Automorphisms of 4 non-isomorphic systems of type F3E2

system 1
{0,2,8}{5,7,9}{1,4,10,3,6}
{0,6,10}{1,3,7}{2,5,8,4,9}
{1,5,10}{2,4,6}{0,7,8,3,9}
{0,1,2,3}{4,5,6,7}{8,9,10}
{0,4,3,5}{1,8,6,9}{2,7,10}
has group of order 2
  0  1  2  3  4  5  6  7  8  9 10
  5  6  7  4  3  0  1  2  9  8 10
r0->r0 r1->r2 r2->r1 r3->r3 r4->r4 
[c1->c2,c2->c1,c3->c3,c1:012->012,c2:012->012,c3:01234->4321]
[c1->c1,c2->c2,c3->c3,c1:012->102,c2:012->210,c3:01234->1043]
[c1->c1,c2->c2,c3->c3,c1:012->102,c2:012->210,c3:01234->1043]
[c1->c2,c2->c1,c3->c3,c1:0123->1230,c2:0123->3012,c3:012->102]
[c1->c1,c2->c2,c3->c3,c1:0123->3210,c2:0123->2301,c3:012->102]
  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,c1:012->012,c2:012->012,c3:01234->0123]
[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]
------------------------------------------------
system 2
{0,4,6}{1,7,8}{2,9,3,5,10}
{0,5,9}{1,4,10}{2,6,8,3,7}
{0,7,10}{2,5,8}{1,3,4,9,6}
{0,1,2,3}{4,5,6,7}{8,9,10}
{0,2,4,8}{1,5,7,9}{3,6,10}
has group of order 1
  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,c1:012->012,c2:012->012,c3:01234->0123]
[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]
------------------------------------------------
system 3
{0,4,8}{1,3,5}{2,7,9,6,10}
{0,5,10}{3,4,9}{1,6,2,8,7}
{1,4,10}{3,6,8}{0,7,5,2,9}
{0,1,2,3}{4,5,6,7}{8,9,10}
{0,2,4,6}{1,8,5,9}{3,7,10}
has group of order 1
  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,c1:012->012,c2:012->012,c3:01234->0123]
[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]
------------------------------------------------
system 4
{0,4,8}{2,6,10}{1,5,3,9,7}
{0,5,10}{2,7,8}{1,3,4,9,6}
{1,4,10}{3,6,8}{0,7,5,2,9}
{0,1,2,3}{4,5,6,7}{8,9,10}
{0,2,4,6}{1,8,5,9}{3,7,10}
has group of order 2
  0  1  2  3  4  5  6  7  8  9 10
  4  5  6  7  0  1  2  3  8  9 10
r0->r0 r1->r2 r2->r1 r3->r3 r4->r4 
[c1->c1,c2->c2,c3->c3,c1:012->102,c2:012->102,c3:01234->1043]
[c1->c1,c2->c2,c3->c3,c1:012->102,c2:012->102,c3:01234->2104]
[c1->c1,c2->c2,c3->c3,c1:012->102,c2:012->102,c3:01234->2104]
[c1->c2,c2->c1,c3->c3,c1:0123->0123,c2:0123->0123,c3:012->012]
[c1->c1,c2->c2,c3->c3,c1:0123->2301,c2:0123->2103,c3:012->102]
  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,c1:012->012,c2:012->012,c3:01234->0123]
[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]
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