B:=[];
G:=[];
# Design 1: autom. group order 12, simple, derived
B[1]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,4,8,11,12],[1,2,5,9,11,13],[1,3,6,9,12,13],[1,3,6,10,11,13],[1,4,6,7,9,12],[1,4,8,10,11,13],[1,5,7,8,10,13],[1,5,7,9,10,12],[1,6,7,8,11,12],[2,3,6,7,10,11],[2,3,8,9,10,12],[2,4,6,10,12,13],[2,4,7,10,12,13],[2,5,6,7,8,13],[2,5,9,11,12,13],[2,6,7,8,9,11],[3,4,5,8,11,12],[3,4,7,8,9,13],[3,4,7,9,11,13],[3,5,6,8,12,13],[3,5,7,10,11,12],[4,5,6,8,9,10],[4,5,6,9,10,11]];
G[1]:=Group([(3,5)(6,7)(8,11)(10,13),(1,6,8)(2,4,9)(3,5,10)(7,11,12)]);
# Design 2: autom. group order 12, simple, derived
B[2]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,4,8,11,12],[1,2,5,9,11,13],[1,3,6,7,12,13],[1,3,6,9,12,13],[1,4,6,9,10,11],[1,4,7,8,11,12],[1,5,7,8,10,13],[1,5,8,10,12,13],[1,6,7,9,10,11],[2,3,6,8,11,13],[2,3,7,8,9,10],[2,4,7,9,12,13],[2,4,9,10,12,13],[2,5,6,7,10,12],[2,5,6,10,11,12],[2,6,7,8,11,13],[3,4,5,10,11,13],[3,4,6,8,10,12],[3,4,7,10,11,13],[3,5,7,9,11,12],[3,5,8,9,11,12],[4,5,6,7,8,9],[4,5,6,8,9,13]];
G[2]:=Group([(1,2,11,5,13,9)(3,8,12,10,4,6),(1,3,2,8,11,12,5,10,13,4,9,6)]);
# Design 3: autom. group order 12, simple
B[3]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,4,8,11,12],[1,2,5,9,11,13],[1,3,6,8,10,13],[1,3,7,11,12,13],[1,4,6,10,11,12],[1,4,7,9,10,13],[1,5,6,9,12,13],[1,5,7,8,10,12],[1,6,7,8,9,11],[2,3,6,11,12,13],[2,3,7,9,10,12],[2,4,6,9,10,13],[2,4,7,8,12,13],[2,5,6,8,10,12],[2,5,7,10,11,13],[2,6,7,8,9,11],[3,4,5,8,9,11],[3,4,6,7,8,13],[3,4,9,10,11,12],[3,5,6,7,9,12],[3,5,8,10,11,13],[4,5,6,7,10,11],[4,5,8,9,12,13]];
G[3]:=Group([(3,4,5)(8,11,9)(10,12,13),(1,2)(4,5)(6,7)(8,9)(12,13),(1,6)(2,7)(3,8)(4,9)(5,11)(10,13)]);
# Design 4: autom. group order 12, simple, derived
B[4]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,4,8,11,12],[1,2,5,9,11,13],[1,3,6,8,12,13],[1,3,7,10,11,12],[1,4,6,10,11,13],[1,4,7,9,12,13],[1,5,6,9,10,12],[1,5,7,8,10,13],[1,6,7,8,9,11],[2,3,6,10,11,12],[2,3,7,8,12,13],[2,4,6,9,12,13],[2,4,7,10,11,13],[2,5,6,8,10,13],[2,5,7,9,10,12],[2,6,7,8,9,11],[3,4,5,8,9,11],[3,4,6,7,9,10],[3,4,8,9,10,13],[3,5,6,7,11,13],[3,5,9,11,12,13],[4,5,6,7,8,12],[4,5,8,10,11,12]];
G[4]:=Group([(3,4,5)(8,11,9)(10,12,13),(1,2)(6,7),(1,6,2,7)(3,8,5,9,4,11)(10,12,13)]);
# Design 5: autom. group order 12, simple, derived
B[5]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,4,8,11,12],[1,2,6,7,8,13],[1,3,5,9,11,13],[1,3,6,9,11,12],[1,4,5,10,12,13],[1,4,7,9,10,12],[1,5,8,10,11,13],[1,6,7,8,9,12],[1,6,7,10,11,13],[2,3,6,10,11,12],[2,3,8,9,10,13],[2,4,7,9,10,11],[2,4,8,11,12,13],[2,5,6,7,10,11],[2,5,6,9,12,13],[2,5,7,9,12,13],[3,4,6,7,8,13],[3,4,6,10,12,13],[3,4,7,9,11,13],[3,5,7,8,10,12],[3,5,7,8,11,12],[4,5,6,8,9,10],[4,5,6,8,9,11]];
G[5]:=Group([(3,4)(6,7)(9,12)(10,11),(1,6,10)(2,5,8)(3,4,9)(7,11,13)]);
# Design 6: autom. group order 12, simple
B[6]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,5,11,12],[1,2,6,7,8,13],[1,3,6,9,11,13],[1,3,7,9,11,12],[1,4,6,10,12,13],[1,4,8,9,10,12],[1,5,7,11,12,13],[1,5,8,9,10,13],[1,6,7,8,10,11],[2,3,6,10,12,13],[2,3,8,10,11,12],[2,4,6,9,11,13],[2,4,7,9,10,11],[2,5,7,9,10,13],[2,5,8,11,12,13],[2,6,7,8,9,12],[3,4,5,7,8,13],[3,4,7,10,12,13],[3,4,8,9,11,13],[3,5,6,7,9,12],[3,5,6,8,10,11],[4,5,6,7,10,11],[4,5,6,8,9,12]];
G[6]:=Group([(3,4)(7,8)(9,12)(10,11),(1,2)(7,8)(9,10)(11,12),(1,3,7)(2,4,8)(5,13,6)(9,12,11)]);
# Design 7: autom. group order 12, simple
B[7]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,5,11,12],[1,2,6,7,8,13],[1,3,6,9,11,13],[1,3,7,10,11,12],[1,4,6,10,12,13],[1,4,8,9,10,11],[1,5,7,9,10,13],[1,5,8,11,12,13],[1,6,7,8,9,12],[2,3,6,10,12,13],[2,3,8,9,11,12],[2,4,6,9,11,13],[2,4,7,9,10,12],[2,5,7,11,12,13],[2,5,8,9,10,13],[2,6,7,8,10,11],[3,4,5,7,8,13],[3,4,7,9,11,13],[3,4,8,10,12,13],[3,5,6,7,9,12],[3,5,6,8,10,11],[4,5,6,7,10,11],[4,5,6,8,9,12]];
G[7]:=Group([(3,4)(7,8)(9,12)(10,11),(1,2)(7,8)(9,10)(11,12),(1,3,7)(2,4,8)(5,13,6)(10,11,12)]);
# Design 8: autom. group order 12, simple, derived
B[8]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,11,12,13],[1,3,6,9,10,13],[1,3,7,11,12,13],[1,4,5,7,10,11],[1,4,5,8,12,13],[1,5,6,8,10,12],[1,6,7,8,9,11],[1,7,8,9,10,13],[2,3,6,8,10,11],[2,3,8,9,12,13],[2,4,6,7,10,13],[2,4,8,10,11,13],[2,5,6,7,9,12],[2,5,7,8,9,11],[2,5,7,10,12,13],[3,4,5,9,11,13],[3,4,6,7,8,12],[3,4,7,9,10,12],[3,5,6,7,11,13],[3,5,8,10,11,12],[4,5,6,8,9,13],[4,6,9,10,11,12]];
G[8]:=Group([(1,2,5,12)(3,7,8,11)(4,9,10,13),(1,3,4,12,11,13,5,8,10,2,7,9)]);
# Design 9: autom. group order 12, simple, derived
B[9]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,9,10,11],[1,2,4,9,12,13],[1,2,5,7,12,13],[1,3,5,6,10,12],[1,3,5,8,9,11],[1,4,7,10,11,12],[1,4,8,9,10,13],[1,5,6,7,11,13],[1,6,7,8,9,12],[1,6,8,10,11,13],[2,3,6,7,9,10],[2,3,7,8,11,13],[2,4,5,10,11,13],[2,4,6,9,11,12],[2,5,6,8,9,13],[2,5,7,8,10,12],[2,6,8,10,11,12],[3,4,5,8,11,12],[3,4,6,7,10,13],[3,4,6,8,12,13],[3,5,9,10,12,13],[3,7,9,11,12,13],[4,5,6,7,9,11],[4,5,7,8,9,10]];
G[9]:=Group([(2,5)(4,6)(7,12)(8,10)(9,11),(1,2)(5,7)(6,8)(10,11)(12,13)]);
# Design 10: autom. group order 12, simple, derived
B[10]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,9,10,11],[1,2,5,7,9,12],[1,2,6,10,11,13],[1,3,5,10,12,13],[1,3,6,9,12,13],[1,4,5,7,10,11],[1,4,5,8,9,13],[1,4,6,8,11,12],[1,6,7,8,9,10],[1,7,8,11,12,13],[2,3,5,7,11,13],[2,3,6,8,10,12],[2,4,5,8,10,12],[2,4,6,7,12,13],[2,4,9,11,12,13],[2,5,6,8,9,11],[2,7,8,9,10,13],[3,4,6,7,9,11],[3,4,7,9,10,12],[3,4,8,10,11,13],[3,5,6,7,8,13],[3,5,8,9,11,12],[4,5,6,9,10,13],[5,6,7,10,11,12]];
G[10]:=Group([(1,2,12)(3,4,13)(5,7,9)(8,11,10),(1,3,7,10,2,4,9,8,12,13,5,11)]);