Automorphisms of 8 non-isomorphic systems of type E2F3 system 1 {0,1,2}{3,4,5}{6,7,8,9,10} {0,3,6}{1,7,9}{2,4,10,5,8} {0,5,7,10}{1,4,6,8}{2,3,9} {0,8,4,9}{2,7,3,10}{1,5,6} {1,3,8,10}{2,5,9,6}{0,4,7} has 2 automorphisms 0 1 2 3 4 5 6 7 8 9 10 0 3 6 1 7 9 2 4 10 5 8 r0->r1 r1->r0 r2->r3 r3->r2 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,c1:0123->0321,c2:0123->2103,c3:012->201] [c1->c1,c2->c2,c3->c3,c1:0123->0321,c2:0123->2103,c3:012->120] [c1->c1,c2->c2,c3->c3,c1:0123->1032,c2:0123->3210,c3:012->021] 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,c1:0123->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} {0,3,6}{1,7,9}{2,4,10,5,8} {0,5,1,10}{4,8,6,9}{2,3,7} {0,8,3,9}{2,5,7,10}{1,4,6} {1,3,10,8}{2,6,5,9}{0,4,7} has 2 automorphisms 0 1 2 3 4 5 6 7 8 9 10 0 3 6 1 7 9 2 4 10 5 8 r0->r1 r1->r0 r2->r3 r3->r2 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,c1:0123->0321,c2:0123->2301,c3:012->201] [c1->c1,c2->c2,c3->c3,c1:0123->0321,c2:0123->2301,c3:012->120] [c1->c1,c2->c2,c3->c3,c1:0123->1032,c2:0123->1032,c3:012->021] 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,c1:0123->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} {0,3,6}{1,7,9}{2,4,10,5,8} {0,5,1,8}{2,3,7,10}{4,6,9} {0,9,3,10}{1,4,8,6}{2,5,7} {1,3,8,10}{2,6,5,9}{0,4,7} has 2 automorphisms 0 1 2 3 4 5 6 7 8 9 10 0 3 6 1 7 9 2 4 10 5 8 r0->r1 r1->r0 r2->r3 r3->r2 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,c1:0123->0123,c2:0123->3012,c3:012->201] [c1->c1,c2->c2,c3->c3,c1:0123->0123,c2:0123->1230,c3:012->120] [c1->c1,c2->c2,c3->c3,c1:0123->1032,c2:0123->1032,c3:012->021] 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,c1:0123->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 4 {0,1,2}{3,4,5}{6,7,8,9,10} {0,3,6}{1,7,9}{2,4,10,5,8} {0,4,7,5}{1,3,8,10}{2,6,9} {0,8,4,9}{2,7,3,10}{1,5,6} {1,4,6,8}{2,3,9,5}{0,7,10} 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,c1:012->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] ------------------------------------------------ system 5 {0,1,2}{3,4,5}{6,7,8,9,10} {0,3,6}{1,7,9}{2,4,8,5,10} {1,3,7,4}{2,5,9,6}{0,8,10} {1,5,6,8}{2,3,10,7}{0,4,9} {1,6,4,10}{2,8,3,9}{0,5,7} has 2 automorphisms 0 1 2 3 4 5 6 7 8 9 10 0 3 6 1 7 9 2 4 8 5 10 r0->r1 r1->r0 r2->r2 r3->r4 r4->r3 [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->1032,c2:0123->3210,c3:012->012] [c1->c2,c2->c1,c3->c3,c1:0123->2301,c2:0123->1032,c3:012->021] [c1->c2,c2->c1,c3->c3,c1:0123->1032,c2:0123->2301,c3:012->021] 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,c1:0123->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 6 {0,1,2}{3,4,5}{6,7,8,9,10} {0,3,6}{1,7,9}{2,4,8,5,10} {0,4,6,9}{1,5,7,10}{2,3,8} {0,5,2,7}{3,9,4,10}{1,6,8} {1,3,7,4}{2,6,5,9}{0,8,10} has 2 automorphisms 0 1 2 3 4 5 6 7 8 9 10 0 3 6 1 7 9 2 4 8 5 10 r0->r1 r1->r0 r2->r3 r3->r2 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,c1:0123->0321,c2:0123->0123,c3:012->102] [c1->c1,c2->c2,c3->c3,c1:0123->0321,c2:0123->0123,c3:012->102] [c1->c1,c2->c2,c3->c3,c1:0123->1032,c2:0123->1032,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,c1:012->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] ------------------------------------------------ system 7 {0,1,2}{3,4,5}{6,7,8,9,10} {0,3,6}{1,4,8}{2,7,9,5,10} {1,3,10,7}{2,5,8,6}{0,4,9} {1,5,6,9}{2,3,7,4}{0,8,10} {1,6,4,10}{2,8,3,9}{0,5,7} has 2 automorphisms 0 1 2 3 4 5 6 7 8 9 10 0 3 6 1 4 8 2 10 5 9 7 r0->r1 r1->r0 r2->r2 r3->r4 r4->r3 [c1->c1,c2->c2,c3->c3,c1:012->012,c2:012->012,c3:01234->0432] [c1->c1,c2->c2,c3->c3,c1:012->012,c2:012->012,c3:01234->0432] [c1->c1,c2->c2,c3->c3,c1:0123->1032,c2:0123->3210,c3:012->012] [c1->c2,c2->c1,c3->c3,c1:0123->2103,c2:0123->1032,c3:012->012] [c1->c2,c2->c1,c3->c3,c1:0123->1032,c2:0123->2103,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,c1:012->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] ------------------------------------------------ system 8 {0,1,2}{3,4,5}{6,7,8,9,10} {0,3,6}{1,4,8}{2,7,9,5,10} {0,5,1,7}{4,6,8,10}{2,3,9} {0,8,3,10}{2,4,7,5}{1,6,9} {1,3,7,10}{2,6,5,8}{0,4,9} has 2 automorphisms 0 1 2 3 4 5 6 7 8 9 10 0 3 6 1 4 8 2 10 5 9 7 r0->r1 r1->r0 r2->r3 r3->r2 r4->r4 [c1->c1,c2->c2,c3->c3,c1:012->012,c2:012->012,c3:01234->0432] [c1->c1,c2->c2,c3->c3,c1:012->012,c2:012->012,c3:01234->0432] [c1->c1,c2->c2,c3->c3,c1:0123->0123,c2:0123->1032,c3:012->102] [c1->c1,c2->c2,c3->c3,c1:0123->0123,c2:0123->1032,c3:012->102] [c1->c1,c2->c2,c3->c3,c1:0123->1032,c2:0123->1032,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,c1:012->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] ------------------------------------------------