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ZG2.m
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ZG2 :=
SequenceToSubgroups([ PowerStructure(Rec) |
rec<recformat<order, length, subgroup, presentation> |
order := 1,
length := 1,
subgroup := MatrixGroup<4, GF(2) | >>,
rec<recformat<order, length, subgroup, presentation> |
order := 2,
length := 15,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1 ])
/* order = 2 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 2,
length := 15,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1 ])
/* order = 2 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 2,
length := 45,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0 ])
/* order = 2 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 3,
length := 20,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1 ])
/* order = 3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 3,
length := 20,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0 ])
/* order = 3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 5,
length := 36,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0 ])
/* order = 5 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 4,
length := 15,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0 ]),
Matrix(GF(2), 4, 4, \[ 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0 ])
/* order = 4 = 2^2 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 4,
length := 15,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1 ]),
Matrix(GF(2), 4, 4, \[ 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0 ])
/* order = 4 = 2^2 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 4,
length := 45,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1 ])
/* order = 4 = 2^2 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 4,
length := 45,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0 ])
/* order = 4 = 2^2 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 4,
length := 45,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0 ]),
Matrix(GF(2), 4, 4, \[ 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0 ])
/* order = 4 = 2^2 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 4,
length := 45,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1 ])
/* order = 4 = 2^2 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 4,
length := 45,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1 ])
/* order = 4 = 2^2 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 6,
length := 20,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1 ])
/* order = 6 = 2 * 3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 6,
length := 20,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0 ])
/* order = 6 = 2 * 3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 6,
length := 60,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0 ]),
Matrix(GF(2), 4, 4, \[ 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0 ])
/* order = 6 = 2 * 3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 6,
length := 60,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1 ])
/* order = 6 = 2 * 3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 6,
length := 60,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1 ])
/* order = 6 = 2 * 3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 6,
length := 60,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0 ]),
Matrix(GF(2), 4, 4, \[ 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0 ])
/* order = 6 = 2 * 3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 9,
length := 10,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1 ])
/* order = 9 = 3^2 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 10,
length := 36,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0 ]),
Matrix(GF(2), 4, 4, \[ 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0 ])
/* order = 10 = 2 * 5 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 8,
length := 15,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1 ])
/* order = 8 = 2^3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 8,
length := 15,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1 ])
/* order = 8 = 2^3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 8,
length := 45,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1 ]),
Matrix(GF(2), 4, 4, \[ 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1 ])
/* order = 8 = 2^3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 8,
length := 45,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1 ])
/* order = 8 = 2^3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 8,
length := 45,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1 ])
/* order = 8 = 2^3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 8,
length := 45,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0 ]),
Matrix(GF(2), 4, 4, \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0 ])
/* order = 8 = 2^3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 8,
length := 45,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1 ])
/* order = 8 = 2^3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 12,
length := 15,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0 ]),
Matrix(GF(2), 4, 4, \[ 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0 ]),
Matrix(GF(2), 4, 4, \[ 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0 ])
/* order = 12 = 2^2 * 3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 12,
length := 15,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1 ]),
Matrix(GF(2), 4, 4, \[ 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0 ])
/* order = 12 = 2^2 * 3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 12,
length := 60,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1 ])
/* order = 12 = 2^2 * 3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 12,
length := 60,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1 ])
/* order = 12 = 2^2 * 3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 18,
length := 10,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1 ]),
Matrix(GF(2), 4, 4, \[ 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1 ])
/* order = 18 = 2 * 3^2 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 18,
length := 20,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0 ]),
Matrix(GF(2), 4, 4, \[ 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1 ])
/* order = 18 = 2 * 3^2 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 18,
length := 20,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0 ]),
Matrix(GF(2), 4, 4, \[ 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1 ])
/* order = 18 = 2 * 3^2 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 20,
length := 36,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0 ])
/* order = 20 = 2^2 * 5 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 16,
length := 45,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1 ])
/* order = 16 = 2^4 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 24,
length := 15,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0 ]),
Matrix(GF(2), 4, 4, \[ 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1 ])
/* order = 24 = 2^3 * 3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 24,
length := 15,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1 ]),
Matrix(GF(2), 4, 4, \[ 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0 ])
/* order = 24 = 2^3 * 3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 24,
length := 15,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1 ])
/* order = 24 = 2^3 * 3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 24,
length := 15,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0 ]),
Matrix(GF(2), 4, 4, \[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0 ]),
Matrix(GF(2), 4, 4, \[ 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1 ])
/* order = 24 = 2^3 * 3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 24,
length := 15,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0 ]),
Matrix(GF(2), 4, 4, \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0 ])
/* order = 24 = 2^3 * 3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 24,
length := 15,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1 ])
/* order = 24 = 2^3 * 3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 36,
length := 10,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1 ]),
Matrix(GF(2), 4, 4, \[ 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1 ])
/* order = 36 = 2^2 * 3^2 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 36,
length := 10,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0 ]),
Matrix(GF(2), 4, 4, \[ 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0 ]),
Matrix(GF(2), 4, 4, \[ 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1 ])
/* order = 36 = 2^2 * 3^2 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 36,
length := 10,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0 ]),
Matrix(GF(2), 4, 4, \[ 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1 ])
/* order = 36 = 2^2 * 3^2 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 60,
length := 6,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1 ])
/* order = 60 = 2^2 * 3 * 5 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 60,
length := 6,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0 ])
/* order = 60 = 2^2 * 3 * 5 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 48,
length := 15,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1 ])
/* order = 48 = 2^4 * 3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 48,
length := 15,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1 ]),
Matrix(GF(2), 4, 4, \[ 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1 ]),
Matrix(GF(2), 4, 4, \[ 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0 ])
/* order = 48 = 2^4 * 3 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 72,
length := 10,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0 ]),
Matrix(GF(2), 4, 4, \[ 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0 ]),
Matrix(GF(2), 4, 4, \[ 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1 ])
/* order = 72 = 2^3 * 3^2 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 120,
length := 6,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0 ]),
Matrix(GF(2), 4, 4, \[ 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1 ])
/* order = 120 = 2^3 * 3 * 5 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 120,
length := 6,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1 ]),
Matrix(GF(2), 4, 4, \[ 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1 ])
/* order = 120 = 2^3 * 3 * 5 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 360,
length := 1,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1 ]),
Matrix(GF(2), 4, 4, \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0 ])
/* order = 360 = 2^3 * 3^2 * 5 */ >>,
rec<recformat<order, length, subgroup, presentation> |
order := 720,
length := 1,
subgroup := MatrixGroup<4, GF(2) |
Matrix(GF(2), 4, 4, \[ 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0 ]),
Matrix(GF(2), 4, 4, \[ 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1 ])
/* order = 720 = 2^4 * 3^2 * 5 */ >>
])
;