Groups with symmetric cross-cap number 3 to 65
.............................................
The symmetric cross-cap number of a finite group G is the smallest genus
of all the compact non-orientable surfaces on which G acts faithfully as
a group of automorphisms. This parameter was considered by Tom Tucker in
the 1980s as a variant of the "symmetric genus" (for actions on orientable
surfaces) and defined by Coy May in the 1990s).
The list below gives all the finite groups that have symmetric cross-cap
number between 3 and 65 inclusive, together with the signature types for
the action(s) of the group on (non-orientable) surfaces of the given
smallest possible genus.
The notation "Group of 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 March 2010.
Marston Conder
June 2013
...........................................................................
Groups with symmetric cross-cap number 3
Number of different groups with symmetric cross-cap number 3 = 0
...........................................................................
Groups with symmetric cross-cap number 4
Group of order 24 # 13 acting with signature (0; +; [6]; {(2)})
Group of order 48 # 48 acting with signature (0; +; [-]; {(2,4,6)})
Number of different groups with symmetric cross-cap number 4 = 2
...........................................................................
Groups with symmetric cross-cap number 5
Group of order 9 # 2 acting with signature (1; -; [3,3]; {-})
Group of order 18 # 3 acting with signature (0; +; [6]; {(3)})
... and with signature (0; +; [2,3]; {(1)})
Group of order 18 # 4 acting with signature (0; +; [2]; {(3,3)})
Group of order 20 # 3 acting with signature (0; +; [4]; {(5)})
Group of order 36 # 9 acting with signature (0; +; [4]; {(3)})
Group of order 36 # 10 acting with signature (0; +; [-]; {(2,6,6)})
... and with signature (0; +; [-]; {(2,2,2,3)})
Group of order 72 # 40 acting with signature (0; +; [-]; {(2,4,6)})
Group of order 120 # 34 acting with signature (0; +; [-]; {(2,4,5)})
Number of different groups with symmetric cross-cap number 5 = 8
...........................................................................
Groups with symmetric cross-cap number 6
Group of order 8 # 4 acting with signature (0; +; [4,4]; {(1)})
Group of order 16 # 3 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
... and with signature (0; +; [-]; {(1),(2)})
Group of order 16 # 6 acting with signature (0; +; [-]; {(1),(2)})
Group of order 16 # 8 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 16 # 13 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 32 # 27 acting with signature (0; +; [-]; {(2,2,2,4)})
Group of order 32 # 43 acting with signature (0; +; [-]; {(2,2,2,4)})
Group of order 80 # 49 acting with signature (0; +; [5]; {(2)})
Group of order 120 # 35 acting with signature (0; +; [-]; {(2,3,10)})
Group of order 160 # 234 acting with signature (0; +; [-]; {(2,4,5)})
Number of different groups with symmetric cross-cap number 6 = 11
...........................................................................
Groups with symmetric cross-cap number 7
Group of order 12 # 1 acting with signature (0; +; [3,4]; {(1)})
Group of order 24 # 8 acting with signature (0; +; [-]; {(2,2,3,4)})
Group of order 36 # 3 acting with signature (0; +; [9]; {(2)})
Group of order 72 # 15 acting with signature (0; +; [-]; {(2,4,9)})
Number of different groups with symmetric cross-cap number 7 = 4
...........................................................................
Groups with symmetric cross-cap number 8
Group of order 24 # 5 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 24 # 10 acting with signature (0; +; [-]; {(1),(2)})
Group of order 48 # 38 acting with signature (0; +; [-]; {(2,2,2,4)})
Group of order 56 # 11 acting with signature (0; +; [7]; {(2)})
Group of order 504 # 156 acting with signature (0; +; [-]; {(2,3,7)})
Number of different groups with symmetric cross-cap number 8 = 5
...........................................................................
Groups with symmetric cross-cap number 9
Group of order 21 # 1 acting with signature (1; -; [3,3]; {-})
Group of order 30 # 1 acting with signature (0; +; [10]; {(3)})
Group of order 30 # 2 acting with signature (0; +; [6]; {(5)})
Group of order 42 # 1 acting with signature (0; +; [2,3]; {(1)})
Group of order 60 # 8 acting with signature (0; +; [-]; {(2,6,10)})
Group of order 168 # 42 acting with signature (0; +; [3]; {(4)})
... and with signature (0; +; [-]; {(3,3,4)})
Group of order 336 # 208 acting with signature (0; +; [-]; {(2,3,8)})
Number of different groups with symmetric cross-cap number 9 = 7
...........................................................................
Groups with symmetric cross-cap number 10
Group of order 16 # 2 acting with signature (0; +; [4,4]; {(1)})
Group of order 16 # 4 acting with signature (0; +; [4,4]; {(1)})
Group of order 16 # 9 acting with signature (0; +; [4,4]; {(1)})
Group of order 16 # 10 acting with signature (0; +; [4]; {(2,2,2)})
... and with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 24 # 3 acting with signature (0; +; [3,3]; {(1)})
Group of order 32 # 5 acting with signature (0; +; [-]; {(1),(2)})
Group of order 32 # 6 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
... and with signature (0; +; [-]; {(1),(2)})
Group of order 32 # 7 acting with signature (0; +; [-]; {(1),(2)})
Group of order 32 # 9 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 32 # 11 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 32 # 17 acting with signature (0; +; [-]; {(1),(2)})
Group of order 32 # 19 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 32 # 28 acting with signature (0; +; [-]; {(2,2,4,4)})
Group of order 32 # 34 acting with signature (0; +; [-]; {(2,2,4,4)})
Group of order 32 # 42 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 48 # 29 acting with signature (0; +; [-]; {(2,2,3,3)})
... and with signature (0; +; [3]; {(2,2)})
... and with signature (0; +; [2,3]; {(1)})
Group of order 48 # 31 acting with signature (0; +; [12]; {(2)})
Group of order 48 # 33 acting with signature (0; +; [3]; {(2,2)})
... and with signature (0; +; [2,3]; {(1)})
Group of order 48 # 50 acting with signature (0; +; [3]; {(2,2)})
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 # 138 acting with signature (0; +; [-]; {(2,2,2,4)})
Group of order 64 # 190 acting with signature (0; +; [-]; {(2,2,2,4)})
Group of order 96 # 70 acting with signature (0; +; [6]; {(2)})
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 # 227 acting with signature (0; +; [-]; {(3,4,4)})
... and with signature (0; +; [-]; {(2,2,2,3)})
Group of order 192 # 955 acting with signature (0; +; [-]; {(2,4,6)})
Number of different groups with symmetric cross-cap number 10 = 30
...........................................................................
Groups with symmetric cross-cap number 11
Group of order 18 # 5 acting with signature (0; +; [3,6]; {(1)})
Group of order 27 # 3 acting with signature (1; -; [3,3]; {-})
Group of order 36 # 13 acting with signature (0; +; [-]; {(2,2,3,6)})
Group of order 54 # 5 acting with signature (0; +; [6]; {(3)})
... and with signature (0; +; [2,3]; {(1)})
Group of order 54 # 8 acting with signature (0; +; [2]; {(3,3)})
Group of order 108 # 15 acting with signature (0; +; [4]; {(3)})
Group of order 108 # 17 acting with signature (0; +; [-]; {(2,6,6)})
... and with signature (0; +; [-]; {(2,2,2,3)})
Group of order 216 # 87 acting with signature (0; +; [-]; {(2,4,6)})
Number of different groups with symmetric cross-cap number 11 = 8
...........................................................................
Groups with symmetric cross-cap number 12
Group of order 20 # 1 acting with signature (0; +; [4,4]; {(1)})
... and with signature (1; -; [4,4]; {-})
Group of order 40 # 5 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 40 # 8 acting with signature (0; +; [-]; {(2,2,4,4)})
... and with signature (0; +; [2]; {(4,4)})
... and with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 40 # 10 acting with signature (0; +; [-]; {(1),(2)})
Group of order 40 # 12 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 80 # 39 acting with signature (0; +; [-]; {(2,2,2,4)})
Group of order 240 # 189 acting with signature (0; +; [-]; {(2,4,6)})
Number of different groups with symmetric cross-cap number 12 = 7
...........................................................................
Groups with symmetric cross-cap number 13
Group of order 42 # 3 acting with signature (0; +; [14]; {(3)})
Group of order 42 # 4 acting with signature (0; +; [6]; {(7)})
Group of order 52 # 3 acting with signature (0; +; [4]; {(13)})
Group of order 60 # 9 acting with signature (0; +; [15]; {(2)})
Group of order 84 # 8 acting with signature (0; +; [-]; {(2,6,14)})
Group of order 120 # 38 acting with signature (0; +; [-]; {(2,4,15)})
Number of different groups with symmetric cross-cap number 13 = 6
...........................................................................
Groups with symmetric cross-cap number 14
Group of order 16 # 12 acting with signature (0; +; [4]; {(1),(1)})
Group of order 24 # 4 acting with signature (0; +; [4,4]; {(1)})
Group of order 24 # 7 acting with signature (0; +; [4,4]; {(1)})
Group of order 24 # 15 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 32 # 48 acting with signature (0; +; [-]; {(2,2,2,2,4)})
Group of order 36 # 11 acting with signature (0; +; [3,3]; {(1)})
... and with signature (1; -; [3,3]; {-})
Group of order 36 # 12 acting with signature (0; +; [6]; {(2,2)})
... and with signature (0; +; [2,6]; {(1)})
... and with signature (0; +; [-]; {(1),(3)})
Group of order 48 # 6 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 48 # 14 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 48 # 21 acting with signature (0; +; [-]; {(1),(2)})
Group of order 48 # 24 acting with signature (0; +; [-]; {(1),(2)})
Group of order 48 # 37 acting with signature (0; +; [-]; {(2,2,4,4)})
Group of order 48 # 43 acting with signature (0; +; [-]; {(2,2,4,4)})
Group of order 48 # 49 acting with signature (0; +; [-]; {(1),(2)})
Group of order 48 # 51 acting with signature (0; +; [-]; {(2,2,2,2,2)})
Group of order 72 # 42 acting with signature (0; +; [2,3]; {(1)})
Group of order 72 # 43 acting with signature (0; +; [-]; {(2,2,3,3)})
... and with signature (0; +; [2]; {(3,3)})
Group of order 72 # 44 acting with signature (0; +; [3]; {(2,2)})
... and with signature (0; +; [2,3]; {(1)})
Group of order 72 # 46 acting with signature (0; +; [-]; {(2,2,2,6)})
Group of order 96 # 89 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 # 226 acting with signature (0; +; [-]; {(2,2,2,4)})
Group of order 144 # 183 acting with signature (0; +; [-]; {(2,2,2,3)})
Group of order 180 # 19 acting with signature (0; +; [3]; {(5)})
Group of order 360 # 121 acting with signature (0; +; [-]; {(2,3,10)})
Number of different groups with symmetric cross-cap number 14 = 25
...........................................................................
Groups with symmetric cross-cap number 15
Group of order 24 # 1 acting with signature (0; +; [3,8]; {(1)})
Group of order 39 # 1 acting with signature (1; -; [3,3]; {-})
Group of order 48 # 15 acting with signature (0; +; [-]; {(2,2,3,8)})
Group of order 78 # 1 acting with signature (0; +; [2,3]; {(1)})
Group of order 1092 # 25 acting with signature (0; +; [-]; {(2,3,7)})
Number of different groups with symmetric cross-cap number 15 = 5
...........................................................................
Groups with symmetric cross-cap number 16
Group of order 28 # 1 acting with signature (0; +; [4,4]; {(1)})
... and with signature (1; -; [4,4]; {-})
Group of order 56 # 4 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 56 # 7 acting with signature (0; +; [-]; {(2,2,4,4)})
... and with signature (0; +; [2]; {(4,4)})
... and with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 56 # 9 acting with signature (0; +; [-]; {(1),(2)})
Group of order 72 # 16 acting with signature (0; +; [18]; {(2)})
Group of order 112 # 31 acting with signature (0; +; [-]; {(2,2,2,4)})
Group of order 144 # 109 acting with signature (0; +; [-]; {(2,4,18)})
Number of different groups with symmetric cross-cap number 16 = 7
...........................................................................
Groups with symmetric cross-cap number 17
Group of order 25 # 2 acting with signature (1; -; [5,5]; {-})
Group of order 27 # 2 acting with signature (1; -; [3,9]; {-})
Group of order 27 # 4 acting with signature (1; -; [3,9]; {-})
Group of order 36 # 6 acting with signature (0; +; [3,4]; {(1)})
Group of order 50 # 3 acting with signature (0; +; [10]; {(5)})
... and with signature (0; +; [2,5]; {(1)})
Group of order 50 # 4 acting with signature (0; +; [2]; {(5,5)})
Group of order 54 # 3 acting with signature (0; +; [6]; {(9)})
Group of order 54 # 4 acting with signature (0; +; [18]; {(3)})
Group of order 54 # 6 acting with signature (0; +; [6]; {(9)})
Group of order 54 # 7 acting with signature (0; +; [2]; {(3,9)})
Group of order 68 # 3 acting with signature (0; +; [4]; {(17)})
Group of order 72 # 23 acting with signature (0; +; [-]; {(2,2,3,4)})
Group of order 72 # 39 acting with signature (0; +; [8]; {(3)})
Group of order 100 # 12 acting with signature (0; +; [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 108 # 16 acting with signature (0; +; [-]; {(2,6,18)})
Group of order 200 # 43 acting with signature (0; +; [-]; {(2,4,10)})
Group of order 360 # 118 acting with signature (0; +; [-]; {(3,3,4)})
Group of order 720 # 764 acting with signature (0; +; [-]; {(2,3,8)})
Number of different groups with symmetric cross-cap number 17 = 19
...........................................................................
Groups with symmetric cross-cap number 18
Group of order 24 # 11 acting with signature (0; +; [4,12]; {(1)})
Group of order 32 # 2 acting with signature (0; +; [4,4]; {(1)})
Group of order 32 # 10 acting with signature (0; +; [4,4]; {(1)})
Group of order 32 # 13 acting with signature (0; +; [4,4]; {(1)})
Group of order 32 # 14 acting with signature (0; +; [4,4]; {(1)})
Group of order 32 # 20 acting with signature (0; +; [4,4]; {(1)})
Group of order 32 # 22 acting with signature (0; +; [4]; {(2,2,2)})
... and with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 32 # 25 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 32 # 30 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 32 # 36 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 32 # 37 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 32 # 38 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 32 # 40 acting with signature (0; +; [4]; {(2,2,2)})
... and with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 32 # 44 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 32 # 51 acting with signature (0; +; [-]; {(2,2,2,2,2,2)})
Group of order 48 # 3 acting with signature (0; +; [3,3]; {(1)})
... and with signature (1; -; [3,3]; {-})
Group of order 48 # 4 acting with signature (0; +; [-]; {(1),(3)})
Group of order 48 # 25 acting with signature (0; +; [6]; {(2,2)})
... and with signature (0; +; [2,6]; {(1)})
Group of order 48 # 41 acting with signature (0; +; [-]; {(2,2,4,12)})
Group of order 64 # 4 acting with signature (0; +; [-]; {(1),(2)})
Group of order 64 # 8 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 64 # 29 acting with signature (0; +; [-]; {(1),(2)})
Group of order 64 # 30 acting with signature (0; +; [-]; {(1),(2)})
Group of order 64 # 32 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
... and with signature (0; +; [-]; {(1),(2)})
Group of order 64 # 34 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 64 # 38 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 64 # 41 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 64 # 51 acting with signature (0; +; [-]; {(1),(2)})
Group of order 64 # 53 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 64 # 73 acting with signature (0; +; [-]; {(2,2,4,4)})
Group of order 64 # 130 acting with signature (0; +; [-]; {(2,2,4,4)})
Group of order 64 # 147 acting with signature (0; +; [-]; {(2,2,4,4)})
Group of order 64 # 150 acting with signature (0; +; [-]; {(2,2,4,4)})
Group of order 64 # 189 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 # 215 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 # 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 96 # 64 acting with signature (0; +; [-]; {(2,2,3,3)})
... and with signature (0; +; [2]; {(3,3)})
... and with signature (0; +; [2,3]; {(1)})
Group of order 96 # 72 acting with signature (0; +; [3]; {(2,2)})
... and with signature (0; +; [2,3]; {(1)})
Group of order 96 # 117 acting with signature (0; +; [-]; {(2,2,2,6)})
Group of order 96 # 229 acting with signature (0; +; [3]; {(2,2)})
Group of order 128 # 327 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 # 995 acting with signature (0; +; [-]; {(2,2,2,4)})
Group of order 192 # 956 acting with signature (0; +; [-]; {(2,2,2,3)})
Group of order 192 # 1538 acting with signature (0; +; [-]; {(2,2,2,3)})
Number of different groups with symmetric cross-cap number 18 = 52
...........................................................................
Groups with symmetric cross-cap number 19
Group of order 84 # 10 acting with signature (0; +; [21]; {(2)})
Group of order 168 # 46 acting with signature (0; +; [-]; {(2,4,21)})
Number of different groups with symmetric cross-cap number 19 = 2
...........................................................................
Groups with symmetric cross-cap number 20
Group of order 36 # 1 acting with signature (0; +; [4,4]; {(1)})
... and with signature (1; -; [4,4]; {-})
Group of order 48 # 5 acting with signature (0; +; [8]; {(2,2)})
... and with signature (0; +; [2,8]; {(1)})
Group of order 48 # 17 acting with signature (0; +; [8]; {(2,2)})
... and with signature (0; +; [2,8]; {(1)})
Group of order 48 # 26 acting with signature (0; +; [-]; {(1),(4)})
Group of order 72 # 5 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 72 # 8 acting with signature (0; +; [-]; {(2,2,4,4)})
... and with signature (0; +; [2]; {(4,4)})
... and with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 72 # 10 acting with signature (0; +; [-]; {(1),(2)})
Group of order 72 # 45 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 96 # 121 acting with signature (0; +; [-]; {(2,2,2,8)})
Group of order 144 # 41 acting with signature (0; +; [-]; {(2,2,2,4)})
Group of order 144 # 186 acting with signature (0; +; [-]; {(2,2,2,4)})
Number of different groups with symmetric cross-cap number 20 = 11
...........................................................................
Groups with symmetric cross-cap number 21
Group of order 57 # 1 acting with signature (1; -; [3,3]; {-})
Group of order 60 # 6 acting with signature (0; +; [12]; {(5)})
Group of order 66 # 1 acting with signature (0; +; [22]; {(3)})
Group of order 66 # 2 acting with signature (0; +; [6]; {(11)})
Group of order 114 # 1 acting with signature (0; +; [2,3]; {(1)})
Group of order 132 # 5 acting with signature (0; +; [-]; {(2,6,22)})
Number of different groups with symmetric cross-cap number 21 = 6
...........................................................................
Groups with symmetric cross-cap number 22
Group of order 32 # 3 acting with signature (0; +; [4,8]; {(1)})
Group of order 32 # 4 acting with signature (0; +; [4,8]; {(1)})
Group of order 32 # 8 acting with signature (0; +; [4,8]; {(1)})
Group of order 32 # 12 acting with signature (0; +; [4,8]; {(1)})
Group of order 32 # 31 acting with signature (0; +; [4]; {(2,2,4)})
Group of order 32 # 50 acting with signature (0; +; [-]; {(2,2,4,4,4)})
Group of order 40 # 4 acting with signature (0; +; [4,4]; {(1)})
Group of order 40 # 7 acting with signature (0; +; [4,4]; {(1)})
Group of order 40 # 14 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 48 # 28 acting with signature (0; +; [3,4]; {(1)})
Group of order 48 # 30 acting with signature (0; +; [3,4]; {(1)})
Group of order 48 # 32 acting with signature (0; +; [3,4]; {(1)})
Group of order 60 # 10 acting with signature (0; +; [6]; {(2,2)})
... and with signature (0; +; [2,6]; {(1)})
Group of order 60 # 11 acting with signature (0; +; [-]; {(1),(3)})
Group of order 64 # 135 acting with signature (0; +; [-]; {(2,2,4,8)})
Group of order 64 # 140 acting with signature (0; +; [-]; {(2,2,4,8)})
Group of order 64 # 174 acting with signature (0; +; [-]; {(2,2,4,8)})
Group of order 64 # 177 acting with signature (0; +; [-]; {(2,2,4,8)})
Group of order 80 # 6 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 80 # 14 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 80 # 21 acting with signature (0; +; [-]; {(1),(2)})
Group of order 80 # 24 acting with signature (0; +; [-]; {(1),(2)})
Group of order 80 # 34 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 80 # 38 acting with signature (0; +; [-]; {(2,2,4,4)})
Group of order 80 # 44 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 96 # 73 acting with signature (0; +; [24]; {(2)})
Group of order 96 # 189 acting with signature (0; +; [-]; {(2,2,3,4)})
Group of order 96 # 192 acting with signature (0; +; [-]; {(2,2,3,4)})
Group of order 96 # 195 acting with signature (0; +; [-]; {(2,2,3,4)})
Group of order 112 # 41 acting with signature (0; +; [14]; {(2)})
Group of order 120 # 42 acting with signature (0; +; [-]; {(2,2,2,6)})
Group of order 160 # 103 acting with signature (0; +; [-]; {(2,2,2,4)})
Group of order 160 # 129 acting with signature (0; +; [-]; {(2,2,2,4)})
Group of order 192 # 961 acting with signature (0; +; [-]; {(2,4,24)})
Group of order 240 # 190 acting with signature (0; +; [-]; {(2,2,2,3)})
Number of different groups with symmetric cross-cap number 22 = 36
...........................................................................
Groups with symmetric cross-cap number 23
Group of order 36 # 8 acting with signature (0; +; [3,12]; {(1)})
Group of order 42 # 2 acting with signature (0; +; [3,6]; {(1)})
Group of order 63 # 3 acting with signature (1; -; [3,3]; {-})
Group of order 72 # 33 acting with signature (0; +; [-]; {(2,2,3,12)})
Group of order 126 # 9 acting with signature (0; +; [2,3]; {(1)})
Group of order 504 # 157 acting with signature (0; +; [3]; {(4)})
Group of order 1008 # 881 acting with signature (0; +; [-]; {(2,3,8)})
Number of different groups with symmetric cross-cap number 23 = 7
...........................................................................
Groups with symmetric cross-cap number 24
Group of order 44 # 1 acting with signature (0; +; [4,4]; {(1)})
... and with signature (1; -; [4,4]; {-})
Group of order 88 # 4 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 88 # 7 acting with signature (0; +; [-]; {(2,2,4,4)})
... and with signature (0; +; [2]; {(4,4)})
... and with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 88 # 9 acting with signature (0; +; [-]; {(1),(2)})
Group of order 176 # 31 acting with signature (0; +; [-]; {(2,2,2,4)})
Number of different groups with symmetric cross-cap number 24 = 5
...........................................................................
Groups with symmetric cross-cap number 25
Group of order 70 # 1 acting with signature (0; +; [14]; {(5)})
Group of order 70 # 2 acting with signature (0; +; [10]; {(7)})
Group of order 78 # 3 acting with signature (0; +; [26]; {(3)})
Group of order 78 # 4 acting with signature (0; +; [6]; {(13)})
Group of order 100 # 3 acting with signature (0; +; [4]; {(25)})
Group of order 108 # 3 acting with signature (0; +; [27]; {(2)})
Group of order 140 # 7 acting with signature (0; +; [-]; {(2,10,14)})
Group of order 156 # 11 acting with signature (0; +; [-]; {(2,6,26)})
Group of order 216 # 21 acting with signature (0; +; [-]; {(2,4,27)})
Number of different groups with symmetric cross-cap number 25 = 9
...........................................................................
Groups with symmetric cross-cap number 26
Group of order 32 # 15 acting with signature (0; +; [8,8]; {(1)})
Group of order 32 # 21 acting with signature (0; +; [4]; {(1),(1)})
Group of order 32 # 23 acting with signature (0; +; [4]; {(1),(1)})
Group of order 32 # 24 acting with signature (0; +; [4]; {(1),(1)})
Group of order 32 # 29 acting with signature (0; +; [4]; {(1),(1)})
Group of order 32 # 41 acting with signature (0; +; [4]; {(1),(1)})
Group of order 32 # 45 acting with signature (0; +; [4]; {(2,2,2,2)})
... and with signature (0; +; [-]; {(2,2,2),(1)})
Group of order 36 # 14 acting with signature (0; +; [6,6]; {(1)})
... and with signature (0; +; [3]; {(1),(1)})
Group of order 48 # 8 acting with signature (0; +; [4,4]; {(1)})
Group of order 48 # 11 acting with signature (0; +; [4,4]; {(1)})
Group of order 48 # 12 acting with signature (0; +; [4,4]; {(1)})
Group of order 48 # 13 acting with signature (0; +; [4,4]; {(1)})
Group of order 48 # 19 acting with signature (0; +; [4,4]; {(1)})
Group of order 48 # 35 acting with signature (0; +; [4]; {(2,2,2)})
... and with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 48 # 39 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 48 # 44 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 48 # 45 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 48 # 47 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 6 acting with signature (0; +; [8]; {(2,2)})
... and with signature (0; +; [2,8]; {(1)})
... and with signature (0; +; [-]; {(1),(4)})
Group of order 64 # 10 acting with signature (0; +; [8]; {(2,2)})
... and with signature (0; +; [2,8]; {(1)})
... and with signature (0; +; [-]; {(1),(4)})
Group of order 64 # 12 acting with signature (0; +; [8]; {(2,2)})
... and with signature (0; +; [2,8]; {(1)})
... and with signature (0; +; [-]; {(1),(4)})
Group of order 64 # 31 acting with signature (0; +; [-]; {(1),(4)})
Group of order 64 # 36 acting with signature (0; +; [8]; {(2,2)})
... and with signature (0; +; [2,8]; {(1)})
... and with signature (0; +; [-]; {(1),(4)})
Group of order 64 # 40 acting with signature (0; +; [8]; {(2,2)})
... and with signature (0; +; [2,8]; {(1)})
Group of order 64 # 42 acting with signature (0; +; [8]; {(2,2)})
... and with signature (0; +; [2,8]; {(1)})
Group of order 64 # 153 acting with signature (0; +; [-]; {(2,2,8,8)})
Group of order 64 # 203 acting with signature (0; +; [-]; {(2,2,2,2,4)})
Group of order 64 # 211 acting with signature (0; +; [-]; {(2,2,2,2,4)})
Group of order 64 # 216 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 # 242 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 # 21 acting with signature (0; +; [-]; {(1),(3)})
Group of order 72 # 25 acting with signature (0; +; [3,3]; {(1)})
Group of order 72 # 27 acting with signature (0; +; [-]; {(1),(3)})
Group of order 72 # 28 acting with signature (0; +; [6]; {(2,2)})
... and with signature (0; +; [2,6]; {(1)})
Group of order 72 # 30 acting with signature (0; +; [6]; {(2,2)})
... and with signature (0; +; [2,6]; {(1)})
Group of order 72 # 49 acting with signature (0; +; [-]; {(2,2,6,6)})
... and with signature (0; +; [-]; {(2,2,2,2,3)})
Group of order 96 # 7 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 96 # 13 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 96 # 28 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 96 # 32 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 96 # 48 acting with signature (0; +; [-]; {(1),(2)})
Group of order 96 # 49 acting with signature (0; +; [-]; {(1),(2)})
Group of order 96 # 50 acting with signature (0; +; [-]; {(1),(2)})
Group of order 96 # 60 acting with signature (0; +; [-]; {(1),(2)})
Group of order 96 # 91 acting with signature (0; +; [-]; {(2,2,4,4)})
Group of order 96 # 111 acting with signature (0; +; [-]; {(2,2,4,4)})
Group of order 96 # 137 acting with signature (0; +; [-]; {(2,2,4,4)})
Group of order 96 # 144 acting with signature (0; +; [-]; {(2,2,4,4)})
Group of order 96 # 147 acting with signature (0; +; [-]; {(2,2,4,4)})
Group of order 96 # 186 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 96 # 196 acting with signature (0; +; [-]; {(1),(2)})
Group of order 96 # 197 acting with signature (0; +; [-]; {(1),(2)})
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 # 216 acting with signature (0; +; [-]; {(2,2,2,2,2)})
Group of order 128 # 351 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 # 924 acting with signature (0; +; [-]; {(2,2,2,8)})
Group of order 128 # 934 acting with signature (0; +; [-]; {(2,2,2,8)})
Group of order 144 # 122 acting with signature (0; +; [3]; {(2,2)})
... and with signature (0; +; [2,3]; {(1)})
Group of order 144 # 125 acting with signature (0; +; [-]; {(2,2,3,3)})
Group of order 144 # 127 acting with signature (0; +; [3]; {(2,2)})
... and with signature (0; +; [2,3]; {(1)})
Group of order 144 # 144 acting with signature (0; +; [-]; {(2,2,2,6)})
Group of order 144 # 154 acting with signature (0; +; [-]; {(2,2,2,6)})
Group of order 160 # 235 acting with signature (0; +; [10]; {(2)})
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 # 467 acting with signature (0; +; [-]; {(2,2,2,4)})
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 288 # 847 acting with signature (0; +; [-]; {(2,2,2,3)})
Group of order 320 # 1636 acting with signature (0; +; [-]; {(2,4,10)})
Number of different groups with symmetric cross-cap number 26 = 77
...........................................................................
Groups with symmetric cross-cap number 27
Group of order 40 # 3 acting with signature (0; +; [4,8]; {(1)})
Group of order 75 # 2 acting with signature (1; -; [3,3]; {-})
Group of order 150 # 5 acting with signature (0; +; [2]; {(3,3)})
... and with signature (0; +; [2,3]; {(1)})
Group of order 150 # 6 acting with signature (0; +; [2,3]; {(1)})
Group of order 300 # 25 acting with signature (0; +; [-]; {(2,2,2,3)})
Number of different groups with symmetric cross-cap number 27 = 5
...........................................................................
Groups with symmetric cross-cap number 28
Group of order 52 # 1 acting with signature (0; +; [4,4]; {(1)})
... and with signature (1; -; [4,4]; {-})
Group of order 104 # 5 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 104 # 8 acting with signature (0; +; [-]; {(2,2,4,4)})
... and with signature (0; +; [2]; {(4,4)})
... and with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 104 # 10 acting with signature (0; +; [-]; {(1),(2)})
Group of order 104 # 12 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 120 # 43 acting with signature (0; +; [30]; {(2)})
Group of order 208 # 39 acting with signature (0; +; [-]; {(2,2,2,4)})
Group of order 240 # 197 acting with signature (0; +; [-]; {(2,4,30)})
Number of different groups with symmetric cross-cap number 28 = 8
...........................................................................
Groups with symmetric cross-cap number 29
Group of order 27 # 5 acting with signature (1; -; [3,3,3]; {-})
Group of order 40 # 1 acting with signature (0; +; [5,8]; {(1)})
Group of order 45 # 2 acting with signature (1; -; [3,15]; {-})
Group of order 54 # 10 acting with signature (0; +; [3,6]; {(1)})
Group of order 54 # 12 acting with signature (0; +; [3,6]; {(1)})
Group of order 54 # 13 acting with signature (0; +; [6]; {(3,3)})
... and with signature (0; +; [2,3]; {(3)})
Group of order 54 # 14 acting with signature (0; +; [2]; {(3,3,3)})
Group of order 80 # 15 acting with signature (0; +; [-]; {(2,2,5,8)})
Group of order 81 # 7 acting with signature (1; -; [3,3]; {-})
Group of order 81 # 9 acting with signature (1; -; [3,3]; {-})
Group of order 90 # 6 acting with signature (0; +; [30]; {(3)})
Group of order 90 # 7 acting with signature (0; +; [6]; {(15)})
Group of order 90 # 9 acting with signature (0; +; [2]; {(3,15)})
Group of order 108 # 28 acting with signature (0; +; [-]; {(2,2,3,6)})
Group of order 108 # 36 acting with signature (0; +; [12]; {(3)})
Group of order 108 # 39 acting with signature (0; +; [-]; {(2,2,3,6)})
Group of order 108 # 40 acting with signature (0; +; [-]; {(6,6,6)})
... and with signature (0; +; [-]; {(2,3,2,6)})
Group of order 116 # 3 acting with signature (0; +; [4]; {(29)})
Group of order 162 # 10 acting with signature (0; +; [6]; {(3)})
Group of order 162 # 11 acting with signature (0; +; [6]; {(3)})
Group of order 162 # 14 acting with signature (0; +; [2,3]; {(1)})
Group of order 162 # 15 acting with signature (0; +; [2,3]; {(1)})
Group of order 162 # 19 acting with signature (0; +; [2]; {(3,3)})
Group of order 162 # 21 acting with signature (0; +; [2]; {(3,3)})
Group of order 180 # 29 acting with signature (0; +; [-]; {(2,6,30)})
Group of order 216 # 159 acting with signature (0; +; [-]; {(2,6,12)})
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 # 160 acting with signature (0; +; [3]; {(6)})
Group of order 648 # 703 acting with signature (0; +; [-]; {(2,3,12)})
Number of different groups with symmetric cross-cap number 29 = 30
...........................................................................
Groups with symmetric cross-cap number 30
Group of order 40 # 11 acting with signature (0; +; [4,20]; {(1)})
Group of order 48 # 16 acting with signature (0; +; [4,6]; {(1)})
Group of order 56 # 3 acting with signature (0; +; [4,4]; {(1)})
Group of order 56 # 6 acting with signature (0; +; [4,4]; {(1)})
Group of order 56 # 13 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 80 # 42 acting with signature (0; +; [-]; {(2,2,4,20)})
Group of order 84 # 7 acting with signature (0; +; [6]; {(2,2)})
... and with signature (0; +; [2,6]; {(1)})
Group of order 84 # 11 acting with signature (0; +; [3,3]; {(1)})
... and with signature (1; -; [3,3]; {-})
Group of order 84 # 12 acting with signature (0; +; [6]; {(2,2)})
... and with signature (0; +; [2,6]; {(1)})
Group of order 84 # 13 acting with signature (0; +; [-]; {(1),(3)})
Group of order 96 # 118 acting with signature (0; +; [-]; {(2,2,4,6)})
Group of order 96 # 204 acting with signature (0; +; [3]; {(2,4)})
Group of order 112 # 5 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 112 # 13 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 112 # 20 acting with signature (0; +; [-]; {(1),(2)})
Group of order 112 # 23 acting with signature (0; +; [-]; {(1),(2)})
Group of order 112 # 30 acting with signature (0; +; [-]; {(2,2,4,4)})
Group of order 112 # 36 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 160 # 199 acting with signature (0; +; [5]; {(4)})
Group of order 168 # 49 acting with signature (0; +; [3]; {(2,2)})
... and with signature (0; +; [2,3]; {(1)})
Group of order 168 # 50 acting with signature (0; +; [-]; {(2,2,2,6)})
Group of order 192 # 1494 acting with signature (0; +; [-]; {(3,4,8)})
Group of order 224 # 77 acting with signature (0; +; [-]; {(2,2,2,4)})
Group of order 224 # 103 acting with signature (0; +; [-]; {(2,2,2,4)})
Group of order 320 # 1582 acting with signature (0; +; [-]; {(2,5,8)})
Group of order 336 # 209 acting with signature (0; +; [-]; {(3,4,4)})
Group of order 672 # 1254 acting with signature (0; +; [-]; {(2,4,6)})
Number of different groups with symmetric cross-cap number 30 = 28
...........................................................................
Groups with symmetric cross-cap number 31
Group of order 48 # 1 acting with signature (0; +; [3,16]; {(1)})
Group of order 96 # 33 acting with signature (0; +; [-]; {(2,2,3,16)})
Group of order 132 # 6 acting with signature (0; +; [33]; {(2)})
Group of order 264 # 32 acting with signature (0; +; [-]; {(2,4,33)})
Number of different groups with symmetric cross-cap number 31 = 4
...........................................................................
Groups with symmetric cross-cap number 32
Group of order 48 # 18 acting with signature (0; +; [4,8]; {(1)})
Group of order 60 # 3 acting with signature (0; +; [4,4]; {(1)})
... and with signature (1; -; [4,4]; {-})
Group of order 60 # 7 acting with signature (0; +; [4,4]; {(1)})
... and with signature (1; -; [4,4]; {-})
Group of order 80 # 4 acting with signature (0; +; [8]; {(2,2)})
... and with signature (0; +; [2,8]; {(1)})
Group of order 80 # 5 acting with signature (0; +; [8]; {(2,2)})
... and with signature (0; +; [2,8]; {(1)})
Group of order 80 # 17 acting with signature (0; +; [8]; {(2,2)})
... and with signature (0; +; [2,8]; {(1)})
Group of order 80 # 25 acting with signature (0; +; [-]; {(1),(4)})
Group of order 80 # 26 acting with signature (0; +; [-]; {(1),(4)})
Group of order 80 # 28 acting with signature (0; +; [8]; {(2,2)})
... and with signature (0; +; [2,8]; {(1)})
Group of order 80 # 29 acting with signature (0; +; [8]; {(2,2)})
... and with signature (0; +; [2,8]; {(1)})
Group of order 96 # 123 acting with signature (0; +; [-]; {(2,2,4,8)})
Group of order 120 # 27 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 120 # 30 acting with signature (0; +; [-]; {(2,2,4,4)})
... and with signature (0; +; [2]; {(4,4)})
... and with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
Group of order 120 # 32 acting with signature (0; +; [-]; {(1),(2)})
Group of order 120 # 36 acting with signature (0; +; [4]; {(2,2)})
... and with signature (0; +; [2,4]; {(1)})
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 240 # 179 acting with signature (0; +; [-]; {(2,2,2,4)})
Group of order 360 # 119 acting with signature (0; +; [6]; {(2)})
Group of order 360 # 120 acting with signature (0; +; [4]; {(3)})
Group of order 720 # 767 acting with signature (0; +; [-]; {(2,4,6)})
Number of different groups with symmetric cross-cap number 32 = 21
...........................................................................
Groups with symmetric cross-cap number 33
Group of order 90 # 1 acting with signature (0; +; [10]; {(9)})
Group of order 90 # 2 acting with signature (0; +; [18]; {(5)})
Group of order 93 # 1 acting with signature (1; -; [3,3]; {-})
Group of order 102 # 1 acting with signature (0; +; [34]; {(3)})
Group of order 102 # 2 acting with signature (0; +; [6]; {(17)})
Group of order 180 # 7 acting with signature (0; +; [-]; {(2,10,18)})
Group of order 186 # 1 acting with signature (0; +; [2,3]; {(1)})
Group of order 204 # 7 acting with signature (0; +; [-]; {(2,6,34)})
Number of different groups with symmetric cross-cap number 33 = 8
...........................................................................
Groups with symmetric cross-cap number 34
Group of order 32 # 33 acting with signature (0; +; [4,4]; {(2,2)})
... and with signature (0; +; [2,4,4]; {(1)})
... and with signature (0; +; [4]; {(1),(2)})
Group of order 32 # 47 acting with signature (0; +; [-]; {(1),(1),(1)})
Group of order 48 # 9 acting with signature (0; +; [3]; {(1),(1)})
Group of order 48 # 20 acting with signature (0; +; [4,12]; {(1)})
Group of order 48 # 22 acting with signature (0; +; [4,12]; {(1)})
Group of order 48 # 27 acting with signature (0; +; [4,12]; {(1)})
Group of order 64 # 9 acting with signature (0; +; [4,4]; {(1)})
Group of order 64 # 18 acting with signature (0; +; [4,4]; {(1)})
Group of order 64 # 20 acting with signature (0; +; [4,4]; {(1)})
Group of order 64 # 21 acting with signature (0; +; [4,4]; {(1)})
Group of order 64 # 23 acting with signature (0; +; [4,4]; {(1)})
Group of order 64 # 33 acting with signature (0; +; [4,4]; {(1)})
Group of order 64 # 35 acting with signature (0; +; [4,4]; {(1)})
Group of order 64 # 39 acting with signature (0; +; [4,4]; {(1)})
Group of order 64 # 47 acting with signature (0; +; [4,4]; {(1)})
Group of order 64 # 48 acting with signature (0; +; [4,4]; {(1)})
Group of order 64 # 54 acting with signature (0; +; [4,4]; {(1)})
Group of order 64 # 60 acting with signature (0; +; [4]; {(2,2,2)})
... and with signature (0; +; [-]; {(2,2),(1)})
Group of order 64 # 67 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 87 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 88 acting with signature (0; +; [-]; {(2,2),(1)})
Group of order 64 # 89 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 90 acting with signature (0; +; [4]; {(2,2,2)})
... and with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 92 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 94 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 95 acting with signature (0; +; [4]; {(2,2,2)})
... and with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 97 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 98 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 99 acting with signature (0; +; [4]; {(2,2,2)})
... and with signature (0; +; [-]; {(2,2),(1)})
Group of order 64 # 101 acting with signature (0; +; [4]; {(2,2,2)})
... and with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 102 acting with signature (0; +; [4]; {(2,2,2)})
... and with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 115 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 116 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 118 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 123 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 124 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 125 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 129 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 131 acting with signature (0; +; [4]; {(2,2,2)})
... and with signature (0; +; [-]; {(2,2),(1)})
Group of order 64 # 136 acting with signature (0; +; [4]; {(2,2,2)})
... and with signature (0; +; [-]; {(2,2),(1)})
Group of order 64 # 139 acting with signature (0; +; [4]; {(2,2,2)})
Group of order 64 # 144 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 146 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 152 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 161 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 162 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 183 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 184 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 185 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 187 acting with signature (0; +; [4]; {(2,2,2)})
... and with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 191 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 64 # 206 acting with signature (0; +; [-]; {(2,2,2,4,4)})
... and with signature (0; +; [-]; {(2,2,4,2,4)})
Group of order 64 # 219 acting with signature (0; +; [-]; {(2,2,2,4,4)})
... and with signature (0; +; [-]; {(2,2,4,2,4)})
Group of order 64 # 241 acting with signature (0; +; [-]; {(2,2,2,4,4)})
... and with signature (0; +; [-]; {(2,2,4,2,4)})
Group of order 64 # 261 acting with signature (0; +; [-]; {(2,2,2,2,2,2)})
Group of order 64 # 263 acting with signature (0; +; [-]; {(2,2,2,2,2,2)})
Group of order 64 # 264 acting with signature (0; +; [-]; {(2,2,2,2,2,2)})
Group of order 64 # 266 acting with signature (0; +; [-]; {(2,2,2,2,2,2)})
Group of order 96 # 3 acting with signature (0; +; [3,3]; {(1)})
Group of order 96 # 4 acting with signature (0; +; [-]; {(1),(3)})
Group of order 96 # 61 acting with signature (0; +; [6]; {(2,2)})
... and with signature (0; +; [2,6]; {(1)})
Group of order 96 # 74 acting with signature (0; +; [24]; {(4)})
Group of order 96 # 81 acting with signature (0; +; [-]; {(2,2,4,12)})
Group of order 96 # 102 acting with signature (0; +; [-]; {(2,2,4,12)})
Group of order 96 # 126 acting with signature (0; +; [-]; {(2,2,4,12)})
Group of order 96 # 138 acting with signature (0; +; [-]; {(2,2,2,2,3)})
Group of order 96 # 190 acting with signature (0; +; [6]; {(2,2)})
... and with signature (0; +; [2,6]; {(1)})
... and with signature (0; +; [-]; {(1),(3)})
Group of order 96 # 200 acting with signature (0; +; [6]; {(2,2)})
... and with signature (0; +; [2,6]; {(1)})
Group of order 96 # 202 acting with signature (0; +; [6]; {(2,2)})
... and with signature (0; +; [2,6]; {(1)})
Group of order 96 # 203 acting with signature (0; +; [3,3]; {(1)})
Number of different groups with symmetric cross-cap number 34 = 70
...........................................................................
Groups with symmetric cross-cap number 35
Group of order 54 # 9 acting with signature (0; +; [3,18]; {(1)})
Group of order 54 # 11 acting with signature (0; +; [3,18]; {(1)})
Group of order 55 # 1 acting with signature (1; -; [5,5]; {-})
Group of order 108 # 27 acting with signature (0; +; [-]; {(2,2,3,18)})
Group of order 110 # 1 acting with signature (0; +; [2,5]; {(1)})
Number of different groups with symmetric cross-cap number 35 = 5
...........................................................................
Groups with symmetric cross-cap number 36
Group of order 48 # 10 acting with signature (0; +; [6,8]; {(1)})
Group of order 68 # 1 acting with signature (0; +; [4,4]; {(1)})
... and with signature (1; -; [4,4]; {-})
Group of order 96 # 156 acting with signature (0; +; [-]; {(2,2,6,8)})
Group of order 120 # 37 acting with signature (0; +; [20]; {(3)})
Group of order 120 # 39 acting with signature (0; +; [6]; {(10)})
Number of different groups with symmetric cross-cap number 36 = 5
...........................................................................
Groups with symmetric cross-cap number 37
Group of order 49 # 2 acting with signature (1; -; [7,7]; {-})
Group of order 50 # 5 acting with signature (0; +; [5,10]; {(1)})
Group of order 84 # 1 acting with signature (0; +; [3,4]; {(1)})
Group of order 98 # 3 acting with signature (0; +; [14]; {(7)})
... and with signature (0; +; [2,7]; {(1)})
Group of order 98 # 4 acting with signature (0; +; [2]; {(7,7)})
Group of order 100 # 9 acting with signature (0; +; [20]; {(5)})
Group of order 100 # 15 acting with signature (0; +; [-]; {(2,2,5,10)})
Group of order 114 # 3 acting with signature (0; +; [38]; {(3)})
Group of order 114 # 4 acting with signature (0; +; [6]; {(19)})
Number of different groups with symmetric cross-cap number 37 = 9
...........................................................................
Groups with symmetric cross-cap number 38
Group of order 48 # 34 acting with signature (0; +; [4]; {(1),(1)})
Group of order 48 # 40 acting with signature (0; +; [4]; {(1),(1)})
Group of order 48 # 42 acting with signature (0; +; [4]; {(1),(1)})
Group of order 48 # 46 acting with signature (0; +; [4]; {(1),(1)})
Group of order 48 # 52 acting with signature (0; +; [-]; {(2,2,2),(1)})
Group of order 72 # 4 acting with signature (0; +; [4,4]; {(1)})
Group of order 72 # 7 acting with signature (0; +; [4,4]; {(1)})
Group of order 72 # 18 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 72 # 41 acting with signature (0; +; [4,4]; {(1)})
Group of order 72 # 47 acting with signature (0; +; [3,6]; {(1)})
Group of order 72 # 48 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 12 acting with signature (0; +; [8]; {(2,2)})
... and with signature (0; +; [2,8]; {(1)})
Group of order 96 # 16 acting with signature (0; +; [8]; {(2,2)})
... and with signature (0; +; [2,8]; {(1)})
Group of order 96 # 27 acting with signature (0; +; [8]; {(2,2)})
... and with signature (0; +; [2,8]; {(1)})
Group of order 96 # 30 acting with signature (0; +; [8]; {(2,2)})
... and with signature (0; +; [2,8]; {(1)})
Group of order 96 # 52 acting with signature (0; +; [-]; {(1),(4)})
Group of order 96 # 54 acting with signature (0; +; [-]; {(1),(4)})
Group of order 96 # 201 acting with signature (0; +; [-]; {(1),(4)})
Group of order 96 # 208 acting with signature (0; +; [-]; {(2,2,2,2,4)})
Group of order 96 # 213 acting with signature (0; +; [-]; {(2,2,2,2,4)})
Group of order 96 # 215 acting with signature (0; +; [-]; {(2,2,2,2,4)})
Group of order 96 # 219 acting with signature (0; +; [-]; {(2,2,2,2,4)})
Group of order 108 # 22 acting with signature (0; +; [3,3]; {(1)})
... and with signature (1; -; [3,3]; {-})
Group of order 108 # 23 acting with signature (0; +; [6]; {(2,2)})
... and with signature (0; +; [2,6]; {(1)})
Group of order 108 # 24 acting with signature (0; +; [-]; {(1),(3)})
Group of order 108 # 25 acting with signature (0; +; [6]; {(2,2)})
... and with signature (0; +; [2,6]; {(1)})
... and with signature (0; +; [-]; {(1),(3)})
Group of order 108 # 26 acting with signature (0; +; [6]; {(2,2)})
... and with signature (0; +; [2,6]; {(1)})
Group of order 108 # 38 acting with signature (0; +; [6]; {(2,2)})
... and with signature (0; +; [2,6]; {(1)})
... and with signature (0; +; [-]; {(1),(3)})
Number of different groups with symmetric cross-cap number 38 = 28
...........................................................................
Groups with symmetric cross-cap number 39
Group of order 60 # 1 acting with signature (0; +; [3,20]; {(1)})
Group of order 111 # 1 acting with signature (1; -; [3,3]; {-})
Group of order 120 # 12 acting with signature (0; +; [-]; {(2,2,3,20)})
Number of different groups with symmetric cross-cap number 39 = 3
...........................................................................
Groups with symmetric cross-cap number 40
Group of order 76 # 1 acting with signature (0; +; [4,4]; {(1)})
... and with signature (1; -; [4,4]; {-})
Number of different groups with symmetric cross-cap number 40 = 1
...........................................................................
Groups with symmetric cross-cap number 41
Group of order 36 # 7 acting with signature (0; +; [3,3,4]; {(1)})
Group of order 63 # 4 acting with signature (1; -; [3,21]; {-})
Group of order 72 # 12 acting with signature (0; +; [3,8]; {(1)})
Group of order 72 # 19 acting with signature (0; +; [3,8]; {(1)})
Group of order 72 # 22 acting with signature (0; +; [-]; {(2,2,3,4,3)})
... and with signature (0; +; [3]; {(2,2,4)})
Group of order 72 # 35 acting with signature (0; +; [-]; {(2,2,3,3,4)})
Group of order 78 # 2 acting with signature (0; +; [3,6]; {(1)})
Group of order 110 # 3 acting with signature (0; +; [22]; {(5)})
Group of order 110 # 4 acting with signature (0; +; [10]; {(11)})
Group of order 117 # 3 acting with signature (1; -; [3,3]; {-})
Group of order 126 # 12 acting with signature (0; +; [42]; {(3)})
Group of order 126 # 13 acting with signature (0; +; [6]; {(21)})
Group of order 126 # 15 acting with signature (0; +; [2]; {(3,21)})
Number of different groups with symmetric cross-cap number 41 = 13
...........................................................................
Groups with symmetric cross-cap number 42
Group of order 32 # 26 acting with signature (0; +; [4,4,4]; {(1)})
Group of order 32 # 32 acting with signature (0; +; [4,4,4]; {(1)})
Group of order 32 # 35 acting with signature (0; +; [4,4,4]; {(1)})
Group of order 56 # 10 acting with signature (0; +; [4,28]; {(1)})
Group of order 60 # 2 acting with signature (0; +; [4,12]; {(1)})
... and with signature (1; -; [4,12]; {-})
Group of order 64 # 5 acting with signature (0; +; [4,8]; {(1)})
Group of order 64 # 7 acting with signature (0; +; [4,8]; {(1)})
Group of order 64 # 11 acting with signature (0; +; [4,8]; {(1)})
Group of order 64 # 13 acting with signature (0; +; [4,8]; {(1)})
Group of order 64 # 14 acting with signature (0; +; [4,8]; {(1)})
Group of order 64 # 17 acting with signature (0; +; [4,8]; {(1)})
Group of order 64 # 24 acting with signature (0; +; [4,8]; {(1)})
Group of order 64 # 25 acting with signature (0; +; [4,8]; {(1)})
Group of order 64 # 37 acting with signature (0; +; [4,8]; {(1)})
Group of order 64 # 43 acting with signature (0; +; [4,8]; {(1)})
Group of order 64 # 46 acting with signature (0; +; [4,8]; {(1)})
Group of order 64 # 71 acting with signature (0; +; [4]; {(2,2,4)})
Group of order 64 # 75 acting with signature (0; +; [4]; {(2,2,4)})
Group of order 64 # 91 acting with signature (0; +; [4]; {(2,2,4)})
Group of order 64 # 133 acting with signature (0; +; [4]; {(2,2,4)})
Group of order 64 # 137 acting with signature (0; +; [4]; {(2,2,4)})
Group of order 64 # 141 acting with signature (0; +; [4]; {(2,2,4)})
Group of order 64 # 149 acting with signature (0; +; [4]; {(2,2,4)})
Group of order 64 # 163 acting with signature (0; +; [4]; {(2,2,4)})
Group of order 64 # 167 acting with signature (0; +; [4]; {(2,2,4)})
Group of order 64 # 171 acting with signature (0; +; [4]; {(2,2,4)})
Group of order 64 # 173 acting with signature (0; +; [4]; {(2,2,4)})
Group of order 64 # 213 acting with signature (0; +; [-]; {(2,2,4,4,4)})
Group of order 64 # 218 acting with signature (0; +; [-]; {(2,2,4,4,4)})
Group of order 64 # 221 acting with signature (0; +; [-]; {(2,2,4,4,4)})
Group of order 64 # 228 acting with signature (0; +; [-]; {(2,2,4,4,4)})
Group of order 64 # 229 acting with signature (0; +; [-]; {(2,2,4,4,4)})
Group of order 64 # 231 acting with signature (0; +; [-]; {(2,2,4,4,4)})
Group of order 64 # 234 acting with signature (0; +; [-]; {(2,2,4,4,4)})
Group of order 64 # 236 acting with signature (0; +; [-]; {(2,2,4,4,4)})
Group of order 64 # 243 acting with signature (0; +; [-]; {(2,2,4,4,4)})
Group of order 64 # 259 acting with signature (0; +; [-]; {(2,2,4,4,4)})
Group of order 80 # 8 acting with signature (0; +; [4,4]; {(1)})
Group of order 80 # 11 acting with signature (0; +; [4,4]; {(1)})
Group of order 80 # 12 acting with signature (0; +; [4,4]; {(1)})
Group of order 80 # 13 acting with signature (0; +; [4,4]; {(1)})
Group of order 80 # 19 acting with signature (0; +; [4,4]; {(1)})
Group of order 80 # 30 acting with signature (0; +; [4,4]; {(1)})
Group of order 80 # 31 acting with signature (0; +; [4,4]; {(1)})
Group of order 80 # 36 acting with signature (0; +; [4]; {(2,2,2)})
... and with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 80 # 40 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 80 # 45 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 80 # 46 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 80 # 48 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 80 # 50 acting with signature (0; +; [4]; {(2,2,2)})
... and with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 5 acting with signature (0; +; [-]; {(1),(6)})
Group of order 96 # 35 acting with signature (0; +; [12]; {(2,2)})
... and with signature (0; +; [2,12]; {(1)})
Group of order 96 # 62 acting with signature (0; +; [12]; {(2,2)})
... and with signature (0; +; [2,12]; {(1)})
Group of order 96 # 66 acting with signature (0; +; [3,4]; {(1)})
Group of order 96 # 67 acting with signature (0; +; [3,4]; {(1)})
Group of order 96 # 68 acting with signature (0; +; [3,4]; {(1)})
Group of order 96 # 69 acting with signature (0; +; [3,4]; {(1)})
Group of order 96 # 71 acting with signature (0; +; [3,4]; {(1)})
Group of order 100 # 14 acting with signature (0; +; [10]; {(2,2)})
... and with signature (0; +; [2,10]; {(1)})
... and with signature (0; +; [-]; {(1),(5)})
Group of order 112 # 34 acting with signature (0; +; [-]; {(2,2,4,28)})
Group of order 120 # 5 acting with signature (0; +; [3,3]; {(1)})
Group of order 120 # 13 acting with signature (0; +; [-]; {(2,2,4,12)})
... and with signature (0; +; [2]; {(4,12)})
Group of order 120 # 18 acting with signature (0; +; [6]; {(2,2)})
... and with signature (0; +; [2,6]; {(1)})
Group of order 120 # 22 acting with signature (0; +; [-]; {(1),(3)})
Number of different groups with symmetric cross-cap number 42 = 64
...........................................................................
Groups with symmetric cross-cap number 43
Group of order 56 # 1 acting with signature (0; +; [7,8]; {(1)})
Group of order 112 # 14 acting with signature (0; +; [-]; {(2,2,7,8)})
Number of different groups with symmetric cross-cap number 43 = 2
...........................................................................
Groups with symmetric cross-cap number 44
Group of order 72 # 20 acting with signature (0; +; [4,6]; {(1)})
Group of order 72 # 29 acting with signature (0; +; [4,6]; {(1)})
Group of order 72 # 32 acting with signature (0; +; [2,4]; {(3)})
... and with signature (0; +; [4]; {(2,2,3)})
Group of order 84 # 5 acting with signature (0; +; [4,4]; {(1)})
... and with signature (1; -; [4,4]; {-})
Group of order 112 # 3 acting with signature (0; +; [8]; {(2,2)})
... and with signature (0; +; [2,8]; {(1)})
Group of order 112 # 4 acting with signature (0; +; [8]; {(2,2)})
... and with signature (0; +; [2,8]; {(1)})
Group of order 112 # 16 acting with signature (0; +; [8]; {(2,2)})
... and with signature (0; +; [2,8]; {(1)})
Group of order 112 # 24 acting with signature (0; +; [-]; {(1),(4)})
Group of order 112 # 25 acting with signature (0; +; [-]; {(1),(4)})
Number of different groups with symmetric cross-cap number 44 = 9
...........................................................................
Groups with symmetric cross-cap number 46
Group of order 64 # 26 acting with signature (0; +; [4,16]; {(1)})
Group of order 64 # 27 acting with signature (0; +; [4,16]; {(1)})
Group of order 64 # 28 acting with signature (0; +; [4,16]; {(1)})
Group of order 64 # 44 acting with signature (0; +; [4,16]; {(1)})
Group of order 64 # 45 acting with signature (0; +; [4,16]; {(1)})
Group of order 64 # 176 acting with signature (0; +; [4]; {(2,2,8)})
Group of order 88 # 3 acting with signature (0; +; [4,4]; {(1)})
Group of order 88 # 6 acting with signature (0; +; [4,4]; {(1)})
Group of order 88 # 12 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 139 acting with signature (0; +; [-]; {(2,2,2,3,4)})
Group of order 96 # 160 acting with signature (0; +; [-]; {(2,2,2,3,4)})
Number of different groups with symmetric cross-cap number 46 = 11
...........................................................................
Groups with symmetric cross-cap number 47
Group of order 72 # 14 acting with signature (0; +; [3,24]; {(1)})
Group of order 81 # 3 acting with signature (1; -; [3,9]; {-})
Group of order 81 # 8 acting with signature (1; -; [3,9]; {-})
Group of order 108 # 8 acting with signature (0; +; [3,4]; {(1)})
Group of order 108 # 37 acting with signature (0; +; [3,4]; {(1)})
Number of different groups with symmetric cross-cap number 47 = 5
...........................................................................
Groups with symmetric cross-cap number 48
Group of order 72 # 3 acting with signature (0; +; [4,9]; {(1)})
... and with signature (1; -; [4,9]; {-})
Group of order 92 # 1 acting with signature (0; +; [4,4]; {(1)})
... and with signature (1; -; [4,4]; {-})
Number of different groups with symmetric cross-cap number 48 = 2
...........................................................................
Groups with symmetric cross-cap number 49
Group of order 63 # 1 acting with signature (1; -; [7,9]; {-})
Group of order 126 # 1 acting with signature (0; +; [18]; {(7)})
Group of order 126 # 3 acting with signature (0; +; [14]; {(9)})
Group of order 126 # 4 acting with signature (0; +; [18]; {(7)})
Number of different groups with symmetric cross-cap number 49 = 4
...........................................................................
Groups with symmetric cross-cap number 50
Group of order 64 # 2 acting with signature (0; +; [8,8]; {(1)})
Group of order 64 # 3 acting with signature (0; +; [8,8]; {(1)})
Group of order 64 # 15 acting with signature (0; +; [8,8]; {(1)})
Group of order 64 # 16 acting with signature (0; +; [8,8]; {(1)})
Group of order 64 # 19 acting with signature (0; +; [8,8]; {(1)})
Group of order 64 # 22 acting with signature (0; +; [8,8]; {(1)})
Group of order 64 # 49 acting with signature (0; +; [8,8]; {(1)})
Group of order 64 # 56 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 58 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 61 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 62 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 66 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 83 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 84 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 86 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 93 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 96 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 100 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 103 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 105 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 106 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 107 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 108 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 109 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 117 acting with signature (0; +; [8]; {(2,2,4)})
... and with signature (0; +; [-]; {(2,2),(2)})
... and with signature (0; +; [-]; {(4,4),(1)})
... and with signature (0; +; [2]; {(1),(2)})
Group of order 64 # 119 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 121 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 132 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 142 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 148 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 154 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 155 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 157 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 159 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 164 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 165 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 188 acting with signature (0; +; [4]; {(1),(1)})
Group of order 64 # 193 acting with signature (0; +; [4]; {(2,2,2,2)})
... and with signature (0; +; [-]; {(2,2,2),(1)})
Group of order 64 # 196 acting with signature (0; +; [4]; {(2,2,2,2)})
... and with signature (0; +; [-]; {(2,2,2),(1)})
Group of order 64 # 199 acting with signature (0; +; [4]; {(2,2,2,2)})
... and with signature (0; +; [-]; {(2,2,2),(1)})
Group of order 64 # 205 acting with signature (0; +; [4]; {(2,2,2,2)})
... and with signature (0; +; [-]; {(2,2,2),(1)})
Group of order 64 # 207 acting with signature (0; +; [4]; {(2,2,2,2)})
Group of order 64 # 232 acting with signature (0; +; [-]; {(2,2,2),(1)})
Group of order 64 # 246 acting with signature (0; +; [-]; {(2,2,2),(1)})
Group of order 64 # 247 acting with signature (0; +; [-]; {(2,2,2),(1)})
Group of order 64 # 248 acting with signature (0; +; [-]; {(2,2,2),(1)})
Group of order 64 # 249 acting with signature (0; +; [-]; {(2,2,2),(1)})
Group of order 64 # 251 acting with signature (0; +; [4]; {(2,2,2,2)})
... and with signature (0; +; [-]; {(2,2,2),(1)})
Group of order 64 # 255 acting with signature (0; +; [4]; {(2,2,2,2)})
... and with signature (0; +; [-]; {(2,2,2),(1)})
Group of order 64 # 265 acting with signature (0; +; [-]; {(2,2,2,2,4,4)})
... and with signature (0; +; [-]; {(2,2,4,2,2,4)})
Group of order 64 # 267 acting with signature (0; +; [-]; {(2,2,2,2,2,2,2)})
Group of order 72 # 24 acting with signature (0; +; [4,12]; {(1)})
Group of order 72 # 26 acting with signature (0; +; [4,12]; {(1)})
Group of order 72 # 36 acting with signature (0; +; [3]; {(1),(1)})
Group of order 72 # 37 acting with signature (0; +; [6,6]; {(1)})
Group of order 96 # 8 acting with signature (0; +; [4,4]; {(1)})
Group of order 96 # 23 acting with signature (0; +; [4,4]; {(1)})
Group of order 96 # 24 acting with signature (0; +; [4,4]; {(1)})
Group of order 96 # 25 acting with signature (0; +; [4,4]; {(1)})
Group of order 96 # 38 acting with signature (0; +; [4,4]; {(1)})
Group of order 96 # 41 acting with signature (0; +; [4,4]; {(1)})
Group of order 96 # 80 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 87 acting with signature (0; +; [4]; {(2,2,2)})
... and with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 88 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 93 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 100 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 101 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 106 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 107 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 108 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 109 acting with signature (0; +; [4]; {(2,2,2)})
... and with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 113 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 114 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 116 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 120 acting with signature (0; +; [4]; {(2,2,2)})
... and with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 125 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 134 acting with signature (0; +; [4]; {(2,2,2)})
... and with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 135 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 136 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 146 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 148 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 149 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 157 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 162 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 165 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 167 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 168 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 170 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 176 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 177 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 178 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 179 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 180 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 182 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 183 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 184 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 185 acting with signature (0; +; [4,4]; {(1)})
Group of order 96 # 194 acting with signature (0; +; [4,4]; {(1)})
Group of order 96 # 228 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 96 # 230 acting with signature (0; +; [-]; {(2,2,2,2,2,2)})
Group of order 120 # 17 acting with signature (0; +; [-]; {(1),(5)})
Group of order 120 # 23 acting with signature (0; +; [10]; {(2,2)})
... and with signature (0; +; [2,10]; {(1)})
Group of order 120 # 40 acting with signature (0; +; [-]; {(1),(5)})
Number of different groups with symmetric cross-cap number 50 = 103
...........................................................................
Groups with symmetric cross-cap number 51
Group of order 84 # 2 acting with signature (0; +; [3,12]; {(1)})
Number of different groups with symmetric cross-cap number 51 = 1
...........................................................................
Groups with symmetric cross-cap number 52
Group of order 80 # 16 acting with signature (0; +; [4,8]; {(1)})
Group of order 80 # 18 acting with signature (0; +; [4,8]; {(1)})
Group of order 80 # 32 acting with signature (0; +; [4,8]; {(1)})
Group of order 80 # 33 acting with signature (0; +; [4,8]; {(1)})
Group of order 100 # 1 acting with signature (0; +; [4,4]; {(1)})
... and with signature (1; -; [4,4]; {-})
Group of order 100 # 10 acting with signature (0; +; [4,4]; {(1)})
... and with signature (1; -; [4,4]; {-})
Group of order 120 # 10 acting with signature (0; +; [12]; {(2,2)})
... and with signature (0; +; [2,12]; {(1)})
Group of order 120 # 20 acting with signature (0; +; [12]; {(2,2)})
... and with signature (0; +; [2,12]; {(1)})
Group of order 120 # 25 acting with signature (0; +; [-]; {(1),(6)})
Number of different groups with symmetric cross-cap number 52 = 9
...........................................................................
Groups with symmetric cross-cap number 53
Group of order 81 # 5 acting with signature (1; -; [3,27]; {-})
Group of order 81 # 6 acting with signature (1; -; [3,27]; {-})
Group of order 90 # 8 acting with signature (0; +; [10]; {(3,3)})
Number of different groups with symmetric cross-cap number 53 = 3
...........................................................................
Groups with symmetric cross-cap number 54
Group of order 72 # 11 acting with signature (0; +; [4,36]; {(1)})
Group of order 96 # 65 acting with signature (0; +; [3,8]; {(1)})
Group of order 104 # 4 acting with signature (0; +; [4,4]; {(1)})
Group of order 104 # 7 acting with signature (0; +; [4,4]; {(1)})
Group of order 104 # 14 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Number of different groups with symmetric cross-cap number 54 = 5
...........................................................................
Groups with symmetric cross-cap number 55
Group of order 84 # 3 acting with signature (0; +; [3,28]; {(1)})
Number of different groups with symmetric cross-cap number 55 = 1
...........................................................................
Groups with symmetric cross-cap number 56
Group of order 72 # 1 acting with signature (0; +; [8,8]; {(1)})
... and with signature (1; -; [8,8]; {-})
Group of order 108 # 1 acting with signature (0; +; [4,4]; {(1)})
... and with signature (1; -; [4,4]; {-})
Number of different groups with symmetric cross-cap number 56 = 2
...........................................................................
Groups with symmetric cross-cap number 57
Group of order 75 # 3 acting with signature (1; -; [5,15]; {-})
Group of order 100 # 6 acting with signature (0; +; [4,5]; {(1)})
Group of order 100 # 11 acting with signature (0; +; [4]; {(5,5)})
Number of different groups with symmetric cross-cap number 57 = 3
...........................................................................
Groups with symmetric cross-cap number 58
Group of order 64 # 85 acting with signature (0; +; [8]; {(1),(1)})
Group of order 64 # 104 acting with signature (0; +; [8]; {(1),(1)})
Group of order 64 # 110 acting with signature (0; +; [8]; {(1),(1)})
Group of order 64 # 111 acting with signature (0; +; [8]; {(1),(1)})
Group of order 64 # 112 acting with signature (0; +; [8]; {(1),(1)})
Group of order 64 # 113 acting with signature (0; +; [8]; {(1),(1)})
Group of order 64 # 198 acting with signature (0; +; [-]; {(2,2,4),(1)})
Group of order 64 # 201 acting with signature (0; +; [-]; {(2,2,4),(1)})
Group of order 64 # 210 acting with signature (0; +; [-]; {(2,2,4),(1)})
Group of order 64 # 217 acting with signature (0; +; [-]; {(2,2,4),(1)})
Group of order 64 # 220 acting with signature (0; +; [-]; {(2,2,4),(1)})
Group of order 64 # 223 acting with signature (0; +; [-]; {(2,2,4),(1)})
Group of order 64 # 240 acting with signature (0; +; [-]; {(2,2,4),(1)})
Group of order 80 # 20 acting with signature (0; +; [4,20]; {(1)})
Group of order 80 # 22 acting with signature (0; +; [4,20]; {(1)})
Group of order 80 # 27 acting with signature (0; +; [4,20]; {(1)})
Group of order 84 # 4 acting with signature (0; +; [4,12]; {(1)})
... and with signature (1; -; [4,12]; {-})
Group of order 84 # 9 acting with signature (0; +; [6,6]; {(1)})
... and with signature (0; +; [3]; {(1),(1)})
Group of order 96 # 34 acting with signature (0; +; [4,6]; {(1)})
Group of order 96 # 39 acting with signature (0; +; [4,6]; {(1)})
Group of order 96 # 44 acting with signature (0; +; [4,6]; {(1)})
Group of order 96 # 119 acting with signature (0; +; [-]; {(2,2,4,3,4)})
Group of order 96 # 145 acting with signature (0; +; [-]; {(2,2,4,3,4)})
... and with signature (0; +; [-]; {(2,2,3,4,4)})
Group of order 96 # 188 acting with signature (0; +; [4,6]; {(1)})
Group of order 96 # 198 acting with signature (0; +; [4,6]; {(1)})
Group of order 112 # 7 acting with signature (0; +; [4,4]; {(1)})
Group of order 112 # 10 acting with signature (0; +; [4,4]; {(1)})
Group of order 112 # 11 acting with signature (0; +; [4,4]; {(1)})
Group of order 112 # 12 acting with signature (0; +; [4,4]; {(1)})
Group of order 112 # 18 acting with signature (0; +; [4,4]; {(1)})
Group of order 112 # 28 acting with signature (0; +; [4]; {(2,2,2)})
... and with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 112 # 32 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 112 # 37 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 112 # 38 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 112 # 40 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Number of different groups with symmetric cross-cap number 58 = 35
...........................................................................
Groups with symmetric cross-cap number 59
Group of order 90 # 10 acting with signature (0; +; [3,30]; {(1)})
Group of order 114 # 2 acting with signature (0; +; [3,6]; {(1)})
Number of different groups with symmetric cross-cap number 59 = 2
...........................................................................
Groups with symmetric cross-cap number 60
Group of order 116 # 1 acting with signature (0; +; [4,4]; {(1)})
... and with signature (1; -; [4,4]; {-})
Number of different groups with symmetric cross-cap number 60 = 1
...........................................................................
Groups with symmetric cross-cap number 61
Group of order 80 # 1 acting with signature (0; +; [5,16]; {(1)})
Group of order 80 # 3 acting with signature (0; +; [5,16]; {(1)})
Number of different groups with symmetric cross-cap number 61 = 2
...........................................................................
Groups with symmetric cross-cap number 62
Group of order 72 # 38 acting with signature (0; +; [12,12]; {(1)})
Group of order 72 # 50 acting with signature (0; +; [6]; {(1),(1)})
Group of order 80 # 9 acting with signature (0; +; [8,8]; {(1)})
Group of order 80 # 10 acting with signature (0; +; [8,8]; {(1)})
Group of order 80 # 35 acting with signature (0; +; [4]; {(1),(1)})
Group of order 80 # 41 acting with signature (0; +; [4]; {(1),(1)})
Group of order 80 # 43 acting with signature (0; +; [4]; {(1),(1)})
Group of order 80 # 47 acting with signature (0; +; [4]; {(1),(1)})
Group of order 80 # 52 acting with signature (0; +; [-]; {(2,2,2),(1)})
Group of order 90 # 5 acting with signature (0; +; [6,6]; {(1)})
... and with signature (1; -; [6,6]; {-})
Group of order 96 # 14 acting with signature (0; +; [4,8]; {(1)})
Group of order 96 # 15 acting with signature (0; +; [4,8]; {(1)})
Group of order 96 # 17 acting with signature (0; +; [4,8]; {(1)})
Group of order 96 # 20 acting with signature (0; +; [4,8]; {(1)})
Group of order 96 # 21 acting with signature (0; +; [4,8]; {(1)})
Group of order 96 # 22 acting with signature (0; +; [4,8]; {(1)})
Group of order 96 # 31 acting with signature (0; +; [4,8]; {(1)})
Group of order 96 # 42 acting with signature (0; +; [4,8]; {(1)})
Group of order 96 # 82 acting with signature (0; +; [4]; {(2,2,4)})
Group of order 96 # 90 acting with signature (0; +; [4]; {(2,2,4)})
Group of order 96 # 92 acting with signature (0; +; [4]; {(2,2,4)})
Group of order 96 # 122 acting with signature (0; +; [4]; {(2,2,4)})
Group of order 96 # 154 acting with signature (0; +; [4]; {(2,2,4)})
Group of order 96 # 191 acting with signature (0; +; [4,8]; {(1)})
Group of order 96 # 210 acting with signature (0; +; [-]; {(2,2,4,4,4)})
Group of order 96 # 214 acting with signature (0; +; [-]; {(2,2,4,4,4)})
Group of order 96 # 217 acting with signature (0; +; [-]; {(2,2,4,4,4)})
Group of order 108 # 18 acting with signature (0; +; [3,9]; {(1)})
... and with signature (1; -; [3,9]; {-})
Group of order 108 # 19 acting with signature (0; +; [3,9]; {(1)})
... and with signature (1; -; [3,9]; {-})
Group of order 120 # 26 acting with signature (0; +; [4,4]; {(1)})
Group of order 120 # 29 acting with signature (0; +; [4,4]; {(1)})
Group of order 120 # 41 acting with signature (0; +; [4,4]; {(1)})
Group of order 120 # 44 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 120 # 45 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Group of order 120 # 47 acting with signature (0; +; [-]; {(2,2),(1)})
... and with signature (0; +; [2]; {(1),(1)})
Number of different groups with symmetric cross-cap number 62 = 35
...........................................................................
Groups with symmetric cross-cap number 63
Group of order 96 # 1 acting with signature (0; +; [3,32]; {(1)})
Number of different groups with symmetric cross-cap number 63 = 1
...........................................................................
Groups with symmetric cross-cap number 64
Group of order 124 # 1 acting with signature (0; +; [4,4]; {(1)})
... and with signature (1; -; [4,4]; {-})
Number of different groups with symmetric cross-cap number 64 = 1
...........................................................................
Groups with symmetric cross-cap number 65
Group of order 54 # 15 acting with signature (0; +; [3,3,6]; {(1)})
Group of order 81 # 2 acting with signature (1; -; [9,9]; {-})
Group of order 81 # 4 acting with signature (1; -; [9,9]; {-})
Group of order 81 # 10 acting with signature (1; -; [9,9]; {-})
Group of order 99 # 2 acting with signature (1; -; [3,33]; {-})
Group of order 105 # 1 acting with signature (1; -; [3,15]; {-})
Group of order 108 # 13 acting with signature (0; +; [3,12]; {(1)})
Group of order 108 # 32 acting with signature (0; +; [3,12]; {(1)})
Group of order 108 # 43 acting with signature (0; +; [3]; {(2,2,6)})
Group of order 108 # 44 acting with signature (0; +; [-]; {(2,2,3,6,3)})
... and with signature (0; +; [-]; {(2,2,3,3,6)})
Group of order 126 # 7 acting with signature (0; +; [3,6]; {(1)})
Group of order 126 # 8 acting with signature (0; +; [3,6]; {(1)})
Group of order 126 # 10 acting with signature (0; +; [3,6]; {(1)})
Number of different groups with symmetric cross-cap number 65 = 13
...........................................................................