B:=[];
G:=[];
# Design 1: autom. group order 6, simple, derived
B[1]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,3,8,9,11],[1,2,6,7,12,13],[1,3,6,7,12,13],[1,4,5,10,11,12],[1,4,5,10,11,13],[1,4,8,9,12,13],[1,5,8,9,12,13],[1,6,7,8,10,11],[1,6,7,9,10,11],[2,3,10,11,12,13],[2,4,6,8,10,12],[2,4,6,8,11,13],[2,4,7,9,10,12],[2,5,6,9,10,13],[2,5,7,8,11,13],[2,5,7,9,11,12],[3,4,6,9,11,13],[3,4,7,8,11,12],[3,4,7,9,10,13],[3,5,6,8,10,12],[3,5,6,9,11,12],[3,5,7,8,10,13],[4,5,6,7,8,9]];
G[1]:=Group([(2,4,10,7,13,8)(3,5,11,6,12,9)]);
# Design 2: autom. group order 6, simple
B[2]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,3,11,12,13],[1,2,6,7,8,11],[1,3,6,9,10,12],[1,4,5,8,9,12],[1,4,6,9,11,13],[1,4,7,9,11,13],[1,5,7,10,12,13],[1,5,8,10,11,13],[1,6,7,8,10,12],[2,3,7,9,10,13],[2,4,5,8,10,13],[2,4,6,10,11,12],[2,4,7,10,11,12],[2,5,6,9,12,13],[2,5,8,9,11,12],[2,6,7,8,9,13],[3,4,6,8,12,13],[3,4,7,8,12,13],[3,4,8,9,10,11],[3,5,6,7,8,11],[3,5,6,10,11,13],[3,5,7,9,11,12],[4,5,6,7,9,10]];
G[2]:=Group([(2,11)(3,13)(5,9)(6,7),(1,2)(6,7)(9,10)(12,13)]);
# Design 3: autom. group order 6, simple, derived
B[3]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,3,6,11,12],[1,2,7,9,11,13],[1,3,8,10,11,13],[1,4,5,7,10,13],[1,4,5,8,9,12],[1,4,5,11,12,13],[1,6,7,8,9,10],[1,6,7,10,11,12],[1,6,8,9,12,13],[2,3,8,9,12,13],[2,4,6,7,12,13],[2,4,6,8,10,11],[2,4,6,9,10,13],[2,5,7,8,11,12],[2,5,7,9,10,12],[2,5,8,10,11,13],[3,4,7,8,10,12],[3,4,7,9,11,13],[3,4,9,10,11,12],[3,5,6,7,8,13],[3,5,6,7,9,11],[3,5,6,10,12,13],[4,5,6,8,9,11]];
G[3]:=Group([(2,3)(4,5)(7,10)(8,9),(1,2)(5,6)(9,11)(10,12)]);
# Design 4: autom. group order 6, simple
B[4]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,3,6,11,12],[1,2,7,9,11,13],[1,3,7,10,12,13],[1,4,5,8,9,13],[1,4,5,8,11,12],[1,4,6,9,10,13],[1,5,7,10,11,13],[1,6,7,8,9,12],[1,6,8,10,11,12],[2,3,8,9,12,13],[2,4,5,11,12,13],[2,4,7,8,10,11],[2,4,7,9,10,12],[2,5,6,7,8,10],[2,5,6,10,12,13],[2,6,8,9,11,13],[3,4,6,7,11,13],[3,4,6,9,10,11],[3,4,8,10,12,13],[3,5,6,7,8,13],[3,5,7,9,11,12],[3,5,8,9,10,11],[4,5,6,7,9,12]];
G[4]:=Group([(1,2,3)(4,5,6)(7,9,12)(8,10,11),(1,7)(2,12)(3,9)(4,6)(10,11)]);
# Design 5: autom. group order 6, simple
B[5]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,3,6,11,12],[1,2,7,8,9,13],[1,3,7,11,12,13],[1,4,5,8,10,11],[1,4,5,9,12,13],[1,4,6,9,10,13],[1,5,7,8,10,12],[1,6,7,9,11,12],[1,6,8,10,11,13],[2,3,9,10,11,13],[2,4,5,11,12,13],[2,4,7,8,9,11],[2,4,7,10,12,13],[2,5,6,7,10,12],[2,5,6,8,11,13],[2,6,8,9,10,12],[3,4,6,7,10,13],[3,4,6,8,9,12],[3,4,8,10,11,12],[3,5,6,7,8,13],[3,5,7,9,10,11],[3,5,8,9,12,13],[4,5,6,7,9,11]];
G[5]:=Group([(1,2,3)(4,5,6)(7,9,11)(8,10,12),(1,7)(2,11)(3,9)(4,6)(8,12)]);
# Design 6: autom. group order 6, simple, derived
B[6]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,3,6,11,12],[1,2,7,9,11,13],[1,3,7,9,11,13],[1,4,5,7,8,12],[1,4,6,10,11,12],[1,4,8,11,12,13],[1,5,6,8,9,10],[1,5,7,8,10,13],[1,6,9,10,12,13],[2,3,8,10,12,13],[2,4,5,9,12,13],[2,4,6,7,10,13],[2,4,8,9,10,11],[2,5,6,8,11,13],[2,5,7,10,11,12],[2,6,7,8,9,12],[3,4,5,9,12,13],[3,4,6,7,10,13],[3,4,8,9,10,11],[3,5,6,8,11,13],[3,5,7,10,11,12],[3,6,7,8,9,12],[4,5,6,7,9,11]];
G[6]:=Group([(4,5,6)(7,9,11)(8,10,12),(2,3)]);
# Design 7: autom. group order 6, simple, derived
B[7]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,3,6,11,12],[1,2,7,9,11,13],[1,3,7,9,11,13],[1,4,5,7,8,12],[1,4,6,10,11,12],[1,4,8,11,12,13],[1,5,6,8,9,10],[1,5,7,8,10,13],[1,6,9,10,12,13],[2,3,8,10,12,13],[2,4,5,10,11,13],[2,4,6,8,9,13],[2,4,7,9,10,12],[2,5,6,7,12,13],[2,5,8,9,11,12],[2,6,7,8,10,11],[3,4,5,10,11,13],[3,4,6,8,9,13],[3,4,7,9,10,12],[3,5,6,7,12,13],[3,5,8,9,11,12],[3,6,7,8,10,11],[4,5,6,7,9,11]];
G[7]:=Group([(4,5,6)(7,9,11)(8,10,12),(2,3)]);
# Design 8: autom. group order 6, simple
B[8]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,3,6,11,12],[1,2,7,9,11,13],[1,3,7,9,11,13],[1,4,5,8,10,11],[1,4,6,8,9,12],[1,4,7,10,12,13],[1,5,6,7,10,12],[1,5,8,9,12,13],[1,6,8,10,11,13],[2,3,8,10,12,13],[2,4,5,7,10,13],[2,4,6,8,11,13],[2,4,9,10,11,12],[2,5,6,9,12,13],[2,5,7,8,11,12],[2,6,7,8,9,10],[3,4,5,8,9,13],[3,4,6,7,12,13],[3,4,9,10,11,12],[3,5,6,10,11,13],[3,5,7,8,11,12],[3,6,7,8,9,10],[4,5,6,7,9,11]];
G[8]:=Group([(4,5,6)(7,9,11)(8,10,12),(2,3)(5,6)(9,11)(10,12)]);
# Design 9: autom. group order 6, simple
B[9]:=[[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],[1,3,6,8,9,12],[1,4,6,9,10,11],[1,4,7,10,11,12],[1,5,7,8,10,13],[1,5,8,10,12,13],[1,6,7,9,11,13],[2,3,6,10,11,13],[2,3,10,11,12,13],[2,4,6,8,12,13],[2,4,7,8,9,13],[2,5,6,7,10,12],[2,5,7,9,11,12],[2,6,7,8,9,10],[3,4,5,9,10,13],[3,4,7,8,10,11],[3,4,7,9,12,13],[3,5,6,7,8,11],[3,5,8,9,11,12],[4,5,6,8,11,13],[4,5,6,9,10,12]];
G[9]:=Group([(1,2)(3,5)(6,7)(8,11)(10,13),(1,3,13)(2,10,5)(4,11,8)(6,12,7)]);
# Design 10: autom. group order 6, simple, derived
B[10]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,4,11,12,13],[1,2,5,8,11,12],[1,3,6,7,8,9],[1,3,8,10,11,12],[1,4,6,7,10,11],[1,4,8,9,10,13],[1,5,6,9,12,13],[1,5,7,9,12,13],[1,6,7,10,11,13],[2,3,6,9,11,13],[2,3,7,9,11,13],[2,4,6,9,10,12],[2,4,7,9,10,12],[2,5,6,8,10,13],[2,5,7,8,10,13],[2,6,7,8,11,12],[3,4,5,10,11,13],[3,4,6,8,12,13],[3,4,7,8,12,13],[3,5,6,7,10,12],[3,5,9,10,11,12],[4,5,6,8,9,11],[4,5,7,8,9,11]];
G[10]:=Group([(6,7),(1,10,11)(2,9,5)(3,12,8)]);
# Design 11: autom. group order 6, simple
B[11]:=[[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],[1,3,6,7,10,13],[1,3,10,11,12,13],[1,4,6,8,10,13],[1,4,7,9,10,11],[1,5,6,8,9,12],[1,5,7,11,12,13],[1,6,7,8,9,12],[2,3,6,9,11,12],[2,3,7,8,12,13],[2,4,6,7,12,13],[2,4,9,10,12,13],[2,5,6,9,10,13],[2,5,7,8,10,11],[2,6,7,8,10,11],[3,4,5,8,10,12],[3,4,6,7,9,11],[3,4,8,9,11,13],[3,5,6,10,11,12],[3,5,7,8,9,13],[4,5,6,8,11,13],[4,5,7,9,10,12]];
G[11]:=Group([(2,8)(3,12)(4,9)(5,6)(10,11),(1,2)(3,4)(6,7)(9,11)(10,12)]);
# Design 12: autom. group order 6, simple, derived
B[12]:=[[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],[1,3,7,10,11,13],[1,4,6,10,11,13],[1,4,7,9,10,12],[1,5,6,9,10,12],[1,5,7,8,12,13],[1,6,7,8,9,11],[2,3,6,11,12,13],[2,3,7,10,11,12],[2,4,6,9,10,13],[2,4,7,9,12,13],[2,5,6,8,10,12],[2,5,7,8,10,13],[2,6,7,8,9,11],[3,4,5,8,9,11],[3,4,6,7,8,10],[3,4,8,9,12,13],[3,5,6,7,9,13],[3,5,9,10,11,12],[4,5,6,7,11,12],[4,5,8,10,11,13]];
G[12]:=Group([(3,4,5)(8,11,9)(10,12,13),(1,6)(2,7)(3,8)(4,9)(5,11)(12,13)]);
# Design 13: autom. group order 6, simple, derived
B[13]:=[[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],[1,3,7,11,12,13],[1,4,6,10,11,13],[1,4,7,9,10,13],[1,5,6,9,10,12],[1,5,7,8,10,12],[1,6,7,8,9,11],[2,3,6,10,11,13],[2,3,7,10,11,12],[2,4,6,9,10,12],[2,4,7,9,12,13],[2,5,6,8,12,13],[2,5,7,8,10,13],[2,6,7,8,9,11],[3,4,5,8,9,11],[3,4,6,7,8,10],[3,4,8,9,12,13],[3,5,6,7,9,13],[3,5,9,10,11,12],[4,5,6,7,11,12],[4,5,8,10,11,13]];
G[13]:=Group([(3,4,5)(8,11,9)(10,12,13),(1,6)(2,7)(3,8)(4,9)(5,11)(12,13)]);
# Design 14: autom. group order 6, simple, derived
B[14]:=[[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],[1,3,7,10,11,13],[1,4,6,10,11,12],[1,4,7,9,10,12],[1,5,6,9,12,13],[1,5,7,8,12,13],[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],[3,4,9,11,12,13],[3,5,6,7,9,12],[3,5,8,10,11,12],[4,5,6,7,10,11],[4,5,8,9,10,13]];
G[14]:=Group([(3,4,5)(8,11,9)(10,12,13),(1,7)(2,6)(3,8,4,11,5,9)(10,13,12)]);
# Design 15: autom. group order 6, simple, derived
B[15]:=[[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],[1,3,7,10,11,12],[1,4,6,10,11,12],[1,4,7,9,12,13],[1,5,6,9,12,13],[1,5,7,8,10,13],[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],[3,4,9,10,11,13],[3,5,6,7,9,12],[3,5,8,11,12,13],[4,5,6,7,10,11],[4,5,8,9,10,12]];
G[15]:=Group([(3,4,5)(8,11,9)(10,12,13),(1,7)(2,6)(3,8,4,11,5,9)(10,13,12)]);
# Design 16: autom. group order 6, simple
B[16]:=[[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],[1,3,6,8,10,12],[1,3,7,10,11,13],[1,4,6,11,12,13],[1,4,7,9,10,12],[1,5,6,9,10,13],[1,5,7,8,12,13],[1,6,7,8,9,11],[2,3,6,10,11,13],[2,3,7,9,12,13],[2,4,6,9,10,12],[2,4,7,8,10,13],[2,5,6,8,12,13],[2,5,7,10,11,12],[2,6,7,8,9,11],[3,4,5,8,9,11],[3,4,6,7,8,13],[3,4,9,11,12,13],[3,5,6,7,9,12],[3,5,8,10,11,12],[4,5,6,7,10,11],[4,5,8,9,10,13]];
G[16]:=Group([(3,4,5)(8,11,9)(10,12,13),(1,7)(2,6)(3,8,4,11,5,9)(10,13,12)]);
# Design 17: autom. group order 6, simple, derived
B[17]:=[[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],[1,3,6,8,10,12],[1,3,7,10,11,13],[1,4,6,11,12,13],[1,4,7,9,10,12],[1,5,6,9,10,13],[1,5,7,8,12,13],[1,6,7,8,9,11],[2,3,6,10,11,12],[2,3,7,9,12,13],[2,4,6,9,12,13],[2,4,7,8,10,13],[2,5,6,8,10,13],[2,5,7,10,11,12],[2,6,7,8,9,11],[3,4,5,8,9,11],[3,4,6,7,8,13],[3,4,9,10,11,13],[3,5,6,7,9,12],[3,5,8,11,12,13],[4,5,6,7,10,11],[4,5,8,9,10,12]];
G[17]:=Group([(3,4,5)(8,11,9)(10,12,13),(1,7)(2,6)(3,8,4,11,5,9)(10,13,12)]);
# Design 18: autom. group order 6, simple, derived
B[18]:=[[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],[1,3,6,8,10,12],[1,3,7,10,11,13],[1,4,6,11,12,13],[1,4,7,9,10,12],[1,5,6,9,10,13],[1,5,7,8,12,13],[1,6,7,8,9,11],[2,3,6,11,12,13],[2,3,7,9,12,13],[2,4,6,9,10,13],[2,4,7,8,10,13],[2,5,6,8,10,12],[2,5,7,10,11,12],[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[18]:=Group([(3,4,5)(8,11,9)(10,12,13),(1,7)(2,6)(3,8,4,11,5,9)(10,13,12)]);
# Design 19: autom. group order 6, simple, derived
B[19]:=[[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],[1,3,6,8,10,12],[1,3,7,10,11,12],[1,4,6,11,12,13],[1,4,7,9,12,13],[1,5,6,9,10,13],[1,5,7,8,10,13],[1,6,7,8,9,11],[2,3,6,10,11,13],[2,3,7,9,12,13],[2,4,6,9,10,12],[2,4,7,8,10,13],[2,5,6,8,12,13],[2,5,7,10,11,12],[2,6,7,8,9,11],[3,4,5,8,9,11],[3,4,6,7,8,13],[3,4,9,10,11,13],[3,5,6,7,9,12],[3,5,8,11,12,13],[4,5,6,7,10,11],[4,5,8,9,10,12]];
G[19]:=Group([(3,4,5)(8,11,9)(10,12,13),(1,7)(2,6)(3,8,4,11,5,9)(10,13,12)]);
# Design 20: autom. group order 6, simple, derived
B[20]:=[[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],[1,3,6,8,10,12],[1,3,7,11,12,13],[1,4,6,11,12,13],[1,4,7,9,10,13],[1,5,6,9,10,13],[1,5,7,8,10,12],[1,6,7,8,9,11],[2,3,6,10,11,13],[2,3,7,9,12,13],[2,4,6,9,10,12],[2,4,7,8,10,13],[2,5,6,8,12,13],[2,5,7,10,11,12],[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[20]:=Group([(3,4,5)(8,11,9)(10,12,13),(1,7)(2,6)(3,8,4,11,5,9)(10,13,12)]);
# Design 21: autom. group order 6, simple
B[21]:=[[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],[1,3,7,9,10,12],[1,4,6,10,11,12],[1,4,7,8,12,13],[1,5,6,9,12,13],[1,5,7,10,11,13],[1,6,7,8,9,11],[2,3,6,11,12,13],[2,3,7,11,12,13],[2,4,6,9,10,13],[2,4,7,9,10,13],[2,5,6,8,10,12],[2,5,7,8,10,12],[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[21]:=Group([(4,5)(6,7)(8,9)(12,13),(3,4)(6,7)(9,11)(10,12)]);
# Design 22: autom. group order 6, simple, derived
B[22]:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,8,9,10],[1,2,4,8,11,12],[1,2,6,9,11,13],[1,3,5,8,12,13],[1,3,6,7,11,12],[1,4,6,8,10,13],[1,4,7,9,12,13],[1,5,7,9,10,11],[1,5,9,10,11,12],[1,6,7,8,10,13],[2,3,7,10,12,13],[2,3,10,11,12,13],[2,4,5,9,10,13],[2,4,6,7,10,11],[2,5,6,8,9,12],[2,5,7,8,11,13],[2,6,7,8,9,12],[3,4,6,9,10,12],[3,4,7,8,9,11],[3,4,8,9,11,13],[3,5,6,7,9,13],[3,5,6,8,10,11],[4,5,6,11,12,13],[4,5,7,8,10,12]];
G[22]:=Group([(1,2,9,10,3,8)(4,6,5,12,11,13)]);
# Design 23: autom. group order 6, simple, derived
B[23]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,5,11,12],[1,2,6,7,9,13],[1,3,6,8,10,13],[1,3,6,11,12,13],[1,4,7,8,10,11],[1,4,8,9,12,13],[1,5,7,10,12,13],[1,5,8,9,10,11],[1,6,7,9,11,12],[2,3,7,9,11,13],[2,3,8,10,12,13],[2,4,6,7,10,12],[2,4,9,10,11,13],[2,5,6,8,9,12],[2,5,7,8,11,13],[2,6,8,10,11,12],[3,4,5,11,12,13],[3,4,6,8,9,11],[3,4,7,9,10,12],[3,5,6,7,10,11],[3,5,7,8,9,12],[4,5,6,7,8,13],[4,5,6,9,10,13]];
G[23]:=Group([(4,5)(7,9)(8,10),(1,12,13)(3,6,11)(4,8,9)(5,10,7)]);
# Design 24: autom. group order 6, simple, derived
B[24]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,5,11,12],[1,2,6,7,9,13],[1,3,6,8,10,13],[1,3,6,11,12,13],[1,4,7,8,10,11],[1,4,9,10,12,13],[1,5,7,8,12,13],[1,5,8,9,10,11],[1,6,7,9,11,12],[2,3,7,9,11,13],[2,3,8,10,12,13],[2,4,6,8,9,12],[2,4,7,10,11,13],[2,5,6,7,10,12],[2,5,8,9,11,13],[2,6,8,10,11,12],[3,4,5,11,12,13],[3,4,6,9,10,11],[3,4,7,8,9,12],[3,5,6,7,8,11],[3,5,7,9,10,12],[4,5,6,7,10,13],[4,5,6,8,9,13]];
G[24]:=Group([(4,5)(7,9)(8,10),(1,12,13)(3,6,11)(4,8,9,5,10,7)]);
# Design 25: autom. group order 6, simple, derived
B[25]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,5,11,12],[1,2,6,7,9,13],[1,3,6,8,10,13],[1,3,6,11,12,13],[1,4,7,10,11,13],[1,4,8,9,10,12],[1,5,7,8,10,12],[1,5,8,9,11,13],[1,6,7,9,11,12],[2,3,7,9,12,13],[2,3,8,10,11,13],[2,4,6,9,10,11],[2,4,8,9,12,13],[2,5,6,7,8,11],[2,5,7,10,12,13],[2,6,8,10,11,12],[3,4,5,11,12,13],[3,4,6,7,10,12],[3,4,7,8,9,11],[3,5,6,8,9,12],[3,5,7,9,10,11],[4,5,6,7,8,13],[4,5,6,9,10,13]];
G[25]:=Group([(4,5)(7,9)(8,10),(1,11,13)(3,6,12)(4,8,7,5,10,9)]);
# Design 26: autom. group order 6, simple, derived
B[26]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,5,11,12],[1,2,6,9,11,13],[1,3,6,7,10,13],[1,3,8,9,12,13],[1,4,6,7,12,13],[1,4,8,10,11,13],[1,5,7,8,9,10],[1,5,7,8,11,12],[1,6,9,10,11,12],[2,3,6,8,11,12],[2,3,7,10,11,13],[2,4,6,8,9,10],[2,4,7,9,12,13],[2,5,7,9,11,13],[2,5,8,10,12,13],[2,6,7,8,10,12],[3,4,5,10,12,13],[3,4,7,8,9,11],[3,4,9,10,11,12],[3,5,6,7,9,12],[3,5,6,8,11,13],[4,5,6,7,10,11],[4,5,6,8,9,13]];
G[26]:=Group([(3,4)(9,11)(10,12),(1,8,13)(3,10,9,4,12,11)(5,6,7)]);
# Design 27: autom. group order 6, simple, derived
B[27]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,5,11,12],[1,2,6,9,11,13],[1,3,6,7,12,13],[1,3,8,10,11,13],[1,4,6,7,10,13],[1,4,8,9,12,13],[1,5,7,8,9,10],[1,5,7,8,11,12],[1,6,9,10,11,12],[2,3,6,8,9,12],[2,3,7,11,12,13],[2,4,6,8,10,11],[2,4,7,9,10,13],[2,5,7,9,11,13],[2,5,8,10,12,13],[2,6,7,8,10,12],[3,4,5,10,12,13],[3,4,7,8,9,11],[3,4,9,10,11,12],[3,5,6,7,10,11],[3,5,6,8,9,13],[4,5,6,7,9,12],[4,5,6,8,11,13]];
G[27]:=Group([(3,4)(9,11)(10,12),(1,8,13)(3,10,11)(4,12,9)(5,6,7)]);
# Design 28: autom. group order 6, simple, derived
B[28]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,5,11,12],[1,2,6,9,11,13],[1,3,6,7,10,13],[1,3,8,11,12,13],[1,4,6,7,12,13],[1,4,8,9,10,13],[1,5,7,8,9,12],[1,5,7,8,10,11],[1,6,9,10,11,12],[2,3,6,8,10,11],[2,3,7,9,12,13],[2,4,6,8,9,12],[2,4,7,10,11,13],[2,5,7,9,11,13],[2,5,8,10,12,13],[2,6,7,8,10,12],[3,4,5,10,12,13],[3,4,7,8,9,11],[3,4,9,10,11,12],[3,5,6,7,11,12],[3,5,6,8,9,13],[4,5,6,7,9,10],[4,5,6,8,11,13]];
G[28]:=Group([(3,4)(9,11)(10,12),(1,8,13)(3,10,11,4,12,9)(5,6,7)]);
# Design 29: autom. group order 6, simple
B[29]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,5,7,11,13],[1,3,6,7,8,10],[1,3,10,11,12,13],[1,4,5,8,12,13],[1,4,6,10,12,13],[1,5,6,8,9,13],[1,6,7,9,11,12],[1,7,8,9,10,11],[2,3,6,10,11,13],[2,3,7,9,12,13],[2,4,6,8,9,11],[2,4,8,10,11,13],[2,5,6,9,10,12],[2,5,7,8,10,12],[2,6,7,8,12,13],[3,4,5,7,11,12],[3,4,6,7,9,13],[3,4,8,9,10,12],[3,5,6,8,11,12],[3,5,8,9,11,13],[4,5,6,7,10,11],[4,5,7,9,10,13]];
G[29]:=Group([(1,2,7,5,13,11)(3,12,4,8,10,9)]);
# Design 30: autom. group order 6, simple
B[30]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,7,11,12],[1,2,5,9,11,13],[1,3,6,7,10,12],[1,3,8,9,11,12],[1,4,6,10,11,13],[1,4,7,8,9,13],[1,5,6,7,12,13],[1,5,8,10,12,13],[1,6,8,9,10,11],[2,3,6,8,9,13],[2,3,7,10,11,13],[2,4,6,9,12,13],[2,4,8,10,12,13],[2,5,6,8,11,12],[2,5,7,9,10,12],[2,6,7,8,10,11],[3,4,5,8,11,12],[3,4,5,10,11,13],[3,4,6,9,10,12],[3,5,6,7,8,13],[3,7,9,11,12,13],[4,5,6,7,9,11],[4,5,7,8,9,10]];
G[30]:=Group([(1,2)(4,5)(7,9)(8,10)(12,13),(1,4)(2,7)(3,8)(5,9)(6,13)]);
# Design 31: autom. group order 6, simple, derived
B[31]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,6,9,11],[1,2,7,8,12,13],[1,3,5,7,11,12],[1,3,6,7,10,13],[1,4,5,10,12,13],[1,4,9,11,12,13],[1,5,8,10,11,13],[1,6,7,8,9,12],[1,6,8,9,10,11],[2,3,6,11,12,13],[2,3,9,10,12,13],[2,4,5,8,11,12],[2,4,6,8,10,13],[2,5,7,8,9,13],[2,5,7,9,10,11],[2,6,7,10,11,12],[3,4,7,8,10,11],[3,4,7,9,11,13],[3,4,8,9,10,12],[3,5,6,8,9,12],[3,5,6,8,11,13],[4,5,6,7,9,13],[4,5,6,7,10,12]];
G[31]:=Group([(1,2)(3,4)(5,6)(7,8)(10,11)(12,13),(1,3,7)(2,4,8)(5,11,12)(6,10,13)]);
# Design 32: autom. group order 6, simple, derived
B[32]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,6,11,12],[1,2,7,9,11,13],[1,3,5,10,12,13],[1,3,6,8,9,12],[1,4,5,8,11,13],[1,4,9,10,12,13],[1,5,7,8,11,12],[1,6,7,8,10,13],[1,6,7,9,10,11],[2,3,7,10,11,12],[2,3,8,11,12,13],[2,4,5,7,10,13],[2,4,8,9,10,11],[2,5,6,7,9,12],[2,5,6,8,9,13],[2,6,8,10,12,13],[3,4,6,7,8,10],[3,4,6,9,11,13],[3,4,7,9,12,13],[3,5,6,7,11,13],[3,5,8,9,10,11],[4,5,6,10,11,12],[4,5,7,8,9,12]];
G[32]:=Group([(1,3)(2,5)(4,10)(6,9)(7,13)(8,12),(1,6)(2,10)(3,8)(4,7)(5,13)(9,12)]);
# Design 33: autom. group order 6, simple, derived
B[33]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,7,11,12],[1,2,6,9,11,13],[1,3,5,8,10,11],[1,3,6,9,12,13],[1,4,5,7,11,13],[1,4,8,9,10,12],[1,5,8,10,12,13],[1,6,7,8,9,12],[1,6,7,10,11,13],[2,3,6,7,10,12],[2,3,8,11,12,13],[2,4,5,9,12,13],[2,4,6,8,10,13],[2,5,6,10,11,12],[2,5,7,8,9,13],[2,7,8,9,10,11],[3,4,6,8,9,11],[3,4,7,10,12,13],[3,4,9,10,11,13],[3,5,6,7,8,13],[3,5,7,9,11,12],[4,5,6,7,9,10],[4,5,6,8,11,12]];
G[33]:=Group([(2,5,8,9,13,7)(3,10,12,6,11,4)]);
# Design 34: autom. group order 6, simple
B[34]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,7,10,11,13],[1,3,5,7,11,12],[1,3,6,9,12,13],[1,4,5,8,11,13],[1,4,6,7,8,13],[1,5,6,8,9,10],[1,6,7,10,11,12],[1,8,9,10,12,13],[2,3,6,10,11,13],[2,3,8,9,11,13],[2,4,5,10,12,13],[2,4,6,8,10,12],[2,5,6,7,12,13],[2,5,7,8,9,12],[2,6,7,8,9,11],[3,4,6,7,9,10],[3,4,7,9,12,13],[3,4,8,10,11,12],[3,5,6,8,11,12],[3,5,7,8,10,13],[4,5,6,9,11,13],[4,5,7,9,10,11]];
G[34]:=Group([(1,2,9,12,4,11)(3,8,13,10,5,7)]);
# Design 35: autom. group order 6, simple
B[35]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,7,10,11,13],[1,3,5,11,12,13],[1,3,6,8,10,11],[1,4,5,8,9,13],[1,4,6,7,10,13],[1,5,6,7,11,12],[1,6,8,9,12,13],[1,7,8,9,10,12],[2,3,6,7,12,13],[2,3,8,9,11,13],[2,4,5,10,12,13],[2,4,6,8,10,12],[2,5,6,7,8,9],[2,5,7,8,11,12],[2,6,9,10,11,13],[3,4,6,7,9,11],[3,4,7,9,12,13],[3,4,8,10,11,12],[3,5,6,9,10,12],[3,5,7,8,10,13],[4,5,6,8,11,13],[4,5,7,9,10,11]];
G[35]:=Group([(1,2,11,12,4,9)(3,13,5,10,7,8)]);
# Design 36: autom. group order 6, simple
B[36]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,9,11,13],[1,3,5,7,11,12],[1,3,6,7,12,13],[1,4,6,8,10,12],[1,4,7,8,11,13],[1,5,6,8,10,11],[1,5,9,10,12,13],[1,7,8,9,10,13],[2,3,6,8,10,13],[2,3,8,10,11,12],[2,4,5,7,10,13],[2,4,10,11,12,13],[2,5,6,7,12,13],[2,5,7,8,9,11],[2,6,7,8,9,12],[3,4,5,8,9,13],[3,4,6,9,11,13],[3,4,7,9,10,12],[3,5,8,11,12,13],[3,6,7,9,10,11],[4,5,6,7,10,11],[4,5,6,8,9,12]];
G[36]:=Group([(2,3)(4,5)(7,9)(8,10)(11,12),(2,7,10)(3,8,9)(4,13,5)(6,11,12)]);
# Design 37: autom. group order 6, simple, derived
B[37]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,7,11,12],[1,2,6,8,9,11],[1,3,5,9,11,13],[1,3,7,8,10,13],[1,4,6,10,11,13],[1,4,9,10,12,13],[1,5,6,8,12,13],[1,5,7,8,11,12],[1,6,7,9,10,12],[2,3,8,9,12,13],[2,3,10,11,12,13],[2,4,5,6,12,13],[2,4,7,9,11,13],[2,5,6,7,9,10],[2,5,8,10,11,12],[2,6,7,8,10,13],[3,4,5,7,10,12],[3,4,6,8,9,12],[3,4,6,8,10,11],[3,5,6,7,11,13],[3,6,7,9,11,12],[4,5,7,8,9,13],[4,5,8,9,10,11]];
G[37]:=Group([(1,2)(3,4)(5,7)(6,8)(9,11)(10,12),(1,6)(2,9)(3,7)(4,12)(5,10)(8,11)]);
# Design 38: autom. group order 6, simple, derived
B[38]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,7,11,12],[1,2,6,8,9,11],[1,3,6,9,10,12],[1,3,7,9,11,13],[1,4,5,6,12,13],[1,4,8,9,10,13],[1,5,7,10,11,13],[1,5,8,10,11,12],[1,6,7,8,12,13],[2,3,6,11,12,13],[2,3,7,8,10,13],[2,4,5,9,11,13],[2,4,8,10,11,12],[2,5,6,8,10,13],[2,5,7,9,12,13],[2,6,7,9,10,12],[3,4,5,7,10,12],[3,4,6,10,11,13],[3,4,8,9,12,13],[3,5,6,7,8,11],[3,5,8,9,11,12],[4,5,6,7,8,9],[4,6,7,9,10,11]];
G[38]:=Group([(1,2)(3,4)(5,7)(6,8)(9,11)(10,12),(1,6,11)(2,9,8)(3,7,12)(4,10,5)]);
# Design 39: autom. group order 6, simple, derived
B[39]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,7,11,12],[1,2,6,8,9,11],[1,3,6,9,10,12],[1,3,7,10,11,13],[1,4,5,9,11,13],[1,4,6,8,10,13],[1,5,6,7,12,13],[1,5,8,10,11,12],[1,7,8,9,12,13],[2,3,6,8,12,13],[2,3,7,9,11,13],[2,4,5,9,12,13],[2,4,8,10,11,12],[2,5,6,10,11,13],[2,5,7,8,10,13],[2,6,7,9,10,12],[3,4,5,7,10,12],[3,4,6,11,12,13],[3,4,8,9,10,13],[3,5,6,7,8,11],[3,5,8,9,11,12],[4,5,6,7,8,9],[4,6,7,9,10,11]];
G[39]:=Group([(1,2)(3,4)(5,7)(6,8)(9,11)(10,12),(1,6,11)(2,9,8)(3,7,12)(4,10,5)]);
# Design 40: autom. group order 6, simple
B[40]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,7,11,12],[1,3,6,8,10,11],[1,3,7,9,11,13],[1,4,5,7,12,13],[1,4,6,9,10,13],[1,5,6,8,12,13],[1,5,8,10,11,13],[1,7,8,9,10,12],[2,3,6,10,12,13],[2,3,8,11,12,13],[2,4,5,8,10,12],[2,4,7,10,11,13],[2,5,6,9,11,13],[2,5,7,8,9,13],[2,6,7,8,9,10],[3,4,5,8,9,11],[3,4,6,7,8,13],[3,4,9,10,12,13],[3,5,6,7,9,12],[3,5,7,10,11,12],[4,5,6,7,10,11],[4,6,8,9,11,12]];
G[40]:=Group([(1,3,13)(2,12,5)(4,10,8)(7,9,11),(1,7,13,11,3,9)(2,8,5,10,12,4)]);
# Design 41: autom. group order 6, simple
B[41]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,9,11,12],[1,2,6,7,10,13],[1,3,6,9,11,13],[1,3,7,11,12,13],[1,4,5,10,12,13],[1,4,6,8,10,12],[1,5,6,7,8,11],[1,5,7,8,9,12],[1,8,9,10,11,13],[2,3,6,8,10,11],[2,3,8,9,12,13],[2,4,5,8,11,13],[2,4,7,9,10,13],[2,5,6,11,12,13],[2,5,7,10,11,12],[2,6,7,8,9,12],[3,4,5,7,9,11],[3,4,6,7,12,13],[3,4,8,10,11,12],[3,5,6,9,10,12],[3,5,7,8,10,13],[4,5,6,8,9,13],[4,6,7,9,10,11]];
G[41]:=Group([(1,2,11)(3,5,13)(4,12,9)(7,10,8),(1,4)(2,12)(3,10)(5,8)(7,13)(9,11)]);
# Design 42: autom. group order 6, simple
B[42]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,5,9,10],[1,2,4,11,12,13],[1,2,6,7,9,11],[1,3,6,10,11,12],[1,3,8,10,12,13],[1,4,5,8,9,12],[1,4,7,9,10,11],[1,5,6,7,12,13],[1,5,7,8,11,13],[1,6,8,9,10,13],[2,3,6,9,12,13],[2,3,7,10,11,13],[2,4,6,8,11,12],[2,4,8,9,10,13],[2,5,6,7,8,10],[2,5,7,9,12,13],[2,5,8,10,11,12],[3,4,5,7,10,12],[3,4,5,9,11,13],[3,4,6,7,8,13],[3,5,6,8,9,11],[3,7,8,9,11,12],[4,5,6,10,11,13],[4,6,7,9,10,12]];
G[42]:=Group([(1,4,9,5,12,8)(2,10,3,7,11,13)]);
# Design 43: autom. group order 6, simple
B[43]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,9,10,11],[1,2,4,9,12,13],[1,2,5,7,10,12],[1,3,5,8,9,10],[1,3,5,11,12,13],[1,4,6,7,11,12],[1,4,6,8,10,11],[1,5,6,8,12,13],[1,6,7,9,10,13],[1,7,8,9,11,13],[2,3,6,7,9,12],[2,3,6,8,11,13],[2,4,5,8,10,13],[2,4,7,10,11,13],[2,5,6,9,11,13],[2,5,7,8,11,12],[2,6,8,9,10,12],[3,4,5,7,9,13],[3,4,6,10,12,13],[3,4,8,9,11,12],[3,5,6,7,10,11],[3,7,8,10,12,13],[4,5,6,7,8,9],[4,5,9,10,11,12]];
G[43]:=Group([(1,2,9,13,4,12)(3,6,7,10,11,5)]);
# Design 44: autom. group order 6, simple, derived
B[44]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,9,10,11],[1,2,4,9,12,13],[1,2,5,7,10,12],[1,3,5,7,9,13],[1,3,6,10,11,13],[1,4,5,8,11,12],[1,4,6,9,11,12],[1,5,6,8,9,10],[1,6,7,8,12,13],[1,7,8,10,11,13],[2,3,5,11,12,13],[2,3,6,7,8,9],[2,4,5,8,10,13],[2,4,6,7,10,11],[2,5,6,8,11,13],[2,6,9,10,12,13],[2,7,8,9,11,12],[3,4,6,8,10,12],[3,4,7,10,12,13],[3,4,8,9,11,13],[3,5,6,7,11,12],[3,5,8,9,10,12],[4,5,6,7,9,13],[4,5,7,9,10,11]];
G[44]:=Group([(1,2,12,5,10,7)(3,9,11,8,4,13)]);
# Design 45: autom. group order 6, simple
B[45]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,9,10,11],[1,2,4,9,10,12],[1,2,5,7,11,12],[1,3,5,6,9,13],[1,3,8,10,11,13],[1,4,5,10,12,13],[1,4,6,7,11,13],[1,5,6,7,8,9],[1,6,8,10,11,12],[1,7,8,9,12,13],[2,3,5,8,12,13],[2,3,7,9,11,13],[2,4,6,9,12,13],[2,4,7,8,10,13],[2,5,6,7,8,10],[2,5,6,10,11,13],[2,6,8,9,11,12],[3,4,5,8,11,12],[3,4,6,7,11,12],[3,4,6,8,9,10],[3,5,7,9,10,12],[3,6,7,10,12,13],[4,5,7,9,10,11],[4,5,8,9,11,13]];
G[45]:=Group([(1,2)(3,4)(5,7)(6,8)(9,10)(11,12),(1,5,11)(2,7,12)(3,9,8)(4,10,6)]);
# Design 46: autom. group order 6, simple, derived
B[46]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,9,10,11],[1,2,4,9,10,12],[1,2,5,7,11,12],[1,3,5,6,12,13],[1,3,8,9,11,13],[1,4,5,10,11,13],[1,4,6,7,9,13],[1,5,6,7,8,9],[1,6,8,10,11,12],[1,7,8,10,12,13],[2,3,5,8,10,13],[2,3,7,9,12,13],[2,4,6,10,12,13],[2,4,7,8,11,13],[2,5,6,7,8,10],[2,5,6,9,11,13],[2,6,8,9,11,12],[3,4,5,8,11,12],[3,4,6,7,11,12],[3,4,6,8,9,10],[3,5,7,9,10,12],[3,6,7,10,11,13],[4,5,7,9,10,11],[4,5,8,9,12,13]];
G[46]:=Group([(1,2)(3,4)(5,7)(6,8)(9,10)(11,12),(1,5,11,2,7,12)(3,10,6,4,9,8)]);
# Design 47: autom. group order 6, simple
B[47]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,9,10,11],[1,2,4,9,10,12],[1,2,5,7,11,12],[1,3,5,6,11,13],[1,3,8,9,12,13],[1,4,5,8,10,13],[1,4,7,9,11,13],[1,5,6,7,8,9],[1,6,7,10,12,13],[1,6,8,10,11,12],[2,3,5,10,12,13],[2,3,6,7,9,13],[2,4,6,10,11,13],[2,4,7,8,12,13],[2,5,6,7,8,10],[2,5,8,9,11,13],[2,6,8,9,11,12],[3,4,5,8,11,12],[3,4,6,7,11,12],[3,4,6,8,9,10],[3,5,7,9,10,12],[3,7,8,10,11,13],[4,5,6,9,12,13],[4,5,7,9,10,11]];
G[47]:=Group([(1,2)(3,4)(5,7)(6,8)(9,10)(11,12),(1,5,12)(2,7,11)(3,10,6)(4,9,8)]);
# Design 48: autom. group order 6, simple
B[48]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,9,10,11],[1,2,4,9,10,12],[1,2,5,7,11,12],[1,3,5,8,12,13],[1,3,6,9,11,13],[1,4,5,6,10,13],[1,4,7,9,12,13],[1,5,6,7,8,10],[1,6,8,9,11,12],[1,7,8,10,11,13],[2,3,5,10,11,13],[2,3,7,8,9,13],[2,4,6,7,11,13],[2,4,8,10,12,13],[2,5,6,7,8,9],[2,5,6,9,12,13],[2,6,8,10,11,12],[3,4,5,8,11,12],[3,4,6,7,11,12],[3,4,6,8,9,10],[3,5,7,9,10,12],[3,6,7,10,12,13],[4,5,7,9,10,11],[4,5,8,9,11,13]];
G[48]:=Group([(1,2)(3,4)(5,7)(6,8)(9,10)(11,12),(1,5,11)(2,7,12)(3,10,8)(4,9,6)]);
# Design 49: autom. group order 6, simple
B[49]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,9,10,11],[1,2,4,9,12,13],[1,2,5,7,10,11],[1,3,5,7,9,12],[1,3,6,8,9,13],[1,4,5,8,10,13],[1,4,6,10,11,13],[1,5,6,8,11,12],[1,6,7,9,10,12],[1,7,8,11,12,13],[2,3,5,8,10,12],[2,3,6,11,12,13],[2,4,6,7,9,11],[2,4,6,8,10,12],[2,5,6,7,12,13],[2,5,8,9,11,13],[2,7,8,9,10,13],[3,4,5,7,11,13],[3,4,7,10,12,13],[3,4,8,9,11,12],[3,5,6,9,10,13],[3,6,7,8,10,11],[4,5,6,7,8,9],[4,5,9,10,11,12]];
G[49]:=Group([(1,2,12)(3,6,7)(4,13,9)(8,11,10),(1,4)(2,13)(3,10)(6,8)(7,11)(9,12)]);
# Design 50: autom. group order 6, simple
B[50]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,9,10,11],[1,2,4,9,10,12],[1,2,5,7,11,12],[1,3,5,8,9,13],[1,3,6,10,12,13],[1,4,5,10,11,13],[1,4,7,8,12,13],[1,5,6,7,8,10],[1,6,7,9,11,13],[1,6,8,9,11,12],[2,3,5,6,11,13],[2,3,7,9,12,13],[2,4,6,7,10,13],[2,4,8,9,11,13],[2,5,6,7,8,9],[2,5,8,10,12,13],[2,6,8,10,11,12],[3,4,5,8,11,12],[3,4,6,7,11,12],[3,4,6,8,9,10],[3,5,7,9,10,12],[3,7,8,10,11,13],[4,5,6,9,12,13],[4,5,7,9,10,11]];
G[50]:=Group([(1,2)(3,4)(5,7)(6,8)(9,10)(11,12),(1,5,12)(2,7,11)(3,9,6)(4,10,8)]);
# Design 51: autom. group order 6, simple, derived
B[51]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,9,10,11],[1,2,4,9,10,12],[1,2,5,7,11,12],[1,3,5,8,11,13],[1,3,6,9,12,13],[1,4,5,10,12,13],[1,4,7,8,9,13],[1,5,6,7,8,10],[1,6,7,10,11,13],[1,6,8,9,11,12],[2,3,5,6,10,13],[2,3,7,9,11,13],[2,4,6,7,12,13],[2,4,8,10,11,13],[2,5,6,7,8,9],[2,5,8,9,12,13],[2,6,8,10,11,12],[3,4,5,8,11,12],[3,4,6,7,11,12],[3,4,6,8,9,10],[3,5,7,9,10,12],[3,7,8,10,12,13],[4,5,6,9,11,13],[4,5,7,9,10,11]];
G[51]:=Group([(1,2)(3,4)(5,7)(6,8)(9,10)(11,12),(1,5,12,2,7,11)(3,10,8,4,9,6)]);
# Design 52: autom. group order 6, simple, derived
B[52]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,9,10,11],[1,2,4,9,12,13],[1,2,5,10,12,13],[1,3,5,6,11,12],[1,3,6,7,9,10],[1,4,7,9,11,13],[1,4,8,10,11,12],[1,5,6,8,10,13],[1,5,7,8,9,12],[1,6,7,8,11,13],[2,3,5,8,9,11],[2,3,7,8,10,13],[2,4,6,8,9,12],[2,4,6,10,11,13],[2,5,6,7,9,13],[2,5,7,10,11,12],[2,6,7,8,11,12],[3,4,5,7,12,13],[3,4,5,8,11,13],[3,4,6,7,10,12],[3,6,9,11,12,13],[3,8,9,10,12,13],[4,5,6,8,9,10],[4,5,7,9,10,11]];
G[52]:=Group([(1,2,8,13,12,6)(4,7,10,9,11,5)]);
# Design 53: autom. group order 6, simple, derived
B[53]:=[[1,2,3,4,5,6],[1,2,3,4,7,8],[1,2,3,9,10,11],[1,2,4,9,12,13],[1,2,10,11,12,13],[1,3,5,7,9,10],[1,3,5,8,11,12],[1,4,6,7,9,12],[1,4,6,8,10,13],[1,5,6,7,11,13],[1,5,6,8,10,12],[1,7,8,9,11,13],[2,3,6,7,10,13],[2,3,6,8,9,11],[2,4,5,7,11,12],[2,4,5,8,9,13],[2,5,6,9,10,12],[2,5,7,8,10,13],[2,6,7,8,11,12],[3,4,5,6,11,13],[3,4,7,8,10,12],[3,4,10,11,12,13],[3,5,7,9,12,13],[3,6,8,9,12,13],[4,5,8,9,10,11],[4,6,7,9,10,11]];
G[53]:=Group([(3,4)(5,6)(10,12)(11,13),(1,10,12)(2,11,13)(3,4,9)(5,8,6)]);