # 159 acting with signature (0; 2,6,12)
Group of order 224 # 6 acting with signature (0; 2,4,112)
Group of order 232 # 8 acting with signature (0; 2,4,58)
Group of order 243 # 3 acting with signature (0; 3,3,9)
Group of order 243 # 28 acting with signature (0; 3,3,9)
Group of order 324 # 39 acting with signature (0; 2,6,6)
Group of order 324 # 41 acting with signature (0; 2,2,2,3)
Group of order 324 # 54 acting with signature (0; 3,3,6)
Group of order 324 # 73 acting with signature (0; 2,6,6)
Group of order 324 # 113 acting with signature (0; 3,4,4)
Group of order 324 # 116 acting with signature (0; 2,6,6)
Group of order 324 # 117 acting with signature (0; 2,6,6)
Group of order 324 # 124 acting with signature (0; 2,2,2,3)
Group of order 432 # 248 acting with signature (0; 2,3,24)
Group of order 432 # 520 acting with signature (0; 2,4,8)
Group of order 486 # 5 acting with signature (0; 2,3,18)
Group of order 486 # 36 acting with signature (0; 2,3,18)
Group of order 486 # 39 acting with signature (0; 2,3,18)
Group of order 648 # 262 acting with signature (0; 2,3,12)
Group of order 648 # 532 acting with signature (0; 3,3,4)
Group of order 648 # 545 acting with signature (0; 2,4,6)
Group of order 648 # 703 acting with signature (0; 2,3,12)
Group of order 1296 # 2889 acting with signature (0; 2,3,8)
Number of different groups of strong symmetric genus 28 = 77

...........................................................................

Small groups with strong symmetric genus 29
Group of order 48 # 52 acting with signature (0; 2,2,2,6,6)
Group of order 64 # 96 acting with signature (0; 2,4,4,8)
Group of order 64 # 100 acting with signature (0; 2,4,4,8)
Group of order 64 # 106 acting with signature (0; 2,4,4,8)
Group of order 64 # 107 acting with signature (0; 2,4,4,8)
Group of order 64 # 108 acting with signature (0; 2,4,4,8)
Group of order 64 # 109 acting with signature (0; 2,4,4,8)
Group of order 64 # 132 acting with signature (0; 2,4,4,8)
Group of order 64 # 148 acting with signature (0; 2,4,4,8)
Group of order 64 # 151 acting with signature (0; 2,4,4,8)
Group of order 64 # 154 acting with signature (0; 2,4,4,8)
Group of order 64 # 164 acting with signature (0; 2,4,4,8)
Group of order 64 # 165 acting with signature (0; 2,4,4,8)
Group of order 64 # 166 acting with signature (0; 2,4,4,8)
Group of order 64 # 183 acting with signature (0; 2,2,16,16)
Group of order 64 # 184 acting with signature (0; 2,2,16,16)
Group of order 64 # 185 acting with signature (0; 2,2,16,16)
Group of order 64 # 259 acting with signature (0; 2,2,2,2,8)
Group of order 96 # 20 acting with signature (0; 4,8,24)
Group of order 96 # 21 acting with signature (0; 4,8,24)
Group of order 96 # 22 acting with signature (0; 4,8,24)
Group of order 96 # 31 acting with signature (0; 4,8,24)
Group of order 96 # 37 acting with signature (0; 6,8,8)
Group of order 96 # 40 acting with signature (0; 6,8,8)
Group of order 96 # 139 acting with signature (0; 2,2,4,6)
Group of order 96 # 145 acting with signature (0; 2,2,4,6)
Group of order 96 # 146 acting with signature (0; 2,2,4,6)
Group of order 96 # 160 acting with signature (0; 2,2,4,6)
Group of order 105 # 1 acting with signature (0; 3,15,15)
Group of order 112 # 21 acting with signature (1; 2)
Group of order 112 # 28 acting with signature (0; 2,2,4,4)
Group of order 112 # 42 acting with signature (0; 2,2,2,2,2)
Group of order 120 # 29 acting with signature (0; 4,4,30)
Group of order 128 # 72 acting with signature (0; 4,4,16)
Group of order 128 # 80 acting with signature (0; 4,4,16)
Group of order 128 # 112 acting with signature (0; 4,4,16)
Group of order 128 # 116 acting with signature (0; 4,4,16)
Group of order 128 # 118 acting with signature (0; 4,4,16)
Group of order 128 # 131 acting with signature (0; 2,32,32)
Group of order 128 # 132 acting with signature (0; 2,32,32)
Group of order 128 # 133 acting with signature (0; 2,32,32)
Group of order 128 # 918 acting with signature (0; 2,2,2,16)
Group of order 128 # 925 acting with signature (0; 2,2,2,16)
Group of order 128 # 947 acting with signature (0; 2,2,2,16)
Group of order 128 # 950 acting with signature (0; 2,2,2,16)
Group of order 128 # 953 acting with signature (0; 2,2,2,16)
Group of order 144 # 33 acting with signature (0; 4,4,9)
Group of order 144 # 110 acting with signature (0; 2,18,18)
Group of order 160 # 27 acting with signature (0; 2,8,40)
Group of order 160 # 30 acting with signature (0; 2,8,40)
Group of order 168 # 8 acting with signature (0; 2,12,12)
Group of order 168 # 50 acting with signature (0; 2,2,2,6)
Group of order 168 # 53 acting with signature (0; 3,6,6)
Group of order 174 # 2 acting with signature (0; 2,6,87)
Group of order 192 # 10 acting with signature (0; 2,8,12)
Group of order 192 # 30 acting with signature (0; 2,8,12)
Group of order 192 # 180 acting with signature (0; 3,4,8)
Group of order 192 # 182 acting with signature (0; 3,4,8)
Group of order 192 # 184 acting with signature (0; 3,4,8)
Group of order 192 # 951 acting with signature (0; 2,8,12)
Group of order 192 # 952 acting with signature (0; 2,8,12)
Group of order 192 # 953 acting with signature (0; 2,8,12)
Group of order 192 # 954 acting with signature (0; 2,8,12)
Group of order 192 # 976 acting with signature (0; 2,8,12)
Group of order 192 # 986 acting with signature (0; 2,8,12)
Group of order 192 # 1014 acting with signature (0; 2,6,24)
Group of order 192 # 1018 acting with signature (0; 2,6,24)
Group of order 192 # 1489 acting with signature (0; 3,4,8)
Group of order 192 # 1490 acting with signature (0; 3,4,8)
Group of order 192 # 1492 acting with signature (0; 3,4,8)
Group of order 210 # 3 acting with signature (0; 2,6,15)
Group of order 224 # 77 acting with signature (0; 2,2,2,4)
Group of order 224 # 90 acting with signature (0; 2,2,2,4)
Group of order 224 # 103 acting with signature (0; 2,2,2,4)
Group of order 232 # 5 acting with signature (0; 2,4,116)
Group of order 240 # 75 acting with signature (0; 2,4,60)
Group of order 256 # 406 acting with signature (0; 2,4,32)
Group of order 256 # 410 acting with signature (0; 2,4,32)
Group of order 288 # 342 acting with signature (0; 2,4,18)
Group of order 336 # 218 acting with signature (0; 2,6,6)
Group of order 672 # 1254 acting with signature (0; 2,4,6)
Number of different groups of strong symmetric genus 29 = 81

...........................................................................

Small groups with strong symmetric genus 30
Group of order 88 # 1 acting with signature (0; 8,8,11)
Group of order 96 # 1 acting with signature (0; 3,32,32)
Group of order 96 # 36 acting with signature (0; 4,12,16)
Group of order 120 # 11 acting with signature (0; 4,6,10)
Group of order 120 # 26 acting with signature (0; 4,4,60)
Group of order 124 # 1 acting with signature (0; 4,4,31)
Group of order 130 # 1 acting with signature (0; 2,26,65)
Group of order 132 # 6 acting with signature (0; 2,33,33)
Group of order 132 # 8 acting with signature (0; 2,22,66)
Group of order 140 # 9 acting with signature (0; 2,14,70)
Group of order 168 # 17 acting with signature (0; 2,12,14)
Group of order 176 # 14 acting with signature (0; 2,8,22)
Group of order 192 # 78 acting with signature (0; 2,6,32)
Group of order 240 # 67 acting with signature (0; 2,4,120)
Group of order 248 # 7 acting with signature (0; 2,4,62)
Group of order 264 # 32 acting with signature (0; 2,4,33)
Number of different groups of strong symmetric genus 30 = 16

...........................................................................

Small groups with strong symmetric genus 31
Group of order 64 # 188 acting with signature (0; 2,4,4,16)
Group of order 80 # 41 acting with signature (0; 2,4,4,4)
Group of order 96 # 53 acting with signature (0; 4,12,24)
Group of order 96 # 56 acting with signature (0; 4,12,24)
Group of order 96 # 57 acting with signature (0; 4,12,24)
Group of order 96 # 120 acting with signature (0; 2,2,4,8)
Group of order 96 # 125 acting with signature (0; 2,2,4,8)
Group of order 108 # 6 acting with signature (0; 4,9,12)
Group of order 108 # 9 acting with signature (0; 4,9,12)
Group of order 120 # 33 acting with signature (1; 2)
Group of order 128 # 148 acting with signature (0; 4,4,32)
Group of order 128 # 155 acting with signature (0; 4,4,32)
Group of order 128 # 156 acting with signature (0; 4,4,32)
Group of order 128 # 160 acting with signature (0; 2,64,64)
Group of order 128 # 994 acting with signature (0; 2,2,2,32)
Group of order 140 # 5 acting with signature (0; 2,28,28)
Group of order 140 # 6 acting with signature (0; 4,4,14)
Group of order 144 # 53 acting with signature (0; 2,24,24)
Group of order 144 # 55 acting with signature (0; 2,24,24)
Group of order 144 # 69 acting with signature (0; 2,24,24)
Group of order 144 # 70 acting with signature (0; 2,24,24)
Group of order 144 # 116 acting with signature (0; 4,4,12)
Group of order 144 # 141 acting with signature (0; 2,2,2,12)
Group of order 144 # 142 acting with signature (0; 2,2,2,12)
Group of order 144 # 145 acting with signature (0; 2,2,2,12)
Group of order 144 # 157 acting with signature (0; 3,6,12)
Group of order 150 # 8 acting with signature (0; 2,15,30)
Group of order 160 # 64 acting with signature (0; 2,16,16)
Group of order 160 # 65 acting with signature (0; 2,16,16)
Group of order 160 # 68 acting with signature (0; 4,4,8)
Group of order 160 # 69 acting with signature (0; 4,4,8)
Group of order 160 # 83 acting with signature (0; 4,4,8)
Group of order 160 # 84 acting with signature (0; 4,4,8)
Group of order 160 # 131 acting with signature (0; 2,2,2,8)
Group of order 160 # 135 acting with signature (0; 2,2,2,8)
Group of order 160 # 140 acting with signature (0; 2,2,2,8)
Group of order 186 # 4 acting with signature (0; 2,6,93)
Group of order 198 # 7 acting with signature (0; 2,6,33)
Group of order 240 # 179 acting with signature (0; 2,2,2,4)
Group of order 240 # 182 acting with signature (0; 2,2,2,4)
Group of order 248 # 4 acting with signature (0; 2,4,124)
Group of order 256 # 525 acting with signature (0; 2,4,64)
Group of order 256 # 528 acting with signature (0; 2,4,64)
Group of order 280 # 32 acting with signature (0; 2,4,28)
Group of order 288 # 377 acting with signature (0; 2,4,24)
Group of order 288 # 379 acting with signature (0; 2,4,24)
Group of order 320 # 242 acting with signature (0; 2,4,16)
Group of order 320 # 245 acting with signature (0; 2,4,16)
Group of order 360 # 119 acting with signature (0; 2,6,6)
Group of order 360 # 120 acting with signature (0; 3,4,4)
Group of order 450 # 20 acting with signature (0; 2,3,30)
Group of order 720 # 767 acting with signature (0; 2,4,6)
Number of different groups of strong symmetric genus 31 = 52

...........................................................................

Small groups with strong symmetric genus 32
Group of order 96 # 63 acting with signature (0; 4,12,48)
Group of order 112 # 15 acting with signature (0; 4,8,14)
Group of order 128 # 163 acting with signature (0; 4,4,64)
Group of order 132 # 3 acting with signature (0; 4,4,33)
Group of order 136 # 10 acting with signature (0; 2,34,68)
Group of order 144 # 25 acting with signature (0; 2,18,72)
Group of order 155 # 1 acting with signature (0; 5,5,5)
Group of order 160 # 35 acting with signature (0; 2,16,20)
Group of order 160 # 61 acting with signature (0; 2,10,80)
Group of order 176 # 16 acting with signature (0; 2,8,44)
Group of order 180 # 7 acting with signature (0; 2,10,18)
Group of order 186 # 2 acting with signature (0; 3,6,6)
Group of order 192 # 177 acting with signature (0; 2,6,96)
Group of order 204 # 7 acting with signature (0; 2,6,34)
Group of order 256 # 540 acting with signature (0; 2,4,128)
Group of order 264 # 27 acting with signature (0; 2,4,66)
Group of order 310 # 1 acting with signature (0; 2,5,10)
Group of order 372 # 7 acting with signature (0; 2,6,6)
Number of different groups of strong symmetric genus 32 = 18

...........................................................................