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n8_unique.txt
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--- magma #0, count=960
[[1, 0, 3, 2, 5, 4, 7, 6],
[0, 0, 0, 0, 0, 0, 0, 0],
[3, 0, 3, 0, 0, 3, 0, 3],
[2, 0, 0, 2, 5, 7, 7, 5],
[5, 0, 0, 5, 5, 0, 0, 5],
[4, 0, 3, 7, 0, 4, 7, 3],
[7, 0, 0, 7, 0, 7, 7, 0],
[6, 0, 3, 5, 5, 3, 0, 6]]
symmetry
perm: (0, 1, 2, 3, 4, 5, 6, 7)
perm: (0, 1, 2, 3, 6, 7, 4, 5)
perm: (0, 1, 4, 5, 2, 3, 6, 7)
perm: (0, 1, 4, 5, 6, 7, 2, 3)
perm: (0, 1, 6, 7, 2, 3, 4, 5)
perm: (0, 1, 6, 7, 4, 5, 2, 3)
Note: this should be the direct product (N=2) x (N=2) x (N=2)
as it is the only one with |symmetry group| = 6.
Also it is the only one with a constant row and collumn.
--- magma #1, count=5760
[[1, 0, 0, 1, 2, 2, 3, 3],
[0, 0, 0, 0, 3, 3, 3, 3],
[4, 4, 5, 4, 5, 5, 4, 5],
[7, 4, 5, 7, 6, 6, 4, 5],
[1, 0, 0, 1, 6, 6, 3, 3],
[7, 4, 5, 7, 2, 2, 4, 5],
[4, 4, 5, 4, 5, 5, 4, 5],
[0, 0, 0, 0, 3, 3, 3, 3]]
perm: (0, 1, 2, 3, 4, 5, 6, 7)
--- magma #2, count=5760
[[1, 0, 0, 1, 2, 2, 3, 3],
[0, 0, 0, 0, 3, 3, 3, 3],
[4, 4, 4, 5, 5, 4, 5, 5],
[6, 4, 4, 6, 7, 7, 5, 5],
[1, 0, 0, 1, 2, 2, 5, 5],
[6, 4, 4, 6, 7, 7, 3, 3],
[0, 0, 0, 0, 3, 3, 3, 3],
[4, 4, 4, 5, 5, 4, 5, 5]]
perm: (0, 1, 2, 3, 4, 5, 6, 7)
--- magma #3, count=2880
[[1, 0, 0, 1, 2, 2, 3, 3],
[0, 0, 0, 0, 3, 3, 3, 3],
[4, 5, 5, 4, 5, 5, 4, 4],
[6, 5, 5, 6, 7, 7, 4, 4],
[6, 0, 0, 6, 7, 7, 3, 3],
[1, 5, 5, 1, 2, 2, 4, 4],
[0, 0, 0, 0, 3, 3, 3, 3],
[4, 5, 5, 4, 5, 5, 4, 4]]
perm: (0, 1, 2, 3, 4, 5, 6, 7)
perm: (5, 2, 1, 4, 3, 0, 7, 6)
--- magma #4, count=5760
[[1, 0, 0, 1, 2, 2, 3, 3],
[0, 0, 0, 0, 3, 3, 3, 3],
[4, 4, 4, 4, 5, 5, 5, 5],
[6, 4, 4, 7, 7, 6, 5, 5],
[1, 0, 0, 1, 2, 2, 3, 3],
[6, 4, 4, 7, 7, 6, 5, 5],
[0, 0, 0, 0, 5, 5, 5, 5],
[4, 4, 4, 4, 3, 3, 3, 3]]
perm: (0, 1, 2, 3, 4, 5, 6, 7)
--- magma #5, count=2880
[[1, 0, 0, 1, 2, 2, 3, 3],
[0, 0, 0, 0, 3, 3, 3, 3],
[4, 4, 4, 4, 5, 5, 5, 5],
[6, 4, 4, 6, 7, 7, 5, 5],
[1, 0, 0, 1, 2, 2, 3, 3],
[6, 4, 4, 6, 7, 7, 5, 5],
[0, 0, 0, 0, 3, 3, 3, 3],
[4, 4, 4, 4, 5, 5, 5, 5]]
perm: (0, 1, 2, 3, 4, 5, 6, 7)
perm: (5, 7, 6, 4, 3, 0, 2, 1)
Note: this is equivalent to the (N=2)x(N=4 central groupoid)
((4,4,5,5, 0,0,1,1),
(6,6,7,7, 2,2,3,3),
(4,4,5,5, 0,0,1,1),
(6,6,7,7, 2,2,3,3),
(0,0,1,1, 0,0,1,1),
(2,2,3,3, 2,2,3,3),
(0,0,1,1, 0,0,1,1),
(2,2,3,3, 2,2,3,3))
--- magma #6, count=5760
[[1, 0, 0, 1, 2, 2, 3, 3],
[0, 0, 0, 0, 3, 3, 3, 3],
[4, 5, 5, 5, 4, 5, 4, 4],
[6, 5, 5, 6, 7, 7, 4, 4],
[6, 0, 0, 6, 7, 7, 4, 4],
[1, 5, 5, 1, 2, 2, 3, 3],
[0, 0, 0, 0, 3, 3, 3, 3],
[4, 5, 5, 5, 4, 5, 4, 4]]
perm: (0, 1, 2, 3, 4, 5, 6, 7)
--- magma #7, count=2880
[[1, 0, 0, 1, 2, 2, 4, 4],
[0, 0, 0, 3, 0, 3, 3, 3],
[5, 5, 5, 4, 5, 4, 4, 4],
[6, 5, 5, 6, 7, 7, 3, 3],
[6, 5, 5, 6, 7, 7, 3, 3],
[1, 0, 0, 1, 2, 2, 4, 4],
[0, 0, 0, 3, 0, 3, 3, 3],
[5, 5, 5, 4, 5, 4, 4, 4]]
perm: (0, 1, 2, 3, 4, 5, 6, 7)
perm: (3, 6, 7, 0, 5, 4, 1, 2)
--- magma #8, count=1440
[[1, 0, 0, 1, 2, 2, 4, 4],
[0, 0, 0, 3, 0, 3, 3, 3],
[4, 5, 5, 5, 4, 5, 4, 4],
[6, 5, 5, 6, 7, 7, 3, 3],
[6, 0, 0, 6, 7, 7, 4, 4],
[1, 5, 5, 1, 2, 2, 3, 3],
[0, 0, 0, 3, 0, 3, 3, 3],
[4, 5, 5, 5, 4, 5, 4, 4]]
perm: (0, 1, 2, 3, 4, 5, 6, 7)
perm: (3, 6, 7, 0, 5, 4, 1, 2)
perm: (4, 7, 6, 5, 0, 3, 2, 1)
perm: (5, 2, 1, 4, 3, 0, 7, 6)
--- magma #9, count=1440
[[1, 2, 1, 1, 1, 2, 2, 2],
[3, 0, 0, 4, 3, 2, 2, 4],
[1, 5, 5, 6, 1, 7, 7, 6],
[1, 0, 0, 4, 1, 7, 7, 4],
[3, 3, 7, 7, 3, 7, 7, 3],
[1, 2, 1, 1, 1, 2, 2, 2],
[3, 3, 7, 7, 3, 7, 7, 3],
[3, 5, 5, 6, 3, 2, 2, 6]]
perm: (0, 1, 2, 3, 4, 5, 6, 7)
perm: (4, 3, 7, 1, 0, 6, 5, 2)
perm: (5, 2, 1, 7, 6, 0, 4, 3)
perm: (6, 7, 3, 2, 5, 4, 0, 1)