Automorphisms of 3 non-isomorphic systems of type F4E1

system 1
{0,1,2}{3,4,5}{6,7,8,9,10}
{0,3,1,6}{2,4,8,10}{5,7,9}
{0,4,1,10}{2,7,3,9}{5,6,8}
{0,5,1,9}{2,6,3,8}{4,7,10}
{0,7,1,8}{2,3,10,5}{4,6,9}
has 2 automorphisms
  0  1  2  3  4  5  6  7  8  9 10
  1  0  2  3  4  5  6  7  8  9 10
r0->r0 r1->r1 r2->r2 r3->r3 r4->r4 
[c1->c1,c2->c2,c3->c3,c1:012->102,c2:012->012,c3:01234->0123]
[c1->c1,c2->c2,c3->c3,c1:0123->2103,c2:0123->0123,c3:012->012]
[c1->c1,c2->c2,c3->c3,c1:0123->2103,c2:0123->0123,c3:012->012]
[c1->c1,c2->c2,c3->c3,c1:0123->2103,c2:0123->0123,c3:012->012]
[c1->c1,c2->c2,c3->c3,c1:0123->2103,c2:0123->0123,c3:012->012]
  0  1  2  3  4  5  6  7  8  9 10
  0  1  2  3  4  5  6  7  8  9 10
r0->r0 r1->r1 r2->r2 r3->r3 r4->r4 
[c1->c1,c2->c2,c3->c3,c1:012->012,c2:012->012,c3:01234->0123]
[c1->c1,c2->c2,c3->c3,c1:0123->0123,c2:0123->0123,c3:012->012]
[c1->c1,c2->c2,c3->c3,c1:0123->0123,c2:0123->0123,c3:012->012]
[c1->c1,c2->c2,c3->c3,c1:0123->0123,c2:0123->0123,c3:012->012]
[c1->c1,c2->c2,c3->c3,c1:0123->0123,c2:0123->0123,c3:012->012]
------------------------------------------------
system 2
{0,1,2}{3,4,5}{6,7,8,9,10}
{0,3,1,6}{2,4,7,9}{5,8,10}
{0,4,1,8}{2,3,7,10}{5,6,9}
{0,5,2,7}{1,9,3,10}{4,6,8}
{0,9,4,10}{2,6,3,8}{1,5,7}
has 1 automorphisms
  0  1  2  3  4  5  6  7  8  9 10
  0  1  2  3  4  5  6  7  8  9 10
r0->r0 r1->r1 r2->r2 r3->r3 r4->r4 
[c1->c1,c2->c2,c3->c3,c1:012->012,c2:012->012,c3:01234->0123]
[c1->c1,c2->c2,c3->c3,c1:0123->0123,c2:0123->0123,c3:012->012]
[c1->c1,c2->c2,c3->c3,c1:0123->0123,c2:0123->0123,c3:012->012]
[c1->c1,c2->c2,c3->c3,c1:0123->0123,c2:0123->0123,c3:012->012]
[c1->c1,c2->c2,c3->c3,c1:0123->0123,c2:0123->0123,c3:012->012]
------------------------------------------------
system 3
{0,1,2}{3,4,5}{6,7,8,9,10}
{0,3,1,6}{2,4,7,9}{5,8,10}
{0,4,1,8}{2,3,7,10}{5,6,9}
{0,5,1,7}{3,9,4,10}{2,6,8}
{0,9,1,10}{3,6,4,8}{2,5,7}
has 4 automorphisms
  0  1  2  3  4  5  6  7  8  9 10
  1  0  2  4  3  5  8  7  6 10  9
r0->r0 r1->r2 r2->r1 r3->r3 r4->r4 
[c1->c1,c2->c2,c3->c3,c1:012->102,c2:012->102,c3:01234->2104]
[c1->c1,c2->c2,c3->c3,c1:0123->2103,c2:0123->0123,c3:012->012]
[c1->c1,c2->c2,c3->c3,c1:0123->2103,c2:0123->0123,c3:012->012]
[c1->c1,c2->c2,c3->c3,c1:0123->2103,c2:0123->2301,c3:012->021]
[c1->c1,c2->c2,c3->c3,c1:0123->2301,c2:0123->2301,c3:012->012]
  0  1  2  3  4  5  6  7  8  9 10
  0  1  2  4  3  5  8  7  6 10  9
r0->r0 r1->r2 r2->r1 r3->r3 r4->r4 
[c1->c1,c2->c2,c3->c3,c1:012->012,c2:012->102,c3:01234->2104]
[c1->c1,c2->c2,c3->c3,c1:0123->0123,c2:0123->0123,c3:012->012]
[c1->c1,c2->c2,c3->c3,c1:0123->0123,c2:0123->0123,c3:012->012]
[c1->c1,c2->c2,c3->c3,c1:0123->0123,c2:0123->2301,c3:012->021]
[c1->c1,c2->c2,c3->c3,c1:0123->0321,c2:0123->2301,c3:012->012]
  0  1  2  3  4  5  6  7  8  9 10
  1  0  2  3  4  5  6  7  8  9 10
r0->r0 r1->r1 r2->r2 r3->r3 r4->r4 
[c1->c1,c2->c2,c3->c3,c1:012->102,c2:012->012,c3:01234->0123]
[c1->c1,c2->c2,c3->c3,c1:0123->2103,c2:0123->0123,c3:012->012]
[c1->c1,c2->c2,c3->c3,c1:0123->2103,c2:0123->0123,c3:012->012]
[c1->c1,c2->c2,c3->c3,c1:0123->2103,c2:0123->0123,c3:012->012]
[c1->c1,c2->c2,c3->c3,c1:0123->2103,c2:0123->0123,c3:012->012]
  0  1  2  3  4  5  6  7  8  9 10
  0  1  2  3  4  5  6  7  8  9 10
r0->r0 r1->r1 r2->r2 r3->r3 r4->r4 
[c1->c1,c2->c2,c3->c3,c1:012->012,c2:012->012,c3:01234->0123]
[c1->c1,c2->c2,c3->c3,c1:0123->0123,c2:0123->0123,c3:012->012]
[c1->c1,c2->c2,c3->c3,c1:0123->0123,c2:0123->0123,c3:012->012]
[c1->c1,c2->c2,c3->c3,c1:0123->0123,c2:0123->0123,c3:012->012]
[c1->c1,c2->c2,c3->c3,c1:0123->0123,c2:0123->0123,c3:012->012]
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