This passport consists of one orbit of size 2, defined over the field \(\mathbb{Q}(\sqrt{7})\), and one of size 4, defined over a \(D_4\) number field.
(5,6),(1,3)(2,5,7,6),(1,4)(2,3,6)(5,7).png "(1,2,3,4)(5,6)_(1,3)(2,5,7,6)_(1,4)(2,3,6)(5,7)")
(5,6),(1,5,3,7)(4,6),(1,6)(2,7,3)(4,5).png "(1,2,3,4)(5,6)_(1,5,3,7)(4,6)_(1,6)(2,7,3)(4,5)")
(5,6),(1,6)(3,5,4,7),(1,5)(2,6,3)(4,7).png "(1,2,3,4)(5,6)_(1,6)(3,5,4,7)_(1,5)(2,6,3)(4,7)")
(5,6),(1,6)(3,7,4,5),(1,5)(2,3,6)(4,7).png "(1,4,3,2)(5,6)_(1,6)(3,7,4,5)_(1,5)(2,3,6)(4,7)")
(5,6),(1,3,6,7)(2,5),(1,4)(2,7,6)(3,5).png "(1,2,3,4)(5,6)_(1,3,6,7)(2,5)_(1,4)(2,7,6)(3,5)")
(5,6),(1,7,6,3)(2,5),(1,4)(2,6,7)(3,5).png "(1,4,3,2)(5,6)_(1,7,6,3)(2,5)_(1,4)(2,6,7)(3,5)")