Symmetric cross-cap number of groups of order 2 to 127 ...................................................... 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 the symmetric cross-cap number of all groups of order 2 to 127 inclusive, together with the signature types for the action(s) of the group on (non-orientable) 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 March 2010. Marston Conder June 2013 ........................................................................... Groups of order 2 Total number of groups = 1 Order 2 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(1)}) ] ........................................................................... Groups of order 3 Total number of groups = 1 Order 3 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[3];{-}) ] ........................................................................... Groups of order 4 Total number of groups = 2 Order 4 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[4];{(1)}) ] Order 4 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,2)}) ] ........................................................................... Groups of order 5 Total number of groups = 1 Order 5 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[5];{-}) ] ........................................................................... Groups of order 6 Total number of groups = 2 Order 6 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(3)}) ] Order 6 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[6];{(1)}) ] ........................................................................... Groups of order 7 Total number of groups = 1 Order 7 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[7];{-}) ] ........................................................................... Groups of order 8 Total number of groups = 5 Order 8 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[8];{(1)}) ] Order 8 # 2 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] Order 8 # 3 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,4)}) ] Order 8 # 4 : Symmetric cross-cap number 6 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 8 # 5 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2)}) ] ........................................................................... Groups of order 9 Total number of groups = 2 Order 9 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[9];{-}) ] Order 9 # 2 : Symmetric cross-cap number 5 Signatures of corresponding actions [ (1;-;[3,3];{-}) ] ........................................................................... Groups of order 10 Total number of groups = 2 Order 10 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(5)}) ] Order 10 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[10];{(1)}) ] ........................................................................... Groups of order 11 Total number of groups = 1 Order 11 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[11];{-}) ] ........................................................................... Groups of order 12 Total number of groups = 5 Order 12 # 1 : Symmetric cross-cap number 7 Signatures of corresponding actions [ (0;+;[3,4];{(1)}) ] Order 12 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[12];{(1)}) ] Order 12 # 3 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[3];{(2)}) ] Order 12 # 4 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,6)}) ] Order 12 # 5 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] ........................................................................... Groups of order 13 Total number of groups = 1 Order 13 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[13];{-}) ] ........................................................................... Groups of order 14 Total number of groups = 2 Order 14 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(7)}) ] Order 14 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[14];{(1)}) ] ........................................................................... Groups of order 15 Total number of groups = 1 Order 15 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[15];{-}) ] ........................................................................... Groups of order 16 Total number of groups = 14 Order 16 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[16];{(1)}) ] Order 16 # 2 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 16 # 3 : Symmetric cross-cap number 6 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}), (0;+;[-];{(1),(2)}) ] Order 16 # 4 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 16 # 5 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] Order 16 # 6 : Symmetric cross-cap number 6 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 16 # 7 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,8)}) ] Order 16 # 8 : Symmetric cross-cap number 6 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 16 # 9 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 16 # 10 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[4];{(2,2,2)}), (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 16 # 11 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2)}) ] Order 16 # 12 : Symmetric cross-cap number 14 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 16 # 13 : Symmetric cross-cap number 6 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}) ] Order 16 # 14 : Symmetric cross-cap number 6 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,2)}) ] ........................................................................... Groups of order 17 Total number of groups = 1 Order 17 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[17];{-}) ] ........................................................................... Groups of order 18 Total number of groups = 5 Order 18 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(9)}) ] Order 18 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[18];{(1)}) ] Order 18 # 3 : Symmetric cross-cap number 5 Signatures of corresponding actions [ (0;+;[6];{(3)}), (0;+;[2,3];{(1)}) ] Order 18 # 4 : Symmetric cross-cap number 5 Signatures of corresponding actions [ (0;+;[2];{(3,3)}) ] Order 18 # 5 : Symmetric cross-cap number 11 Signatures of corresponding actions [ (0;+;[3,6];{(1)}) ] ........................................................................... Groups of order 19 Total number of groups = 1 Order 19 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[19];{-}) ] ........................................................................... Groups of order 20 Total number of groups = 5 Order 20 # 1 : Symmetric cross-cap number 12 Signatures of corresponding actions [ (0;+;[4,4];{(1)}), (1;-;[4,4];{-}) ] Order 20 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[20];{(1)}) ] Order 20 # 3 : Symmetric cross-cap number 5 Signatures of corresponding actions [ (0;+;[4];{(5)}) ] Order 20 # 4 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,10)}) ] Order 20 # 5 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] ........................................................................... Groups of order 21 Total number of groups = 2 Order 21 # 1 : Symmetric cross-cap number 9 Signatures of corresponding actions [ (1;-;[3,3];{-}) ] Order 21 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[21];{-}) ] ........................................................................... Groups of order 22 Total number of groups = 2 Order 22 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(11)}) ] Order 22 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[22];{(1)}) ] ........................................................................... Groups of order 23 Total number of groups = 1 Order 23 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[23];{-}) ] ........................................................................... Groups of order 24 Total number of groups = 15 Order 24 # 1 : Symmetric cross-cap number 15 Signatures of corresponding actions [ (0;+;[3,8];{(1)}) ] Order 24 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[24];{(1)}) ] Order 24 # 3 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[3,3];{(1)}) ] Order 24 # 4 : Symmetric cross-cap number 14 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 24 # 5 : Symmetric cross-cap number 8 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 24 # 6 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,12)}) ] Order 24 # 7 : Symmetric cross-cap number 14 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 24 # 8 : Symmetric cross-cap number 7 Signatures of corresponding actions [ (0;+;[-];{(2,2,3,4)}) ] Order 24 # 9 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] Order 24 # 10 : Symmetric cross-cap number 8 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 24 # 11 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[4,12];{(1)}) ] Order 24 # 12 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,3,4)}) ] Order 24 # 13 : Symmetric cross-cap number 4 Signatures of corresponding actions [ (0;+;[6];{(2)}) ] Order 24 # 14 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2)}) ] Order 24 # 15 : Symmetric cross-cap number 14 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] ........................................................................... Groups of order 25 Total number of groups = 2 Order 25 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[25];{-}) ] Order 25 # 2 : Symmetric cross-cap number 17 Signatures of corresponding actions [ (1;-;[5,5];{-}) ] ........................................................................... Groups of order 26 Total number of groups = 2 Order 26 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(13)}) ] Order 26 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[26];{(1)}) ] ........................................................................... Groups of order 27 Total number of groups = 5 Order 27 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[27];{-}) ] Order 27 # 2 : Symmetric cross-cap number 17 Signatures of corresponding actions [ (1;-;[3,9];{-}) ] Order 27 # 3 : Symmetric cross-cap number 11 Signatures of corresponding actions [ (1;-;[3,3];{-}) ] Order 27 # 4 : Symmetric cross-cap number 17 Signatures of corresponding actions [ (1;-;[3,9];{-}) ] Order 27 # 5 : Symmetric cross-cap number 29 Signatures of corresponding actions [ (1;-;[3,3,3];{-}) ] ........................................................................... Groups of order 28 Total number of groups = 4 Order 28 # 1 : Symmetric cross-cap number 16 Signatures of corresponding actions [ (0;+;[4,4];{(1)}), (1;-;[4,4];{-}) ] Order 28 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[28];{(1)}) ] Order 28 # 3 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,14)}) ] Order 28 # 4 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] ........................................................................... Groups of order 29 Total number of groups = 1 Order 29 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[29];{-}) ] ........................................................................... Groups of order 30 Total number of groups = 4 Order 30 # 1 : Symmetric cross-cap number 9 Signatures of corresponding actions [ (0;+;[10];{(3)}) ] Order 30 # 2 : Symmetric cross-cap number 9 Signatures of corresponding actions [ (0;+;[6];{(5)}) ] Order 30 # 3 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(15)}) ] Order 30 # 4 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[30];{(1)}) ] ........................................................................... Groups of order 31 Total number of groups = 1 Order 31 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[31];{-}) ] ........................................................................... Groups of order 32 Total number of groups = 51 Order 32 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[32];{(1)}) ] Order 32 # 2 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 32 # 3 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 32 # 4 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 32 # 5 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 32 # 6 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}), (0;+;[-];{(1),(2)}) ] Order 32 # 7 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 32 # 8 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 32 # 9 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 32 # 10 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 32 # 11 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 32 # 12 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 32 # 13 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 32 # 14 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 32 # 15 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[8,8];{(1)}) ] Order 32 # 16 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] Order 32 # 17 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 32 # 18 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,16)}) ] Order 32 # 19 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 32 # 20 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 32 # 21 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 32 # 22 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[4];{(2,2,2)}), (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 32 # 23 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 32 # 24 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 32 # 25 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 32 # 26 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 32 # 27 : Symmetric cross-cap number 6 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,4)}) ] Order 32 # 28 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}) ] Order 32 # 29 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 32 # 30 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 32 # 31 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[4];{(2,2,4)}) ] Order 32 # 32 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 32 # 33 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[4,4];{(2,2)}), (0;+;[2,4,4];{(1)}), (0;+;[4];{(1),(2)}) ] Order 32 # 34 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}) ] Order 32 # 35 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 32 # 36 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 32 # 37 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 32 # 38 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 32 # 39 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2)}) ] Order 32 # 40 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[4];{(2,2,2)}), (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 32 # 41 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 32 # 42 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}) ] Order 32 # 43 : Symmetric cross-cap number 6 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,4)}) ] Order 32 # 44 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 32 # 45 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[4];{(2,2,2,2)}), (0;+;[-];{(2,2,2),(1)}) ] Order 32 # 46 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,2)}) ] Order 32 # 47 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(1),(1),(1)}) ] Order 32 # 48 : Symmetric cross-cap number 14 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,4)}) ] Order 32 # 49 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,2)}) ] Order 32 # 50 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4,4)}) ] Order 32 # 51 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,2,2)}) ] ........................................................................... Groups of order 33 Total number of groups = 1 Order 33 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[33];{-}) ] ........................................................................... Groups of order 34 Total number of groups = 2 Order 34 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(17)}) ] Order 34 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[34];{(1)}) ] ........................................................................... Groups of order 35 Total number of groups = 1 Order 35 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[35];{-}) ] ........................................................................... Groups of order 36 Total number of groups = 14 Order 36 # 1 : Symmetric cross-cap number 20 Signatures of corresponding actions [ (0;+;[4,4];{(1)}), (1;-;[4,4];{-}) ] Order 36 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[36];{(1)}) ] Order 36 # 3 : Symmetric cross-cap number 7 Signatures of corresponding actions [ (0;+;[9];{(2)}) ] Order 36 # 4 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,18)}) ] Order 36 # 5 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] Order 36 # 6 : Symmetric cross-cap number 17 Signatures of corresponding actions [ (0;+;[3,4];{(1)}) ] Order 36 # 7 : Symmetric cross-cap number 41 Signatures of corresponding actions [ (0;+;[3,3,4];{(1)}) ] Order 36 # 8 : Symmetric cross-cap number 23 Signatures of corresponding actions [ (0;+;[3,12];{(1)}) ] Order 36 # 9 : Symmetric cross-cap number 5 Signatures of corresponding actions [ (0;+;[4];{(3)}) ] Order 36 # 10 : Symmetric cross-cap number 5 Signatures of corresponding actions [ (0;+;[-];{(2,6,6)}), (0;+;[-];{(2,2,2,3)}) ] Order 36 # 11 : Symmetric cross-cap number 14 Signatures of corresponding actions [ (0;+;[3,3];{(1)}), (1;-;[3,3];{-}) ] Order 36 # 12 : Symmetric cross-cap number 14 Signatures of corresponding actions [ (0;+;[6];{(2,2)}), (0;+;[2,6];{(1)}), (0;+;[-];{(1),(3)}) ] Order 36 # 13 : Symmetric cross-cap number 11 Signatures of corresponding actions [ (0;+;[-];{(2,2,3,6)}) ] Order 36 # 14 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[6,6];{(1)}), (0;+;[3];{(1),(1)}) ] ........................................................................... Groups of order 37 Total number of groups = 1 Order 37 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[37];{-}) ] ........................................................................... Groups of order 38 Total number of groups = 2 Order 38 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(19)}) ] Order 38 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[38];{(1)}) ] ........................................................................... Groups of order 39 Total number of groups = 2 Order 39 # 1 : Symmetric cross-cap number 15 Signatures of corresponding actions [ (1;-;[3,3];{-}) ] Order 39 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[39];{-}) ] ........................................................................... Groups of order 40 Total number of groups = 14 Order 40 # 1 : Symmetric cross-cap number 29 Signatures of corresponding actions [ (0;+;[5,8];{(1)}) ] Order 40 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[40];{(1)}) ] Order 40 # 3 : Symmetric cross-cap number 27 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 40 # 4 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 40 # 5 : Symmetric cross-cap number 12 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 40 # 6 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,20)}) ] Order 40 # 7 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 40 # 8 : Symmetric cross-cap number 12 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}), (0;+;[2];{(4,4)}), (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 40 # 9 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] Order 40 # 10 : Symmetric cross-cap number 12 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 40 # 11 : Symmetric cross-cap number 30 Signatures of corresponding actions [ (0;+;[4,20];{(1)}) ] Order 40 # 12 : Symmetric cross-cap number 12 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 40 # 13 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2)}) ] Order 40 # 14 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] ........................................................................... Groups of order 41 Total number of groups = 1 Order 41 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[41];{-}) ] ........................................................................... Groups of order 42 Total number of groups = 6 Order 42 # 1 : Symmetric cross-cap number 9 Signatures of corresponding actions [ (0;+;[2,3];{(1)}) ] Order 42 # 2 : Symmetric cross-cap number 23 Signatures of corresponding actions [ (0;+;[3,6];{(1)}) ] Order 42 # 3 : Symmetric cross-cap number 13 Signatures of corresponding actions [ (0;+;[14];{(3)}) ] Order 42 # 4 : Symmetric cross-cap number 13 Signatures of corresponding actions [ (0;+;[6];{(7)}) ] Order 42 # 5 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(21)}) ] Order 42 # 6 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[42];{(1)}) ] ........................................................................... Groups of order 43 Total number of groups = 1 Order 43 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[43];{-}) ] ........................................................................... Groups of order 44 Total number of groups = 4 Order 44 # 1 : Symmetric cross-cap number 24 Signatures of corresponding actions [ (0;+;[4,4];{(1)}), (1;-;[4,4];{-}) ] Order 44 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[44];{(1)}) ] Order 44 # 3 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,22)}) ] Order 44 # 4 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] ........................................................................... Groups of order 45 Total number of groups = 2 Order 45 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[45];{-}) ] Order 45 # 2 : Symmetric cross-cap number 29 Signatures of corresponding actions [ (1;-;[3,15];{-}) ] ........................................................................... Groups of order 46 Total number of groups = 2 Order 46 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(23)}) ] Order 46 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[46];{(1)}) ] ........................................................................... Groups of order 47 Total number of groups = 1 Order 47 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[47];{-}) ] ........................................................................... Groups of order 48 Total number of groups = 52 Order 48 # 1 : Symmetric cross-cap number 31 Signatures of corresponding actions [ (0;+;[3,16];{(1)}) ] Order 48 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[48];{(1)}) ] Order 48 # 3 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[3,3];{(1)}), (1;-;[3,3];{-}) ] Order 48 # 4 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(1),(3)}) ] Order 48 # 5 : Symmetric cross-cap number 20 Signatures of corresponding actions [ (0;+;[8];{(2,2)}), (0;+;[2,8];{(1)}) ] Order 48 # 6 : Symmetric cross-cap number 14 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 48 # 7 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,24)}) ] Order 48 # 8 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 48 # 9 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[3];{(1),(1)}) ] Order 48 # 10 : Symmetric cross-cap number 36 Signatures of corresponding actions [ (0;+;[6,8];{(1)}) ] Order 48 # 11 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 48 # 12 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 48 # 13 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 48 # 14 : Symmetric cross-cap number 14 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 48 # 15 : Symmetric cross-cap number 15 Signatures of corresponding actions [ (0;+;[-];{(2,2,3,8)}) ] Order 48 # 16 : Symmetric cross-cap number 30 Signatures of corresponding actions [ (0;+;[4,6];{(1)}) ] Order 48 # 17 : Symmetric cross-cap number 20 Signatures of corresponding actions [ (0;+;[8];{(2,2)}), (0;+;[2,8];{(1)}) ] Order 48 # 18 : Symmetric cross-cap number 32 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 48 # 19 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 48 # 20 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[4,12];{(1)}) ] Order 48 # 21 : Symmetric cross-cap number 14 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 48 # 22 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[4,12];{(1)}) ] Order 48 # 23 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] Order 48 # 24 : Symmetric cross-cap number 14 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 48 # 25 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[6];{(2,2)}), (0;+;[2,6];{(1)}) ] Order 48 # 26 : Symmetric cross-cap number 20 Signatures of corresponding actions [ (0;+;[-];{(1),(4)}) ] Order 48 # 27 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[4,12];{(1)}) ] Order 48 # 28 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[3,4];{(1)}) ] Order 48 # 29 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[-];{(2,2,3,3)}), (0;+;[3];{(2,2)}), (0;+;[2,3];{(1)}) ] Order 48 # 30 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[3,4];{(1)}) ] Order 48 # 31 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[12];{(2)}) ] Order 48 # 32 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[3,4];{(1)}) ] Order 48 # 33 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[3];{(2,2)}), (0;+;[2,3];{(1)}) ] Order 48 # 34 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 48 # 35 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[4];{(2,2,2)}), (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 48 # 36 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2)}) ] Order 48 # 37 : Symmetric cross-cap number 14 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}) ] Order 48 # 38 : Symmetric cross-cap number 8 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,4)}) ] Order 48 # 39 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 48 # 40 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 48 # 41 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,12)}) ] Order 48 # 42 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 48 # 43 : Symmetric cross-cap number 14 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}) ] Order 48 # 44 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 48 # 45 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 48 # 46 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 48 # 47 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 48 # 48 : Symmetric cross-cap number 4 Signatures of corresponding actions [ (0;+;[-];{(2,4,6)}) ] Order 48 # 49 : Symmetric cross-cap number 14 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 48 # 50 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[3];{(2,2)}) ] Order 48 # 51 : Symmetric cross-cap number 14 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,2)}) ] Order 48 # 52 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[-];{(2,2,2),(1)}) ] ........................................................................... Groups of order 49 Total number of groups = 2 Order 49 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[49];{-}) ] Order 49 # 2 : Symmetric cross-cap number 37 Signatures of corresponding actions [ (1;-;[7,7];{-}) ] ........................................................................... Groups of order 50 Total number of groups = 5 Order 50 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(25)}) ] Order 50 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[50];{(1)}) ] Order 50 # 3 : Symmetric cross-cap number 17 Signatures of corresponding actions [ (0;+;[10];{(5)}), (0;+;[2,5];{(1)}) ] Order 50 # 4 : Symmetric cross-cap number 17 Signatures of corresponding actions [ (0;+;[2];{(5,5)}) ] Order 50 # 5 : Symmetric cross-cap number 37 Signatures of corresponding actions [ (0;+;[5,10];{(1)}) ] ........................................................................... Groups of order 51 Total number of groups = 1 Order 51 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[51];{-}) ] ........................................................................... Groups of order 52 Total number of groups = 5 Order 52 # 1 : Symmetric cross-cap number 28 Signatures of corresponding actions [ (0;+;[4,4];{(1)}), (1;-;[4,4];{-}) ] Order 52 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[52];{(1)}) ] Order 52 # 3 : Symmetric cross-cap number 13 Signatures of corresponding actions [ (0;+;[4];{(13)}) ] Order 52 # 4 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,26)}) ] Order 52 # 5 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] ........................................................................... Groups of order 53 Total number of groups = 1 Order 53 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[53];{-}) ] ........................................................................... Groups of order 54 Total number of groups = 15 Order 54 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(27)}) ] Order 54 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[54];{(1)}) ] Order 54 # 3 : Symmetric cross-cap number 17 Signatures of corresponding actions [ (0;+;[6];{(9)}) ] Order 54 # 4 : Symmetric cross-cap number 17 Signatures of corresponding actions [ (0;+;[18];{(3)}) ] Order 54 # 5 : Symmetric cross-cap number 11 Signatures of corresponding actions [ (0;+;[6];{(3)}), (0;+;[2,3];{(1)}) ] Order 54 # 6 : Symmetric cross-cap number 17 Signatures of corresponding actions [ (0;+;[6];{(9)}) ] Order 54 # 7 : Symmetric cross-cap number 17 Signatures of corresponding actions [ (0;+;[2];{(3,9)}) ] Order 54 # 8 : Symmetric cross-cap number 11 Signatures of corresponding actions [ (0;+;[2];{(3,3)}) ] Order 54 # 9 : Symmetric cross-cap number 35 Signatures of corresponding actions [ (0;+;[3,18];{(1)}) ] Order 54 # 10 : Symmetric cross-cap number 29 Signatures of corresponding actions [ (0;+;[3,6];{(1)}) ] Order 54 # 11 : Symmetric cross-cap number 35 Signatures of corresponding actions [ (0;+;[3,18];{(1)}) ] Order 54 # 12 : Symmetric cross-cap number 29 Signatures of corresponding actions [ (0;+;[3,6];{(1)}) ] Order 54 # 13 : Symmetric cross-cap number 29 Signatures of corresponding actions [ (0;+;[6];{(3,3)}), (0;+;[2,3];{(3)}) ] Order 54 # 14 : Symmetric cross-cap number 29 Signatures of corresponding actions [ (0;+;[2];{(3,3,3)}) ] Order 54 # 15 : Symmetric cross-cap number 65 Signatures of corresponding actions [ (0;+;[3,3,6];{(1)}) ] ........................................................................... Groups of order 55 Total number of groups = 2 Order 55 # 1 : Symmetric cross-cap number 35 Signatures of corresponding actions [ (1;-;[5,5];{-}) ] Order 55 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[55];{-}) ] ........................................................................... Groups of order 56 Total number of groups = 13 Order 56 # 1 : Symmetric cross-cap number 43 Signatures of corresponding actions [ (0;+;[7,8];{(1)}) ] Order 56 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[56];{(1)}) ] Order 56 # 3 : Symmetric cross-cap number 30 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 56 # 4 : Symmetric cross-cap number 16 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 56 # 5 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,28)}) ] Order 56 # 6 : Symmetric cross-cap number 30 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 56 # 7 : Symmetric cross-cap number 16 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}), (0;+;[2];{(4,4)}), (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 56 # 8 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] Order 56 # 9 : Symmetric cross-cap number 16 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 56 # 10 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4,28];{(1)}) ] Order 56 # 11 : Symmetric cross-cap number 8 Signatures of corresponding actions [ (0;+;[7];{(2)}) ] Order 56 # 12 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2)}) ] Order 56 # 13 : Symmetric cross-cap number 30 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] ........................................................................... Groups of order 57 Total number of groups = 2 Order 57 # 1 : Symmetric cross-cap number 21 Signatures of corresponding actions [ (1;-;[3,3];{-}) ] Order 57 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[57];{-}) ] ........................................................................... Groups of order 58 Total number of groups = 2 Order 58 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(29)}) ] Order 58 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[58];{(1)}) ] ........................................................................... Groups of order 59 Total number of groups = 1 Order 59 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[59];{-}) ] ........................................................................... Groups of order 60 Total number of groups = 13 Order 60 # 1 : Symmetric cross-cap number 39 Signatures of corresponding actions [ (0;+;[3,20];{(1)}) ] Order 60 # 2 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4,12];{(1)}), (1;-;[4,12];{-}) ] Order 60 # 3 : Symmetric cross-cap number 32 Signatures of corresponding actions [ (0;+;[4,4];{(1)}), (1;-;[4,4];{-}) ] Order 60 # 4 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[60];{(1)}) ] Order 60 # 5 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,3,5)}) ] Order 60 # 6 : Symmetric cross-cap number 21 Signatures of corresponding actions [ (0;+;[12];{(5)}) ] Order 60 # 7 : Symmetric cross-cap number 32 Signatures of corresponding actions [ (0;+;[4,4];{(1)}), (1;-;[4,4];{-}) ] Order 60 # 8 : Symmetric cross-cap number 9 Signatures of corresponding actions [ (0;+;[-];{(2,6,10)}) ] Order 60 # 9 : Symmetric cross-cap number 13 Signatures of corresponding actions [ (0;+;[15];{(2)}) ] Order 60 # 10 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[6];{(2,2)}), (0;+;[2,6];{(1)}) ] Order 60 # 11 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[-];{(1),(3)}) ] Order 60 # 12 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,30)}) ] Order 60 # 13 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] ........................................................................... Groups of order 61 Total number of groups = 1 Order 61 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[61];{-}) ] ........................................................................... Groups of order 62 Total number of groups = 2 Order 62 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(31)}) ] Order 62 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[62];{(1)}) ] ........................................................................... Groups of order 63 Total number of groups = 4 Order 63 # 1 : Symmetric cross-cap number 49 Signatures of corresponding actions [ (1;-;[7,9];{-}) ] Order 63 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[63];{-}) ] Order 63 # 3 : Symmetric cross-cap number 23 Signatures of corresponding actions [ (1;-;[3,3];{-}) ] Order 63 # 4 : Symmetric cross-cap number 41 Signatures of corresponding actions [ (1;-;[3,21];{-}) ] ........................................................................... Groups of order 64 Total number of groups = 267 Order 64 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[64];{(1)}) ] Order 64 # 2 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[8,8];{(1)}) ] Order 64 # 3 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[8,8];{(1)}) ] Order 64 # 4 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 64 # 5 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 64 # 6 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[8];{(2,2)}), (0;+;[2,8];{(1)}), (0;+;[-];{(1),(4)}) ] Order 64 # 7 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 64 # 8 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 64 # 9 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 64 # 10 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[8];{(2,2)}), (0;+;[2,8];{(1)}), (0;+;[-];{(1),(4)}) ] Order 64 # 11 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 64 # 12 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[8];{(2,2)}), (0;+;[2,8];{(1)}), (0;+;[-];{(1),(4)}) ] Order 64 # 13 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 64 # 14 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 64 # 15 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[8,8];{(1)}) ] Order 64 # 16 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[8,8];{(1)}) ] Order 64 # 17 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 64 # 18 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 64 # 19 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[8,8];{(1)}) ] Order 64 # 20 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 64 # 21 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 64 # 22 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[8,8];{(1)}) ] Order 64 # 23 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 64 # 24 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 64 # 25 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 64 # 26 : Symmetric cross-cap number 46 Signatures of corresponding actions [ (0;+;[4,16];{(1)}) ] Order 64 # 27 : Symmetric cross-cap number 46 Signatures of corresponding actions [ (0;+;[4,16];{(1)}) ] Order 64 # 28 : Symmetric cross-cap number 46 Signatures of corresponding actions [ (0;+;[4,16];{(1)}) ] Order 64 # 29 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 64 # 30 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 64 # 31 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(1),(4)}) ] Order 64 # 32 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}), (0;+;[-];{(1),(2)}) ] Order 64 # 33 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 64 # 34 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 64 # 35 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 64 # 36 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[8];{(2,2)}), (0;+;[2,8];{(1)}), (0;+;[-];{(1),(4)}) ] Order 64 # 37 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 64 # 38 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 64 # 39 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 64 # 40 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[8];{(2,2)}), (0;+;[2,8];{(1)}) ] Order 64 # 41 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 64 # 42 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[8];{(2,2)}), (0;+;[2,8];{(1)}) ] Order 64 # 43 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 64 # 44 : Symmetric cross-cap number 46 Signatures of corresponding actions [ (0;+;[4,16];{(1)}) ] Order 64 # 45 : Symmetric cross-cap number 46 Signatures of corresponding actions [ (0;+;[4,16];{(1)}) ] Order 64 # 46 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 64 # 47 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 64 # 48 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 64 # 49 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[8,8];{(1)}) ] Order 64 # 50 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] Order 64 # 51 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 64 # 52 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,32)}) ] Order 64 # 53 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 64 # 54 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 64 # 55 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 56 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 57 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 58 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 59 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 60 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[4];{(2,2,2)}), (0;+;[-];{(2,2),(1)}) ] Order 64 # 61 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 62 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 63 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 64 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 65 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 66 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 67 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 68 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 69 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[4,4];{(2,2)}), (0;+;[2,4,4];{(1)}), (0;+;[4];{(1),(2)}) ] Order 64 # 70 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 71 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4];{(2,2,4)}) ] Order 64 # 72 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 73 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}) ] Order 64 # 74 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[4,4];{(2,2)}), (0;+;[2,4,4];{(1)}), (0;+;[4];{(1),(2)}) ] Order 64 # 75 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4];{(2,2,4)}) ] Order 64 # 76 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 77 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[4,4];{(2,2)}), (0;+;[2,4,4];{(1)}), (0;+;[4];{(1),(2)}) ] Order 64 # 78 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[4,4];{(2,2)}), (0;+;[2,4,4];{(1)}), (0;+;[4];{(1),(2)}) ] Order 64 # 79 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 80 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[4,4];{(2,2)}), (0;+;[2,4,4];{(1)}), (0;+;[4];{(1),(2)}) ] Order 64 # 81 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 82 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 83 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 84 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 85 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[8];{(1),(1)}) ] Order 64 # 86 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 87 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 88 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}) ] Order 64 # 89 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 90 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[4];{(2,2,2)}), (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 91 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4];{(2,2,4)}) ] Order 64 # 92 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 93 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 94 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 95 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[4];{(2,2,2)}), (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 96 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 97 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 98 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 99 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[4];{(2,2,2)}), (0;+;[-];{(2,2),(1)}) ] Order 64 # 100 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 101 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[4];{(2,2,2)}), (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 102 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[4];{(2,2,2)}), (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 103 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 104 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[8];{(1),(1)}) ] Order 64 # 105 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 106 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 107 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 108 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 109 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 110 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[8];{(1),(1)}) ] Order 64 # 111 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[8];{(1),(1)}) ] Order 64 # 112 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[8];{(1),(1)}) ] Order 64 # 113 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[8];{(1),(1)}) ] Order 64 # 114 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[4];{(1),(2)}) ] Order 64 # 115 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 116 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 117 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[8];{(2,2,4)}), (0;+;[-];{(2,2),(2)}), (0;+;[-];{(4,4),(1)}), (0;+;[2];{(1),(2)}) ] Order 64 # 118 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 119 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 120 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 121 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 122 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 123 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 124 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 125 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 126 : Symmetric cross-cap number 90 Signatures of corresponding actions [ (0;+;[4,4,8];{(1)}) ] Order 64 # 127 : Symmetric cross-cap number 90 Signatures of corresponding actions [ (0;+;[4,4,8];{(1)}) ] Order 64 # 128 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,4)}) ] Order 64 # 129 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 130 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}) ] Order 64 # 131 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[4];{(2,2,2)}), (0;+;[-];{(2,2),(1)}) ] Order 64 # 132 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 133 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4];{(2,2,4)}) ] Order 64 # 134 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,4)}) ] Order 64 # 135 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,8)}) ] Order 64 # 136 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[4];{(2,2,2)}), (0;+;[-];{(2,2),(1)}) ] Order 64 # 137 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4];{(2,2,4)}) ] Order 64 # 138 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,4)}) ] Order 64 # 139 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[4];{(2,2,2)}) ] Order 64 # 140 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,8)}) ] Order 64 # 141 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4];{(2,2,4)}) ] Order 64 # 142 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 143 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 144 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 145 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[4,4];{(2,2)}), (0;+;[2,4,4];{(1)}), (0;+;[4];{(1),(2)}) ] Order 64 # 146 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 147 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}) ] Order 64 # 148 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 149 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4];{(2,2,4)}) ] Order 64 # 150 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}) ] Order 64 # 151 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[4,4];{(2,2)}), (0;+;[2,4,4];{(1)}), (0;+;[4];{(1),(2)}) ] Order 64 # 152 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 153 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(2,2,8,8)}) ] Order 64 # 154 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 155 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 156 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 157 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 158 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 159 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 160 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 161 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 162 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 163 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4];{(2,2,4)}) ] Order 64 # 164 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 165 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 166 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[4,4];{(2,2)}), (0;+;[2,4,4];{(1)}), (0;+;[4];{(1),(2)}) ] Order 64 # 167 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4];{(2,2,4)}) ] Order 64 # 168 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 169 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[4,4];{(2,2)}), (0;+;[2,4,4];{(1)}), (0;+;[4];{(1),(2)}) ] Order 64 # 170 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[4,4];{(2,2)}), (0;+;[2,4,4];{(1)}), (0;+;[4];{(1),(2)}) ] Order 64 # 171 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4];{(2,2,4)}) ] Order 64 # 172 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 173 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4];{(2,2,4)}) ] Order 64 # 174 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,8)}) ] Order 64 # 175 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 176 : Symmetric cross-cap number 46 Signatures of corresponding actions [ (0;+;[4];{(2,2,8)}) ] Order 64 # 177 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,8)}) ] Order 64 # 178 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[4,4];{(2,2)}), (0;+;[2,4,4];{(1)}), (0;+;[4];{(1),(2)}) ] Order 64 # 179 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 180 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 181 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 182 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 64 # 183 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 184 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 185 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 186 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2)}) ] Order 64 # 187 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[4];{(2,2,2)}), (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 188 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 64 # 189 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}) ] Order 64 # 190 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,4)}) ] Order 64 # 191 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 64 # 192 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[-];{(1),(1),(1)}) ] Order 64 # 193 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(2,2,2,2)}), (0;+;[-];{(2,2,2),(1)}) ] Order 64 # 194 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[-];{(1),(1),(1)}) ] Order 64 # 195 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[-];{(1),(1),(1)}) ] Order 64 # 196 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(2,2,2,2)}), (0;+;[-];{(2,2,2),(1)}) ] Order 64 # 197 : Symmetric cross-cap number 98 Signatures of corresponding actions [ (0;+;[4,4];{(1),(1)}) ] Order 64 # 198 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[-];{(2,2,4),(1)}) ] Order 64 # 199 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(2,2,2,2)}), (0;+;[-];{(2,2,2),(1)}) ] Order 64 # 200 : Symmetric cross-cap number 98 Signatures of corresponding actions [ (0;+;[4,4];{(1),(1)}) ] Order 64 # 201 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[-];{(2,2,4),(1)}) ] Order 64 # 202 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,2)}) ] Order 64 # 203 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,4)}) ] Order 64 # 204 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[-];{(1),(1),(1)}) ] Order 64 # 205 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(2,2,2,2)}), (0;+;[-];{(2,2,2),(1)}) ] Order 64 # 206 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,4,4)}), (0;+;[-];{(2,2,4,2,4)}) ] Order 64 # 207 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(2,2,2,2)}) ] Order 64 # 208 : Symmetric cross-cap number 98 Signatures of corresponding actions [ (0;+;[4,4];{(1),(1)}) ] Order 64 # 209 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,4];{(2,2,2)}), (0;+;[4];{(2,2),(1)}), (0;+;[2,4];{(1),(1)}), (0;+;[-];{(1),(1),(2)}) ] Order 64 # 210 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[-];{(2,2,4),(1)}) ] Order 64 # 211 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,4)}) ] Order 64 # 212 : Symmetric cross-cap number 98 Signatures of corresponding actions [ (0;+;[4,4];{(1),(1)}) ] Order 64 # 213 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4,4)}) ] Order 64 # 214 : Symmetric cross-cap number 98 Signatures of corresponding actions [ (0;+;[4,4];{(1),(1)}) ] Order 64 # 215 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,2)}) ] Order 64 # 216 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,4)}) ] Order 64 # 217 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[-];{(2,2,4),(1)}) ] Order 64 # 218 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4,4)}) ] Order 64 # 219 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,4,4)}), (0;+;[-];{(2,2,4,2,4)}) ] Order 64 # 220 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[-];{(2,2,4),(1)}) ] Order 64 # 221 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4,4)}) ] Order 64 # 222 : Symmetric cross-cap number 98 Signatures of corresponding actions [ (0;+;[4,4];{(1),(1)}) ] Order 64 # 223 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[-];{(2,2,4),(1)}) ] Order 64 # 224 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[-];{(1),(1),(1)}) ] Order 64 # 225 : Symmetric cross-cap number 98 Signatures of corresponding actions [ (0;+;[4,4];{(1),(1)}) ] Order 64 # 226 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,2)}) ] Order 64 # 227 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,4)}) ] Order 64 # 228 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4,4)}) ] Order 64 # 229 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4,4)}) ] Order 64 # 230 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[-];{(1),(1),(1)}) ] Order 64 # 231 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4,4)}) ] Order 64 # 232 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2,2),(1)}) ] Order 64 # 233 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[-];{(1),(1),(1)}) ] Order 64 # 234 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4,4)}) ] Order 64 # 235 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[-];{(1),(1),(1)}) ] Order 64 # 236 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4,4)}) ] Order 64 # 237 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4];{(2,2),(1)}), (0;+;[2,4];{(1),(1)}), (0;+;[-];{(1),(1),(2)}) ] Order 64 # 238 : Symmetric cross-cap number 130 Signatures of corresponding actions [ (0;+;[4,4,4,4];{(1)}) ] Order 64 # 239 : Symmetric cross-cap number 130 Signatures of corresponding actions [ (0;+;[4,4,4,4];{(1)}) ] Order 64 # 240 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[-];{(2,2,4),(1)}) ] Order 64 # 241 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,4,4)}), (0;+;[-];{(2,2,4,2,4)}) ] Order 64 # 242 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,4)}) ] Order 64 # 243 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4,4)}) ] Order 64 # 244 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[-];{(1),(1),(1)}) ] Order 64 # 245 : Symmetric cross-cap number 130 Signatures of corresponding actions [ (0;+;[4,4,4,4];{(1)}) ] Order 64 # 246 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2,2),(1)}) ] Order 64 # 247 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2,2),(1)}) ] Order 64 # 248 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2,2),(1)}) ] Order 64 # 249 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2,2),(1)}) ] Order 64 # 250 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,2)}) ] Order 64 # 251 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(2,2,2,2)}), (0;+;[-];{(2,2,2),(1)}) ] Order 64 # 252 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[-];{(1),(1),(1)}) ] Order 64 # 253 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,4)}) ] Order 64 # 254 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,2)}) ] Order 64 # 255 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(2,2,2,2)}), (0;+;[-];{(2,2,2),(1)}) ] Order 64 # 256 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,2)}) ] Order 64 # 257 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,2)}) ] Order 64 # 258 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,4)}) ] Order 64 # 259 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4,4)}) ] Order 64 # 260 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[4];{(2,2,2,2,2)}), (0;+;[-];{(2,2,2,2),(1)}) ] Order 64 # 261 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,2,2)}) ] Order 64 # 262 : Symmetric cross-cap number 98 Signatures of corresponding actions [ (0;+;[4,4];{(2,2,2,2)}), (0;+;[4];{(2,2,2),(1)}), (0;+;[-];{(2,2),(1),(1)}), (0;+;[2];{(1),(1),(1)}) ] Order 64 # 263 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,2,2)}) ] Order 64 # 264 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,2,2)}) ] Order 64 # 265 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,4,4)}), (0;+;[-];{(2,2,4,2,2,4)}) ] Order 64 # 266 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,2,2)}) ] Order 64 # 267 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,2,2,2)}) ] ........................................................................... Groups of order 65 Total number of groups = 1 Order 65 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[65];{-}) ] ........................................................................... Groups of order 66 Total number of groups = 4 Order 66 # 1 : Symmetric cross-cap number 21 Signatures of corresponding actions [ (0;+;[22];{(3)}) ] Order 66 # 2 : Symmetric cross-cap number 21 Signatures of corresponding actions [ (0;+;[6];{(11)}) ] Order 66 # 3 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(33)}) ] Order 66 # 4 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[66];{(1)}) ] ........................................................................... Groups of order 67 Total number of groups = 1 Order 67 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[67];{-}) ] ........................................................................... Groups of order 68 Total number of groups = 5 Order 68 # 1 : Symmetric cross-cap number 36 Signatures of corresponding actions [ (0;+;[4,4];{(1)}), (1;-;[4,4];{-}) ] Order 68 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[68];{(1)}) ] Order 68 # 3 : Symmetric cross-cap number 17 Signatures of corresponding actions [ (0;+;[4];{(17)}) ] Order 68 # 4 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,34)}) ] Order 68 # 5 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] ........................................................................... Groups of order 69 Total number of groups = 1 Order 69 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[69];{-}) ] ........................................................................... Groups of order 70 Total number of groups = 4 Order 70 # 1 : Symmetric cross-cap number 25 Signatures of corresponding actions [ (0;+;[14];{(5)}) ] Order 70 # 2 : Symmetric cross-cap number 25 Signatures of corresponding actions [ (0;+;[10];{(7)}) ] Order 70 # 3 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(35)}) ] Order 70 # 4 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[70];{(1)}) ] ........................................................................... Groups of order 71 Total number of groups = 1 Order 71 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[71];{-}) ] ........................................................................... Groups of order 72 Total number of groups = 50 Order 72 # 1 : Symmetric cross-cap number 56 Signatures of corresponding actions [ (0;+;[8,8];{(1)}), (1;-;[8,8];{-}) ] Order 72 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[72];{(1)}) ] Order 72 # 3 : Symmetric cross-cap number 48 Signatures of corresponding actions [ (0;+;[4,9];{(1)}), (1;-;[4,9];{-}) ] Order 72 # 4 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 72 # 5 : Symmetric cross-cap number 20 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 72 # 6 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,36)}) ] Order 72 # 7 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 72 # 8 : Symmetric cross-cap number 20 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}), (0;+;[2];{(4,4)}), (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 72 # 9 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] Order 72 # 10 : Symmetric cross-cap number 20 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 72 # 11 : Symmetric cross-cap number 54 Signatures of corresponding actions [ (0;+;[4,36];{(1)}) ] Order 72 # 12 : Symmetric cross-cap number 41 Signatures of corresponding actions [ (0;+;[3,8];{(1)}) ] Order 72 # 13 : Symmetric cross-cap number 89 Signatures of corresponding actions [ (0;+;[3,3,8];{(1)}) ] Order 72 # 14 : Symmetric cross-cap number 47 Signatures of corresponding actions [ (0;+;[3,24];{(1)}) ] Order 72 # 15 : Symmetric cross-cap number 7 Signatures of corresponding actions [ (0;+;[-];{(2,4,9)}) ] Order 72 # 16 : Symmetric cross-cap number 16 Signatures of corresponding actions [ (0;+;[18];{(2)}) ] Order 72 # 17 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2)}) ] Order 72 # 18 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 72 # 19 : Symmetric cross-cap number 41 Signatures of corresponding actions [ (0;+;[3,8];{(1)}) ] Order 72 # 20 : Symmetric cross-cap number 44 Signatures of corresponding actions [ (0;+;[4,6];{(1)}) ] Order 72 # 21 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(1),(3)}) ] Order 72 # 22 : Symmetric cross-cap number 41 Signatures of corresponding actions [ (0;+;[-];{(2,2,3,4,3)}), (0;+;[3];{(2,2,4)}) ] Order 72 # 23 : Symmetric cross-cap number 17 Signatures of corresponding actions [ (0;+;[-];{(2,2,3,4)}) ] Order 72 # 24 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4,12];{(1)}) ] Order 72 # 25 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[3,3];{(1)}) ] Order 72 # 26 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4,12];{(1)}) ] Order 72 # 27 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(1),(3)}) ] Order 72 # 28 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[6];{(2,2)}), (0;+;[2,6];{(1)}) ] Order 72 # 29 : Symmetric cross-cap number 44 Signatures of corresponding actions [ (0;+;[4,6];{(1)}) ] Order 72 # 30 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[6];{(2,2)}), (0;+;[2,6];{(1)}) ] Order 72 # 31 : Symmetric cross-cap number 86 Signatures of corresponding actions [ (0;+;[3,4,4];{(1)}) ] Order 72 # 32 : Symmetric cross-cap number 44 Signatures of corresponding actions [ (0;+;[2,4];{(3)}), (0;+;[4];{(2,2,3)}) ] Order 72 # 33 : Symmetric cross-cap number 23 Signatures of corresponding actions [ (0;+;[-];{(2,2,3,12)}) ] Order 72 # 34 : Symmetric cross-cap number 86 Signatures of corresponding actions [ (0;+;[3,4,4];{(1)}) ] Order 72 # 35 : Symmetric cross-cap number 41 Signatures of corresponding actions [ (0;+;[-];{(2,2,3,3,4)}) ] Order 72 # 36 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[3];{(1),(1)}) ] Order 72 # 37 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[6,6];{(1)}) ] Order 72 # 38 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[12,12];{(1)}) ] Order 72 # 39 : Symmetric cross-cap number 17 Signatures of corresponding actions [ (0;+;[8];{(3)}) ] Order 72 # 40 : Symmetric cross-cap number 5 Signatures of corresponding actions [ (0;+;[-];{(2,4,6)}) ] Order 72 # 41 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 72 # 42 : Symmetric cross-cap number 14 Signatures of corresponding actions [ (0;+;[2,3];{(1)}) ] Order 72 # 43 : Symmetric cross-cap number 14 Signatures of corresponding actions [ (0;+;[-];{(2,2,3,3)}), (0;+;[2];{(3,3)}) ] Order 72 # 44 : Symmetric cross-cap number 14 Signatures of corresponding actions [ (0;+;[3];{(2,2)}), (0;+;[2,3];{(1)}) ] Order 72 # 45 : Symmetric cross-cap number 20 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 72 # 46 : Symmetric cross-cap number 14 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,6)}) ] Order 72 # 47 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[3,6];{(1)}) ] Order 72 # 48 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 72 # 49 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(2,2,6,6)}), (0;+;[-];{(2,2,2,2,3)}) ] Order 72 # 50 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[6];{(1),(1)}) ] ........................................................................... Groups of order 73 Total number of groups = 1 Order 73 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[73];{-}) ] ........................................................................... Groups of order 74 Total number of groups = 2 Order 74 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(37)}) ] Order 74 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[74];{(1)}) ] ........................................................................... Groups of order 75 Total number of groups = 3 Order 75 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[75];{-}) ] Order 75 # 2 : Symmetric cross-cap number 27 Signatures of corresponding actions [ (1;-;[3,3];{-}) ] Order 75 # 3 : Symmetric cross-cap number 57 Signatures of corresponding actions [ (1;-;[5,15];{-}) ] ........................................................................... Groups of order 76 Total number of groups = 4 Order 76 # 1 : Symmetric cross-cap number 40 Signatures of corresponding actions [ (0;+;[4,4];{(1)}), (1;-;[4,4];{-}) ] Order 76 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[76];{(1)}) ] Order 76 # 3 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,38)}) ] Order 76 # 4 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] ........................................................................... Groups of order 77 Total number of groups = 1 Order 77 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[77];{-}) ] ........................................................................... Groups of order 78 Total number of groups = 6 Order 78 # 1 : Symmetric cross-cap number 15 Signatures of corresponding actions [ (0;+;[2,3];{(1)}) ] Order 78 # 2 : Symmetric cross-cap number 41 Signatures of corresponding actions [ (0;+;[3,6];{(1)}) ] Order 78 # 3 : Symmetric cross-cap number 25 Signatures of corresponding actions [ (0;+;[26];{(3)}) ] Order 78 # 4 : Symmetric cross-cap number 25 Signatures of corresponding actions [ (0;+;[6];{(13)}) ] Order 78 # 5 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(39)}) ] Order 78 # 6 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[78];{(1)}) ] ........................................................................... Groups of order 79 Total number of groups = 1 Order 79 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[79];{-}) ] ........................................................................... Groups of order 80 Total number of groups = 52 Order 80 # 1 : Symmetric cross-cap number 61 Signatures of corresponding actions [ (0;+;[5,16];{(1)}) ] Order 80 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[80];{(1)}) ] Order 80 # 3 : Symmetric cross-cap number 61 Signatures of corresponding actions [ (0;+;[5,16];{(1)}) ] Order 80 # 4 : Symmetric cross-cap number 32 Signatures of corresponding actions [ (0;+;[8];{(2,2)}), (0;+;[2,8];{(1)}) ] Order 80 # 5 : Symmetric cross-cap number 32 Signatures of corresponding actions [ (0;+;[8];{(2,2)}), (0;+;[2,8];{(1)}) ] Order 80 # 6 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 80 # 7 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,40)}) ] Order 80 # 8 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 80 # 9 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[8,8];{(1)}) ] Order 80 # 10 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[8,8];{(1)}) ] Order 80 # 11 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 80 # 12 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 80 # 13 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 80 # 14 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 80 # 15 : Symmetric cross-cap number 29 Signatures of corresponding actions [ (0;+;[-];{(2,2,5,8)}) ] Order 80 # 16 : Symmetric cross-cap number 52 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 80 # 17 : Symmetric cross-cap number 32 Signatures of corresponding actions [ (0;+;[8];{(2,2)}), (0;+;[2,8];{(1)}) ] Order 80 # 18 : Symmetric cross-cap number 52 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 80 # 19 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 80 # 20 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[4,20];{(1)}) ] Order 80 # 21 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 80 # 22 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[4,20];{(1)}) ] Order 80 # 23 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] Order 80 # 24 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 80 # 25 : Symmetric cross-cap number 32 Signatures of corresponding actions [ (0;+;[-];{(1),(4)}) ] Order 80 # 26 : Symmetric cross-cap number 32 Signatures of corresponding actions [ (0;+;[-];{(1),(4)}) ] Order 80 # 27 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[4,20];{(1)}) ] Order 80 # 28 : Symmetric cross-cap number 32 Signatures of corresponding actions [ (0;+;[8];{(2,2)}), (0;+;[2,8];{(1)}) ] Order 80 # 29 : Symmetric cross-cap number 32 Signatures of corresponding actions [ (0;+;[8];{(2,2)}), (0;+;[2,8];{(1)}) ] Order 80 # 30 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 80 # 31 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 80 # 32 : Symmetric cross-cap number 52 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 80 # 33 : Symmetric cross-cap number 52 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 80 # 34 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 80 # 35 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 80 # 36 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4];{(2,2,2)}), (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 80 # 37 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2)}) ] Order 80 # 38 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}) ] Order 80 # 39 : Symmetric cross-cap number 12 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,4)}) ] Order 80 # 40 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 80 # 41 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 80 # 42 : Symmetric cross-cap number 30 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,20)}) ] Order 80 # 43 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 80 # 44 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}) ] Order 80 # 45 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 80 # 46 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 80 # 47 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 80 # 48 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 80 # 49 : Symmetric cross-cap number 6 Signatures of corresponding actions [ (0;+;[5];{(2)}) ] Order 80 # 50 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[4];{(2,2,2)}), (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 80 # 51 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,2)}) ] Order 80 # 52 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[-];{(2,2,2),(1)}) ] ........................................................................... Groups of order 81 Total number of groups = 15 Order 81 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[81];{-}) ] Order 81 # 2 : Symmetric cross-cap number 65 Signatures of corresponding actions [ (1;-;[9,9];{-}) ] Order 81 # 3 : Symmetric cross-cap number 47 Signatures of corresponding actions [ (1;-;[3,9];{-}) ] Order 81 # 4 : Symmetric cross-cap number 65 Signatures of corresponding actions [ (1;-;[9,9];{-}) ] Order 81 # 5 : Symmetric cross-cap number 53 Signatures of corresponding actions [ (1;-;[3,27];{-}) ] Order 81 # 6 : Symmetric cross-cap number 53 Signatures of corresponding actions [ (1;-;[3,27];{-}) ] Order 81 # 7 : Symmetric cross-cap number 29 Signatures of corresponding actions [ (1;-;[3,3];{-}) ] Order 81 # 8 : Symmetric cross-cap number 47 Signatures of corresponding actions [ (1;-;[3,9];{-}) ] Order 81 # 9 : Symmetric cross-cap number 29 Signatures of corresponding actions [ (1;-;[3,3];{-}) ] Order 81 # 10 : Symmetric cross-cap number 65 Signatures of corresponding actions [ (1;-;[9,9];{-}) ] Order 81 # 11 : Symmetric cross-cap number 101 Signatures of corresponding actions [ (1;-;[3,3,9];{-}) ] Order 81 # 12 : Symmetric cross-cap number 83 Signatures of corresponding actions [ (1;-;[3,3,3];{-}) ] Order 81 # 13 : Symmetric cross-cap number 101 Signatures of corresponding actions [ (1;-;[3,3,9];{-}) ] Order 81 # 14 : Symmetric cross-cap number 101 Signatures of corresponding actions [ (1;-;[3,3,9];{-}) ] Order 81 # 15 : Symmetric cross-cap number 137 Signatures of corresponding actions [ (1;-;[3,3,3,3];{-}) ] ........................................................................... Groups of order 82 Total number of groups = 2 Order 82 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(41)}) ] Order 82 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[82];{(1)}) ] ........................................................................... Groups of order 83 Total number of groups = 1 Order 83 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[83];{-}) ] ........................................................................... Groups of order 84 Total number of groups = 15 Order 84 # 1 : Symmetric cross-cap number 37 Signatures of corresponding actions [ (0;+;[3,4];{(1)}) ] Order 84 # 2 : Symmetric cross-cap number 51 Signatures of corresponding actions [ (0;+;[3,12];{(1)}) ] Order 84 # 3 : Symmetric cross-cap number 55 Signatures of corresponding actions [ (0;+;[3,28];{(1)}) ] Order 84 # 4 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[4,12];{(1)}), (1;-;[4,12];{-}) ] Order 84 # 5 : Symmetric cross-cap number 44 Signatures of corresponding actions [ (0;+;[4,4];{(1)}), (1;-;[4,4];{-}) ] Order 84 # 6 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[84];{(1)}) ] Order 84 # 7 : Symmetric cross-cap number 30 Signatures of corresponding actions [ (0;+;[6];{(2,2)}), (0;+;[2,6];{(1)}) ] Order 84 # 8 : Symmetric cross-cap number 13 Signatures of corresponding actions [ (0;+;[-];{(2,6,14)}) ] Order 84 # 9 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[6,6];{(1)}), (0;+;[3];{(1),(1)}) ] Order 84 # 10 : Symmetric cross-cap number 19 Signatures of corresponding actions [ (0;+;[21];{(2)}) ] Order 84 # 11 : Symmetric cross-cap number 30 Signatures of corresponding actions [ (0;+;[3,3];{(1)}), (1;-;[3,3];{-}) ] Order 84 # 12 : Symmetric cross-cap number 30 Signatures of corresponding actions [ (0;+;[6];{(2,2)}), (0;+;[2,6];{(1)}) ] Order 84 # 13 : Symmetric cross-cap number 30 Signatures of corresponding actions [ (0;+;[-];{(1),(3)}) ] Order 84 # 14 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,42)}) ] Order 84 # 15 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] ........................................................................... Groups of order 85 Total number of groups = 1 Order 85 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[85];{-}) ] ........................................................................... Groups of order 86 Total number of groups = 2 Order 86 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(43)}) ] Order 86 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[86];{(1)}) ] ........................................................................... Groups of order 87 Total number of groups = 1 Order 87 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[87];{-}) ] ........................................................................... Groups of order 88 Total number of groups = 12 Order 88 # 1 : Symmetric cross-cap number 68 Signatures of corresponding actions [ (0;+;[8,8];{(1)}), (1;-;[8,8];{-}) ] Order 88 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[88];{(1)}) ] Order 88 # 3 : Symmetric cross-cap number 46 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 88 # 4 : Symmetric cross-cap number 24 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 88 # 5 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,44)}) ] Order 88 # 6 : Symmetric cross-cap number 46 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 88 # 7 : Symmetric cross-cap number 24 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}), (0;+;[2];{(4,4)}), (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 88 # 8 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] Order 88 # 9 : Symmetric cross-cap number 24 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 88 # 10 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[4,44];{(1)}) ] Order 88 # 11 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2)}) ] Order 88 # 12 : Symmetric cross-cap number 46 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] ........................................................................... Groups of order 89 Total number of groups = 1 Order 89 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[89];{-}) ] ........................................................................... Groups of order 90 Total number of groups = 10 Order 90 # 1 : Symmetric cross-cap number 33 Signatures of corresponding actions [ (0;+;[10];{(9)}) ] Order 90 # 2 : Symmetric cross-cap number 33 Signatures of corresponding actions [ (0;+;[18];{(5)}) ] Order 90 # 3 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(45)}) ] Order 90 # 4 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[90];{(1)}) ] Order 90 # 5 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[6,6];{(1)}), (1;-;[6,6];{-}) ] Order 90 # 6 : Symmetric cross-cap number 29 Signatures of corresponding actions [ (0;+;[30];{(3)}) ] Order 90 # 7 : Symmetric cross-cap number 29 Signatures of corresponding actions [ (0;+;[6];{(15)}) ] Order 90 # 8 : Symmetric cross-cap number 53 Signatures of corresponding actions [ (0;+;[10];{(3,3)}) ] Order 90 # 9 : Symmetric cross-cap number 29 Signatures of corresponding actions [ (0;+;[2];{(3,15)}) ] Order 90 # 10 : Symmetric cross-cap number 59 Signatures of corresponding actions [ (0;+;[3,30];{(1)}) ] ........................................................................... Groups of order 91 Total number of groups = 1 Order 91 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[91];{-}) ] ........................................................................... Groups of order 92 Total number of groups = 4 Order 92 # 1 : Symmetric cross-cap number 48 Signatures of corresponding actions [ (0;+;[4,4];{(1)}), (1;-;[4,4];{-}) ] Order 92 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[92];{(1)}) ] Order 92 # 3 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,46)}) ] Order 92 # 4 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] ........................................................................... Groups of order 93 Total number of groups = 2 Order 93 # 1 : Symmetric cross-cap number 33 Signatures of corresponding actions [ (1;-;[3,3];{-}) ] Order 93 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[93];{-}) ] ........................................................................... Groups of order 94 Total number of groups = 2 Order 94 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(47)}) ] Order 94 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[94];{(1)}) ] ........................................................................... Groups of order 95 Total number of groups = 1 Order 95 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[95];{-}) ] ........................................................................... Groups of order 96 Total number of groups = 231 Order 96 # 1 : Symmetric cross-cap number 63 Signatures of corresponding actions [ (0;+;[3,32];{(1)}) ] Order 96 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[96];{(1)}) ] Order 96 # 3 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[3,3];{(1)}) ] Order 96 # 4 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(1),(3)}) ] Order 96 # 5 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[-];{(1),(6)}) ] Order 96 # 6 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,48)}) ] Order 96 # 7 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 96 # 8 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 96 # 9 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[8,8];{(1)}) ] Order 96 # 10 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[8,8];{(1)}) ] Order 96 # 11 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[8,8];{(1)}) ] Order 96 # 12 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[8];{(2,2)}), (0;+;[2,8];{(1)}) ] Order 96 # 13 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 96 # 14 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 96 # 15 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 96 # 16 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[8];{(2,2)}), (0;+;[2,8];{(1)}) ] Order 96 # 17 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 96 # 18 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[3];{(1),(1)}) ] Order 96 # 19 : Symmetric cross-cap number 76 Signatures of corresponding actions [ (0;+;[6,16];{(1)}) ] Order 96 # 20 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 96 # 21 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 96 # 22 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 96 # 23 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 96 # 24 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 96 # 25 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 96 # 26 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[8,8];{(1)}) ] Order 96 # 27 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[8];{(2,2)}), (0;+;[2,8];{(1)}) ] Order 96 # 28 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 96 # 29 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[8,8];{(1)}) ] Order 96 # 30 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[8];{(2,2)}), (0;+;[2,8];{(1)}) ] Order 96 # 31 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 96 # 32 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 96 # 33 : Symmetric cross-cap number 31 Signatures of corresponding actions [ (0;+;[-];{(2,2,3,16)}) ] Order 96 # 34 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[4,6];{(1)}) ] Order 96 # 35 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[12];{(2,2)}), (0;+;[2,12];{(1)}) ] Order 96 # 36 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[4,12];{(1)}) ] Order 96 # 37 : Symmetric cross-cap number 70 Signatures of corresponding actions [ (0;+;[6,8];{(1)}) ] Order 96 # 38 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 96 # 39 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[4,6];{(1)}) ] Order 96 # 40 : Symmetric cross-cap number 70 Signatures of corresponding actions [ (0;+;[6,8];{(1)}) ] Order 96 # 41 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 96 # 42 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 96 # 43 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[8,8];{(1)}) ] Order 96 # 44 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[4,6];{(1)}) ] Order 96 # 45 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[4,12];{(1)}) ] Order 96 # 46 : Symmetric cross-cap number 70 Signatures of corresponding actions [ (0;+;[4,24];{(1)}) ] Order 96 # 47 : Symmetric cross-cap number 70 Signatures of corresponding actions [ (0;+;[4,24];{(1)}) ] Order 96 # 48 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 96 # 49 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 96 # 50 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 96 # 51 : Symmetric cross-cap number 70 Signatures of corresponding actions [ (0;+;[4,24];{(1)}) ] Order 96 # 52 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[-];{(1),(4)}) ] Order 96 # 53 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[4,12];{(1)}) ] Order 96 # 54 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[-];{(1),(4)}) ] Order 96 # 55 : Symmetric cross-cap number 70 Signatures of corresponding actions [ (0;+;[4,24];{(1)}) ] Order 96 # 56 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[4,12];{(1)}) ] Order 96 # 57 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[4,12];{(1)}) ] Order 96 # 58 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[8,24];{(1)}) ] Order 96 # 59 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] Order 96 # 60 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 96 # 61 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[6];{(2,2)}), (0;+;[2,6];{(1)}) ] Order 96 # 62 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[12];{(2,2)}), (0;+;[2,12];{(1)}) ] Order 96 # 63 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[4,12];{(1)}) ] Order 96 # 64 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(2,2,3,3)}), (0;+;[2];{(3,3)}), (0;+;[2,3];{(1)}) ] Order 96 # 65 : Symmetric cross-cap number 54 Signatures of corresponding actions [ (0;+;[3,8];{(1)}) ] Order 96 # 66 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[3,4];{(1)}) ] Order 96 # 67 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[3,4];{(1)}) ] Order 96 # 68 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[3,4];{(1)}) ] Order 96 # 69 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[3,4];{(1)}) ] Order 96 # 70 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[6];{(2)}) ] Order 96 # 71 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[3,4];{(1)}) ] Order 96 # 72 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[3];{(2,2)}), (0;+;[2,3];{(1)}) ] Order 96 # 73 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[24];{(2)}) ] Order 96 # 74 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[24];{(4)}) ] Order 96 # 75 : Symmetric cross-cap number 122 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 96 # 76 : Symmetric cross-cap number 122 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 96 # 77 : Symmetric cross-cap number 122 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 96 # 78 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 79 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 80 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 81 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,12)}) ] Order 96 # 82 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[4];{(2,2,4)}) ] Order 96 # 83 : Symmetric cross-cap number 98 Signatures of corresponding actions [ (0;+;[4,4];{(2,2)}), (0;+;[2,4,4];{(1)}), (0;+;[4];{(1),(2)}) ] Order 96 # 84 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 85 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 86 : Symmetric cross-cap number 98 Signatures of corresponding actions [ (0;+;[4,4];{(2,2)}), (0;+;[2,4,4];{(1)}), (0;+;[4];{(1),(2)}) ] Order 96 # 87 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(2,2,2)}), (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 88 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 89 : Symmetric cross-cap number 14 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,4)}) ] Order 96 # 90 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[4];{(2,2,4)}) ] Order 96 # 91 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}) ] Order 96 # 92 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[4];{(2,2,4)}) ] Order 96 # 93 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 94 : Symmetric cross-cap number 122 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 96 # 95 : Symmetric cross-cap number 122 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 96 # 96 : Symmetric cross-cap number 122 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 96 # 97 : Symmetric cross-cap number 122 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 96 # 98 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 99 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 100 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 101 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 102 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,12)}) ] Order 96 # 103 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 104 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 105 : Symmetric cross-cap number 98 Signatures of corresponding actions [ (0;+;[4,4];{(2,2)}), (0;+;[2,4,4];{(1)}), (0;+;[4];{(1),(2)}) ] Order 96 # 106 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 107 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 108 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 109 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(2,2,2)}), (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 110 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2)}) ] Order 96 # 111 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}) ] Order 96 # 112 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 113 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 114 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 115 : Symmetric cross-cap number 14 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,4)}) ] Order 96 # 116 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 117 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,6)}) ] Order 96 # 118 : Symmetric cross-cap number 30 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,6)}) ] Order 96 # 119 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,3,4)}) ] Order 96 # 120 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(2,2,2)}), (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 121 : Symmetric cross-cap number 20 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,8)}) ] Order 96 # 122 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[4];{(2,2,4)}) ] Order 96 # 123 : Symmetric cross-cap number 32 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,8)}) ] Order 96 # 124 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 125 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 126 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,12)}) ] Order 96 # 127 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[6];{(1),(1)}) ] Order 96 # 128 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[6];{(1),(1)}) ] Order 96 # 129 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 130 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 131 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 132 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 133 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 134 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4];{(2,2,2)}), (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 135 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 136 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 137 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}) ] Order 96 # 138 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,3)}) ] Order 96 # 139 : Symmetric cross-cap number 46 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,3,4)}) ] Order 96 # 140 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 141 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 142 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 143 : Symmetric cross-cap number 98 Signatures of corresponding actions [ (0;+;[4,4];{(2,2)}), (0;+;[2,4,4];{(1)}), (0;+;[4];{(1),(2)}) ] Order 96 # 144 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}) ] Order 96 # 145 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,3,4)}), (0;+;[-];{(2,2,3,4,4)}) ] Order 96 # 146 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 147 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}) ] Order 96 # 148 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 149 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 150 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 151 : Symmetric cross-cap number 122 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 96 # 152 : Symmetric cross-cap number 122 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 96 # 153 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 154 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[4];{(2,2,4)}) ] Order 96 # 155 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[6];{(1),(1)}) ] Order 96 # 156 : Symmetric cross-cap number 36 Signatures of corresponding actions [ (0;+;[-];{(2,2,6,8)}) ] Order 96 # 157 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 158 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 159 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 160 : Symmetric cross-cap number 46 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,3,4)}) ] Order 96 # 161 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 162 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 163 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 164 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 165 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 166 : Symmetric cross-cap number 138 Signatures of corresponding actions [ (0;+;[4,4,12];{(1)}) ] Order 96 # 167 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 168 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 169 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 170 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 171 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[-];{(2,2),(2)}), (0;+;[-];{(4,4),(1)}), (0;+;[2];{(1),(2)}) ] Order 96 # 172 : Symmetric cross-cap number 138 Signatures of corresponding actions [ (0;+;[4,4,12];{(1)}) ] Order 96 # 173 : Symmetric cross-cap number 98 Signatures of corresponding actions [ (0;+;[4];{(1),(2)}) ] Order 96 # 174 : Symmetric cross-cap number 70 Signatures of corresponding actions [ (0;+;[6];{(2,2,4)}) ] Order 96 # 175 : Symmetric cross-cap number 138 Signatures of corresponding actions [ (0;+;[4,4,12];{(1)}) ] Order 96 # 176 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 177 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 178 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 179 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 180 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 181 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 96 # 182 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 183 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 184 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 185 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 96 # 186 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 96 # 187 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[-];{(2,4,12)}) ] Order 96 # 188 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[4,6];{(1)}) ] Order 96 # 189 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[-];{(2,2,3,4)}) ] Order 96 # 190 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[6];{(2,2)}), (0;+;[2,6];{(1)}), (0;+;[-];{(1),(3)}) ] Order 96 # 191 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 96 # 192 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[-];{(2,2,3,4)}) ] Order 96 # 193 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,3)}) ] Order 96 # 194 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 96 # 195 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[-];{(2,2,3,4)}) ] Order 96 # 196 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 96 # 197 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 96 # 198 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[4,6];{(1)}) ] Order 96 # 199 : Symmetric cross-cap number 66 Signatures of corresponding actions [ (0;+;[4,12];{(1)}) ] Order 96 # 200 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[6];{(2,2)}), (0;+;[2,6];{(1)}) ] Order 96 # 201 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[-];{(1),(4)}) ] Order 96 # 202 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[6];{(2,2)}), (0;+;[2,6];{(1)}) ] Order 96 # 203 : Symmetric cross-cap number 34 Signatures of corresponding actions [ (0;+;[3,3];{(1)}) ] Order 96 # 204 : Symmetric cross-cap number 30 Signatures of corresponding actions [ (0;+;[3];{(2,4)}) ] Order 96 # 205 : Symmetric cross-cap number 98 Signatures of corresponding actions [ (0;+;[-];{(1),(1),(1)}) ] Order 96 # 206 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[4];{(2,2,2,2)}), (0;+;[-];{(2,2,2),(1)}) ] Order 96 # 207 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,2)}) ] Order 96 # 208 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,4)}) ] Order 96 # 209 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,2)}) ] Order 96 # 210 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4,4)}) ] Order 96 # 211 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,2)}) ] Order 96 # 212 : Symmetric cross-cap number 98 Signatures of corresponding actions [ (0;+;[-];{(1),(1),(1)}) ] Order 96 # 213 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,4)}) ] Order 96 # 214 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4,4)}) ] Order 96 # 215 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,4)}) ] Order 96 # 216 : Symmetric cross-cap number 26 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,2)}) ] Order 96 # 217 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4,4)}) ] Order 96 # 218 : Symmetric cross-cap number 98 Signatures of corresponding actions [ (0;+;[-];{(1),(1),(1)}) ] Order 96 # 219 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,4)}) ] Order 96 # 220 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[-];{(2,2,2),(1)}) ] Order 96 # 221 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[-];{(2,2,2),(1)}) ] Order 96 # 222 : Symmetric cross-cap number 98 Signatures of corresponding actions [ (0;+;[-];{(1),(1),(1)}) ] Order 96 # 223 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[-];{(2,2,2),(1)}) ] Order 96 # 224 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[-];{(2,2,2),(1)}) ] Order 96 # 225 : Symmetric cross-cap number 86 Signatures of corresponding actions [ (0;+;[-];{(2,2,4),(1)}) ] Order 96 # 226 : Symmetric cross-cap number 14 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,4)}) ] Order 96 # 227 : Symmetric cross-cap number 10 Signatures of corresponding actions [ (0;+;[-];{(3,4,4)}), (0;+;[-];{(2,2,2,3)}) ] Order 96 # 228 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 96 # 229 : Symmetric cross-cap number 18 Signatures of corresponding actions [ (0;+;[3];{(2,2)}) ] Order 96 # 230 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,2,2)}) ] Order 96 # 231 : Symmetric cross-cap number 98 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2),(1)}) ] ........................................................................... Groups of order 97 Total number of groups = 1 Order 97 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[97];{-}) ] ........................................................................... Groups of order 98 Total number of groups = 5 Order 98 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(49)}) ] Order 98 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[98];{(1)}) ] Order 98 # 3 : Symmetric cross-cap number 37 Signatures of corresponding actions [ (0;+;[14];{(7)}), (0;+;[2,7];{(1)}) ] Order 98 # 4 : Symmetric cross-cap number 37 Signatures of corresponding actions [ (0;+;[2];{(7,7)}) ] Order 98 # 5 : Symmetric cross-cap number 79 Signatures of corresponding actions [ (0;+;[7,14];{(1)}) ] ........................................................................... Groups of order 99 Total number of groups = 2 Order 99 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[99];{-}) ] Order 99 # 2 : Symmetric cross-cap number 65 Signatures of corresponding actions [ (1;-;[3,33];{-}) ] ........................................................................... Groups of order 100 Total number of groups = 16 Order 100 # 1 : Symmetric cross-cap number 52 Signatures of corresponding actions [ (0;+;[4,4];{(1)}), (1;-;[4,4];{-}) ] Order 100 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[100];{(1)}) ] Order 100 # 3 : Symmetric cross-cap number 25 Signatures of corresponding actions [ (0;+;[4];{(25)}) ] Order 100 # 4 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,50)}) ] Order 100 # 5 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] Order 100 # 6 : Symmetric cross-cap number 57 Signatures of corresponding actions [ (0;+;[4,5];{(1)}) ] Order 100 # 7 : Symmetric cross-cap number 127 Signatures of corresponding actions [ (0;+;[4,4,4];{(1)}) ] Order 100 # 8 : Symmetric cross-cap number 77 Signatures of corresponding actions [ (0;+;[5,20];{(1)}) ] Order 100 # 9 : Symmetric cross-cap number 37 Signatures of corresponding actions [ (0;+;[20];{(5)}) ] Order 100 # 10 : Symmetric cross-cap number 52 Signatures of corresponding actions [ (0;+;[4,4];{(1)}), (1;-;[4,4];{-}) ] Order 100 # 11 : Symmetric cross-cap number 57 Signatures of corresponding actions [ (0;+;[4];{(5,5)}) ] Order 100 # 12 : Symmetric cross-cap number 17 Signatures of corresponding actions [ (0;+;[4];{(5)}) ] Order 100 # 13 : Symmetric cross-cap number 17 Signatures of corresponding actions [ (0;+;[-];{(2,10,10)}), (0;+;[-];{(2,2,2,5)}) ] Order 100 # 14 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[10];{(2,2)}), (0;+;[2,10];{(1)}), (0;+;[-];{(1),(5)}) ] Order 100 # 15 : Symmetric cross-cap number 37 Signatures of corresponding actions [ (0;+;[-];{(2,2,5,10)}) ] Order 100 # 16 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[10,10];{(1)}), (0;+;[5];{(1),(1)}) ] ........................................................................... Groups of order 101 Total number of groups = 1 Order 101 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[101];{-}) ] ........................................................................... Groups of order 102 Total number of groups = 4 Order 102 # 1 : Symmetric cross-cap number 33 Signatures of corresponding actions [ (0;+;[34];{(3)}) ] Order 102 # 2 : Symmetric cross-cap number 33 Signatures of corresponding actions [ (0;+;[6];{(17)}) ] Order 102 # 3 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(51)}) ] Order 102 # 4 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[102];{(1)}) ] ........................................................................... Groups of order 103 Total number of groups = 1 Order 103 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[103];{-}) ] ........................................................................... Groups of order 104 Total number of groups = 14 Order 104 # 1 : Symmetric cross-cap number 80 Signatures of corresponding actions [ (0;+;[8,8];{(1)}), (1;-;[8,8];{-}) ] Order 104 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[104];{(1)}) ] Order 104 # 3 : Symmetric cross-cap number 67 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 104 # 4 : Symmetric cross-cap number 54 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 104 # 5 : Symmetric cross-cap number 28 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 104 # 6 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,52)}) ] Order 104 # 7 : Symmetric cross-cap number 54 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 104 # 8 : Symmetric cross-cap number 28 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}), (0;+;[2];{(4,4)}), (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 104 # 9 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] Order 104 # 10 : Symmetric cross-cap number 28 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 104 # 11 : Symmetric cross-cap number 78 Signatures of corresponding actions [ (0;+;[4,52];{(1)}) ] Order 104 # 12 : Symmetric cross-cap number 28 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 104 # 13 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2)}) ] Order 104 # 14 : Symmetric cross-cap number 54 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] ........................................................................... Groups of order 105 Total number of groups = 2 Order 105 # 1 : Symmetric cross-cap number 65 Signatures of corresponding actions [ (1;-;[3,15];{-}) ] Order 105 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[105];{-}) ] ........................................................................... Groups of order 106 Total number of groups = 2 Order 106 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(53)}) ] Order 106 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[106];{(1)}) ] ........................................................................... Groups of order 107 Total number of groups = 1 Order 107 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[107];{-}) ] ........................................................................... Groups of order 108 Total number of groups = 45 Order 108 # 1 : Symmetric cross-cap number 56 Signatures of corresponding actions [ (0;+;[4,4];{(1)}), (1;-;[4,4];{-}) ] Order 108 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[108];{(1)}) ] Order 108 # 3 : Symmetric cross-cap number 25 Signatures of corresponding actions [ (0;+;[27];{(2)}) ] Order 108 # 4 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,54)}) ] Order 108 # 5 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] Order 108 # 6 : Symmetric cross-cap number 71 Signatures of corresponding actions [ (0;+;[4,9];{(1)}) ] Order 108 # 7 : Symmetric cross-cap number 71 Signatures of corresponding actions [ (0;+;[3,36];{(1)}), (0;+;[4,9];{(1)}) ] Order 108 # 8 : Symmetric cross-cap number 47 Signatures of corresponding actions [ (0;+;[3,4];{(1)}) ] Order 108 # 9 : Symmetric cross-cap number 71 Signatures of corresponding actions [ (0;+;[4,9];{(1)}) ] Order 108 # 10 : Symmetric cross-cap number 128 Signatures of corresponding actions [ (0;+;[3,4,4];{(1)}), (1;-;[3,4,4];{-}) ] Order 108 # 11 : Symmetric cross-cap number 119 Signatures of corresponding actions [ (0;+;[3,3,4];{(1)}) ] Order 108 # 12 : Symmetric cross-cap number 71 Signatures of corresponding actions [ (0;+;[3,36];{(1)}) ] Order 108 # 13 : Symmetric cross-cap number 65 Signatures of corresponding actions [ (0;+;[3,12];{(1)}) ] Order 108 # 14 : Symmetric cross-cap number 71 Signatures of corresponding actions [ (0;+;[3,36];{(1)}) ] Order 108 # 15 : Symmetric cross-cap number 11 Signatures of corresponding actions [ (0;+;[4];{(3)}) ] Order 108 # 16 : Symmetric cross-cap number 17 Signatures of corresponding actions [ (0;+;[-];{(2,6,18)}) ] Order 108 # 17 : Symmetric cross-cap number 11 Signatures of corresponding actions [ (0;+;[-];{(2,6,6)}), (0;+;[-];{(2,2,2,3)}) ] Order 108 # 18 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[3,9];{(1)}), (1;-;[3,9];{-}) ] Order 108 # 19 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[3,9];{(1)}), (1;-;[3,9];{-}) ] Order 108 # 20 : Symmetric cross-cap number 80 Signatures of corresponding actions [ (1;-;[6,9];{-}) ] Order 108 # 21 : Symmetric cross-cap number 80 Signatures of corresponding actions [ (1;-;[6,9];{-}) ] Order 108 # 22 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[3,3];{(1)}), (1;-;[3,3];{-}) ] Order 108 # 23 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[6];{(2,2)}), (0;+;[2,6];{(1)}) ] Order 108 # 24 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[-];{(1),(3)}) ] Order 108 # 25 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[6];{(2,2)}), (0;+;[2,6];{(1)}), (0;+;[-];{(1),(3)}) ] Order 108 # 26 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[6];{(2,2)}), (0;+;[2,6];{(1)}) ] Order 108 # 27 : Symmetric cross-cap number 35 Signatures of corresponding actions [ (0;+;[-];{(2,2,3,18)}) ] Order 108 # 28 : Symmetric cross-cap number 29 Signatures of corresponding actions [ (0;+;[-];{(2,2,3,6)}) ] Order 108 # 29 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[3];{(1),(1)}) ] Order 108 # 30 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[6,6];{(1)}), (0;+;[3];{(1),(1)}) ] Order 108 # 31 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[3];{(1),(1)}) ] Order 108 # 32 : Symmetric cross-cap number 65 Signatures of corresponding actions [ (0;+;[3,12];{(1)}) ] Order 108 # 33 : Symmetric cross-cap number 119 Signatures of corresponding actions [ (0;+;[3,3,4];{(1)}) ] Order 108 # 34 : Symmetric cross-cap number 191 Signatures of corresponding actions [ (0;+;[3,3,3,4];{(1)}) ] Order 108 # 35 : Symmetric cross-cap number 137 Signatures of corresponding actions [ (0;+;[3,3,12];{(1)}) ] Order 108 # 36 : Symmetric cross-cap number 29 Signatures of corresponding actions [ (0;+;[12];{(3)}) ] Order 108 # 37 : Symmetric cross-cap number 47 Signatures of corresponding actions [ (0;+;[3,4];{(1)}) ] Order 108 # 38 : Symmetric cross-cap number 38 Signatures of corresponding actions [ (0;+;[6];{(2,2)}), (0;+;[2,6];{(1)}), (0;+;[-];{(1),(3)}) ] Order 108 # 39 : Symmetric cross-cap number 29 Signatures of corresponding actions [ (0;+;[-];{(2,2,3,6)}) ] Order 108 # 40 : Symmetric cross-cap number 29 Signatures of corresponding actions [ (0;+;[-];{(6,6,6)}), (0;+;[-];{(2,3,2,6)}) ] Order 108 # 41 : Symmetric cross-cap number 110 Signatures of corresponding actions [ (0;+;[3,3,3];{(1)}), (1;-;[3,3,3];{-}) ] Order 108 # 42 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[6,6];{(1)}), (0;+;[3];{(1),(1)}) ] Order 108 # 43 : Symmetric cross-cap number 65 Signatures of corresponding actions [ (0;+;[3];{(2,2,6)}) ] Order 108 # 44 : Symmetric cross-cap number 65 Signatures of corresponding actions [ (0;+;[-];{(2,2,3,6,3)}), (0;+;[-];{(2,2,3,3,6)}) ] Order 108 # 45 : Symmetric cross-cap number 146 Signatures of corresponding actions [ (0;+;[3,6,6];{(1)}), (0;+;[3,3];{(1),(1)}) ] ........................................................................... Groups of order 109 Total number of groups = 1 Order 109 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[109];{-}) ] ........................................................................... Groups of order 110 Total number of groups = 6 Order 110 # 1 : Symmetric cross-cap number 35 Signatures of corresponding actions [ (0;+;[2,5];{(1)}) ] Order 110 # 2 : Symmetric cross-cap number 79 Signatures of corresponding actions [ (0;+;[5,10];{(1)}) ] Order 110 # 3 : Symmetric cross-cap number 41 Signatures of corresponding actions [ (0;+;[22];{(5)}) ] Order 110 # 4 : Symmetric cross-cap number 41 Signatures of corresponding actions [ (0;+;[10];{(11)}) ] Order 110 # 5 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(55)}) ] Order 110 # 6 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[110];{(1)}) ] ........................................................................... Groups of order 111 Total number of groups = 2 Order 111 # 1 : Symmetric cross-cap number 39 Signatures of corresponding actions [ (1;-;[3,3];{-}) ] Order 111 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[111];{-}) ] ........................................................................... Groups of order 112 Total number of groups = 43 Order 112 # 1 : Symmetric cross-cap number 91 Signatures of corresponding actions [ (0;+;[7,16];{(1)}) ] Order 112 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[112];{(1)}) ] Order 112 # 3 : Symmetric cross-cap number 44 Signatures of corresponding actions [ (0;+;[8];{(2,2)}), (0;+;[2,8];{(1)}) ] Order 112 # 4 : Symmetric cross-cap number 44 Signatures of corresponding actions [ (0;+;[8];{(2,2)}), (0;+;[2,8];{(1)}) ] Order 112 # 5 : Symmetric cross-cap number 30 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 112 # 6 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,56)}) ] Order 112 # 7 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 112 # 8 : Symmetric cross-cap number 86 Signatures of corresponding actions [ (0;+;[8,8];{(1)}) ] Order 112 # 9 : Symmetric cross-cap number 86 Signatures of corresponding actions [ (0;+;[8,8];{(1)}) ] Order 112 # 10 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 112 # 11 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 112 # 12 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 112 # 13 : Symmetric cross-cap number 30 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 112 # 14 : Symmetric cross-cap number 43 Signatures of corresponding actions [ (0;+;[-];{(2,2,7,8)}) ] Order 112 # 15 : Symmetric cross-cap number 72 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 112 # 16 : Symmetric cross-cap number 44 Signatures of corresponding actions [ (0;+;[8];{(2,2)}), (0;+;[2,8];{(1)}) ] Order 112 # 17 : Symmetric cross-cap number 72 Signatures of corresponding actions [ (0;+;[4,8];{(1)}) ] Order 112 # 18 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 112 # 19 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,28];{(1)}) ] Order 112 # 20 : Symmetric cross-cap number 30 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 112 # 21 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,28];{(1)}) ] Order 112 # 22 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] Order 112 # 23 : Symmetric cross-cap number 30 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 112 # 24 : Symmetric cross-cap number 44 Signatures of corresponding actions [ (0;+;[-];{(1),(4)}) ] Order 112 # 25 : Symmetric cross-cap number 44 Signatures of corresponding actions [ (0;+;[-];{(1),(4)}) ] Order 112 # 26 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,28];{(1)}) ] Order 112 # 27 : Symmetric cross-cap number 86 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 112 # 28 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[4];{(2,2,2)}), (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 112 # 29 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2)}) ] Order 112 # 30 : Symmetric cross-cap number 30 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}) ] Order 112 # 31 : Symmetric cross-cap number 16 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,4)}) ] Order 112 # 32 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 112 # 33 : Symmetric cross-cap number 86 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 112 # 34 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,28)}) ] Order 112 # 35 : Symmetric cross-cap number 86 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 112 # 36 : Symmetric cross-cap number 30 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}) ] Order 112 # 37 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 112 # 38 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 112 # 39 : Symmetric cross-cap number 86 Signatures of corresponding actions [ (0;+;[4];{(1),(1)}) ] Order 112 # 40 : Symmetric cross-cap number 58 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 112 # 41 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[14];{(2)}) ] Order 112 # 42 : Symmetric cross-cap number 30 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2,2)}) ] Order 112 # 43 : Symmetric cross-cap number 86 Signatures of corresponding actions [ (0;+;[-];{(2,2,2),(1)}) ] ........................................................................... Groups of order 113 Total number of groups = 1 Order 113 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[113];{-}) ] ........................................................................... Groups of order 114 Total number of groups = 6 Order 114 # 1 : Symmetric cross-cap number 21 Signatures of corresponding actions [ (0;+;[2,3];{(1)}) ] Order 114 # 2 : Symmetric cross-cap number 59 Signatures of corresponding actions [ (0;+;[3,6];{(1)}) ] Order 114 # 3 : Symmetric cross-cap number 37 Signatures of corresponding actions [ (0;+;[38];{(3)}) ] Order 114 # 4 : Symmetric cross-cap number 37 Signatures of corresponding actions [ (0;+;[6];{(19)}) ] Order 114 # 5 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(57)}) ] Order 114 # 6 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[114];{(1)}) ] ........................................................................... Groups of order 115 Total number of groups = 1 Order 115 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[115];{-}) ] ........................................................................... Groups of order 116 Total number of groups = 5 Order 116 # 1 : Symmetric cross-cap number 60 Signatures of corresponding actions [ (0;+;[4,4];{(1)}), (1;-;[4,4];{-}) ] Order 116 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[116];{(1)}) ] Order 116 # 3 : Symmetric cross-cap number 29 Signatures of corresponding actions [ (0;+;[4];{(29)}) ] Order 116 # 4 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,58)}) ] Order 116 # 5 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] ........................................................................... Groups of order 117 Total number of groups = 4 Order 117 # 1 : Symmetric cross-cap number 93 Signatures of corresponding actions [ (1;-;[9,9];{-}) ] Order 117 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[117];{-}) ] Order 117 # 3 : Symmetric cross-cap number 41 Signatures of corresponding actions [ (1;-;[3,3];{-}) ] Order 117 # 4 : Symmetric cross-cap number 77 Signatures of corresponding actions [ (1;-;[3,39];{-}) ] ........................................................................... Groups of order 118 Total number of groups = 2 Order 118 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(59)}) ] Order 118 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[118];{(1)}) ] ........................................................................... Groups of order 119 Total number of groups = 1 Order 119 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[119];{-}) ] ........................................................................... Groups of order 120 Total number of groups = 47 Order 120 # 1 : Symmetric cross-cap number 79 Signatures of corresponding actions [ (0;+;[3,40];{(1)}) ] Order 120 # 2 : Symmetric cross-cap number 93 Signatures of corresponding actions [ (0;+;[5,24];{(1)}) ] Order 120 # 3 : Symmetric cross-cap number 92 Signatures of corresponding actions [ (0;+;[8,8];{(1)}), (1;-;[8,8];{-}) ] Order 120 # 4 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[120];{(1)}) ] Order 120 # 5 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[3,3];{(1)}) ] Order 120 # 6 : Symmetric cross-cap number 87 Signatures of corresponding actions [ (0;+;[4,24];{(1)}) ] Order 120 # 7 : Symmetric cross-cap number 92 Signatures of corresponding actions [ (0;+;[8,8];{(1)}), (1;-;[8,8];{-}) ] Order 120 # 8 : Symmetric cross-cap number 72 Signatures of corresponding actions [ (0;+;[4,6];{(1)}) ] Order 120 # 9 : Symmetric cross-cap number 80 Signatures of corresponding actions [ (0;+;[4,10];{(1)}) ] Order 120 # 10 : Symmetric cross-cap number 52 Signatures of corresponding actions [ (0;+;[12];{(2,2)}), (0;+;[2,12];{(1)}) ] Order 120 # 11 : Symmetric cross-cap number 72 Signatures of corresponding actions [ (0;+;[6];{(4,4)}), (0;+;[2,4];{(3)}), (0;+;[4,6];{(1)}), (0;+;[-];{(2,2,4,3,4)}), (0;+;[2];{(3,4,4)}) ] Order 120 # 12 : Symmetric cross-cap number 39 Signatures of corresponding actions [ (0;+;[-];{(2,2,3,20)}) ] Order 120 # 13 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,12)}), (0;+;[2];{(4,12)}) ] Order 120 # 14 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,12];{(1)}) ] Order 120 # 15 : Symmetric cross-cap number 74 Signatures of corresponding actions [ (0;+;[3,15];{(1)}) ] Order 120 # 16 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,12];{(1)}) ] Order 120 # 17 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(1),(5)}) ] Order 120 # 18 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[6];{(2,2)}), (0;+;[2,6];{(1)}) ] Order 120 # 19 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[4,12];{(1)}) ] Order 120 # 20 : Symmetric cross-cap number 52 Signatures of corresponding actions [ (0;+;[12];{(2,2)}), (0;+;[2,12];{(1)}) ] Order 120 # 21 : Symmetric cross-cap number 86 Signatures of corresponding actions [ (0;+;[4,20];{(1)}) ] Order 120 # 22 : Symmetric cross-cap number 42 Signatures of corresponding actions [ (0;+;[-];{(1),(3)}) ] Order 120 # 23 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[10];{(2,2)}), (0;+;[2,10];{(1)}) ] Order 120 # 24 : Symmetric cross-cap number 82 Signatures of corresponding actions [ (0;+;[3];{(1),(1)}) ] Order 120 # 25 : Symmetric cross-cap number 52 Signatures of corresponding actions [ (0;+;[-];{(1),(6)}) ] Order 120 # 26 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 120 # 27 : Symmetric cross-cap number 32 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 120 # 28 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,60)}) ] Order 120 # 29 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 120 # 30 : Symmetric cross-cap number 32 Signatures of corresponding actions [ (0;+;[-];{(2,2,4,4)}), (0;+;[2];{(4,4)}), (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 120 # 31 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] Order 120 # 32 : Symmetric cross-cap number 32 Signatures of corresponding actions [ (0;+;[-];{(1),(2)}) ] Order 120 # 33 : Symmetric cross-cap number 90 Signatures of corresponding actions [ (0;+;[4,60];{(1)}) ] Order 120 # 34 : Symmetric cross-cap number 5 Signatures of corresponding actions [ (0;+;[-];{(2,4,5)}) ] Order 120 # 35 : Symmetric cross-cap number 6 Signatures of corresponding actions [ (0;+;[-];{(2,3,10)}) ] Order 120 # 36 : Symmetric cross-cap number 32 Signatures of corresponding actions [ (0;+;[4];{(2,2)}), (0;+;[2,4];{(1)}) ] Order 120 # 37 : Symmetric cross-cap number 36 Signatures of corresponding actions [ (0;+;[20];{(3)}) ] Order 120 # 38 : Symmetric cross-cap number 13 Signatures of corresponding actions [ (0;+;[-];{(2,4,15)}) ] Order 120 # 39 : Symmetric cross-cap number 36 Signatures of corresponding actions [ (0;+;[6];{(10)}) ] Order 120 # 40 : Symmetric cross-cap number 50 Signatures of corresponding actions [ (0;+;[-];{(1),(5)}) ] Order 120 # 41 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[4,4];{(1)}) ] Order 120 # 42 : Symmetric cross-cap number 22 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,6)}) ] Order 120 # 43 : Symmetric cross-cap number 28 Signatures of corresponding actions [ (0;+;[30];{(2)}) ] Order 120 # 44 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 120 # 45 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] Order 120 # 46 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(2,2,2,2)}) ] Order 120 # 47 : Symmetric cross-cap number 62 Signatures of corresponding actions [ (0;+;[-];{(2,2),(1)}), (0;+;[2];{(1),(1)}) ] ........................................................................... Groups of order 121 Total number of groups = 2 Order 121 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[121];{-}) ] Order 121 # 2 : Symmetric cross-cap number 101 Signatures of corresponding actions [ (1;-;[11,11];{-}) ] ........................................................................... Groups of order 122 Total number of groups = 2 Order 122 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(61)}) ] Order 122 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[122];{(1)}) ] ........................................................................... Groups of order 123 Total number of groups = 1 Order 123 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[123];{-}) ] ........................................................................... Groups of order 124 Total number of groups = 4 Order 124 # 1 : Symmetric cross-cap number 64 Signatures of corresponding actions [ (0;+;[4,4];{(1)}), (1;-;[4,4];{-}) ] Order 124 # 2 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[124];{(1)}) ] Order 124 # 3 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[-];{(2,2,62)}) ] Order 124 # 4 : Symmetric cross-cap number 2 Signatures of corresponding actions [ (0;+;[-];{(1),(1)}) ] ........................................................................... Groups of order 125 Total number of groups = 5 Order 125 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[125];{-}) ] Order 125 # 2 : Symmetric cross-cap number 97 Signatures of corresponding actions [ (1;-;[5,25];{-}) ] Order 125 # 3 : Symmetric cross-cap number 77 Signatures of corresponding actions [ (1;-;[5,5];{-}) ] Order 125 # 4 : Symmetric cross-cap number 97 Signatures of corresponding actions [ (1;-;[5,25];{-}) ] Order 125 # 5 : Symmetric cross-cap number 177 Signatures of corresponding actions [ (1;-;[5,5,5];{-}) ] ........................................................................... Groups of order 126 Total number of groups = 16 Order 126 # 1 : Symmetric cross-cap number 49 Signatures of corresponding actions [ (0;+;[18];{(7)}) ] Order 126 # 2 : Symmetric cross-cap number 103 Signatures of corresponding actions [ (0;+;[7,18];{(1)}) ] Order 126 # 3 : Symmetric cross-cap number 49 Signatures of corresponding actions [ (0;+;[14];{(9)}) ] Order 126 # 4 : Symmetric cross-cap number 49 Signatures of corresponding actions [ (0;+;[18];{(7)}) ] Order 126 # 5 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[2];{(63)}) ] Order 126 # 6 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (0;+;[126];{(1)}) ] Order 126 # 7 : Symmetric cross-cap number 65 Signatures of corresponding actions [ (0;+;[3,6];{(1)}) ] Order 126 # 8 : Symmetric cross-cap number 65 Signatures of corresponding actions [ (0;+;[3,6];{(1)}) ] Order 126 # 9 : Symmetric cross-cap number 23 Signatures of corresponding actions [ (0;+;[2,3];{(1)}) ] Order 126 # 10 : Symmetric cross-cap number 65 Signatures of corresponding actions [ (0;+;[3,6];{(1)}) ] Order 126 # 11 : Symmetric cross-cap number 86 Signatures of corresponding actions [ (0;+;[6,6];{(1)}), (1;-;[6,6];{-}) ] Order 126 # 12 : Symmetric cross-cap number 41 Signatures of corresponding actions [ (0;+;[42];{(3)}) ] Order 126 # 13 : Symmetric cross-cap number 41 Signatures of corresponding actions [ (0;+;[6];{(21)}) ] Order 126 # 14 : Symmetric cross-cap number 77 Signatures of corresponding actions [ (0;+;[14];{(3,3)}) ] Order 126 # 15 : Symmetric cross-cap number 41 Signatures of corresponding actions [ (0;+;[2];{(3,21)}) ] Order 126 # 16 : Symmetric cross-cap number 83 Signatures of corresponding actions [ (0;+;[3,42];{(1)}) ] ........................................................................... Groups of order 127 Total number of groups = 1 Order 127 # 1 : Symmetric cross-cap number 1 Signatures of corresponding actions [ (1;-;[127];{-}) ] ...........................................................................