Restriction to the Maximal Elementary Abelian Subgroup

The images of the generators of the cohomology of G restricted to E are

z + y + x ,

0 ,

z + y + x ,

0 ,

0 ,

0 ,

x⁴ ,

z⁴ + x⁴
in the cohomology of E.

The kernel of the restriction to E (Minimal Prime) of the cohomology of G is generated by

z + x ,

y ,

w ,

v ,

u .

This ideal is also the nilradical of the cohomology of G.

It is nilpotent of degree 5.

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Restrictions to Maximal Subgroups

Maximal Subgroup H #1 Generated by [ G.1, G.6, G.2, G.5, G.3 ] .

The group H is abelian of type [ 4, 4, 2 ]

The cohomology ring of H is a the quotient of a polynomial ring in the variables
[ z, y, x, w, v ] , in degrees [ 1, 1, 1, 2, 2 ] , by the ideal of relations

z² , y² .

The images of the generators of the cohomology of G restricted to H are

y + x ,

z + y ,

x ,

0 ,

yv ,

yw ,

zyw + w² + v² ,

zyv + w²
in the cohomology of H.

The kernel of the restriction to H of the cohomology of G is generated by

w .

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Maximal Subgroup H #2 Generated by [ G.2 * G.3, G.1 * G.3, G.3 * G.4 * G.6, G.6, G.5 ] .

The Group H is Isomorphic to the Group of Order 32 Number12 GrpPC of order 32 = 2^5 PC-Relations: $.1^2 = $.4, $.2^2 = $.5, $.3^2 = $.5, $.2^$.1 = $.2 * $.5, $.3^$.1 = $.3 * $.5 Generated by [ G.1 * G.2 * G.3 * G.4 * G.5, G.1 * G.4, G.3 * G.4 * G.5 * G.6 ]

of type Cyclic(2) x Group(16)#10 .

The images of the generators of the cohomology of G restricted to H are

z + x ,

z ,

z + y ,

z + y + x ,

y²x + yx² + zw + yv + xv ,

y³ + zyx + yx² + zw + yw + xw + zv ,

y³x + yx³ + y²w + x²w + y²v + x²v + w² ,

y²x² + y²v + x²v + v²
in the cohomology of H.

The kernel of the restriction to H of the cohomology of G is generated by

z + y + x + w .

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Maximal Subgroup H #3 Generated by [ G.1 * G.2, G.4, G.6, G.5, G.3 ] .

The Group H is Isomorphic to the Group of Order 32 Number40 GrpPC of order 32 = 2^5 PC-Relations: $.1^2 = $.4 * $.5, $.2^2 = $.4 * $.5, $.3^2 = $.5, $.2^$.1 = $.2 * $.4, $.3^$.2 = $.3 * $.5 Generated by [ G.1 * G.2 * G.3, G.1 * G.2, G.4 ] .

The images of the generators of the cohomology of G restricted to H are

z + x ,

z + x ,

x ,

y ,

y²x + w + v ,

zyx + y²x + w ,

xw + yv + u ,

xw + yv + xv + u + t
in the cohomology of H.

The kernel of the restriction to H of the cohomology of G is generated by

z + y .

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Maximal Subgroup H #4 Generated by [ G.1 * G.4, G.6, G.2, G.5, G.3 ] .

The Group H is Isomorphic to the Group of Order 32 Number40 GrpPC of order 32 = 2^5 PC-Relations: $.1^2 = $.4 * $.5, $.2^2 = $.4 * $.5, $.3^2 = $.5, $.2^$.1 = $.2 * $.4, $.3^$.2 = $.3 * $.5 Generated by [ G.1 * G.2 * G.3 * G.4, G.2 * G.3 * G.5 * G.6, G.2 ] .

The images of the generators of the cohomology of G restricted to H are

y ,

z + y + x ,

z + y ,

y ,

zyx + y²x + w + v ,

w ,

yw + xw + yv + u ,

yw + xw + xv + u + t
in the cohomology of H.

The kernel of the restriction to H of the cohomology of G is generated by

z + w .

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Maximal Subgroup H #5 Generated by [ G.1, G.4, G.6, G.2, G.5 ] .

The Group H is Isomorphic to the Group of Order 32 Number40 GrpPC of order 32 = 2^5 PC-Relations: $.1^2 = $.4 * $.5, $.2^2 = $.4 * $.5, $.3^2 = $.5, $.2^$.1 = $.2 * $.4, $.3^$.2 = $.3 * $.5 Generated by [ G.1, G.1 * G.2 * G.4, G.2 ] .

The images of the generators of the cohomology of G restricted to H are

z + y ,

y + x ,

0 ,

y ,

zyx + w + v ,

v ,

yw + yv + xv + u + t ,

xw + yv + xv + u
in the cohomology of H.

The kernel of the restriction to H of the cohomology of G is generated by

x .

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Maximal Subgroup H #6 Generated by [ G.4, G.6, G.2, G.5, G.3 ] .

The Group H is Isomorphic to the Group of Order 32 Number40 GrpPC of order 32 = 2^5 PC-Relations: $.1^2 = $.4 * $.5, $.2^2 = $.4 * $.5, $.3^2 = $.5, $.2^$.1 = $.2 * $.4, $.3^$.2 = $.3 * $.5 Generated by [ G.2 * G.3 * G.4, G.2, G.3 ] .

The images of the generators of the cohomology of G restricted to H are

0 ,

y + x ,

z + y ,

y ,

zyx + w + v ,

v ,

yw + yv + xv + u + t ,

xw + yv + xv + u
in the cohomology of H.

The kernel of the restriction to H of the cohomology of G is generated by

z .

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Maximal Subgroup H #7 Generated by [ G.1 * G.3, G.5, G.6, G.4, G.2 ] .

The Group H is Isomorphic to the Group of Order 32 Number12 GrpPC of order 32 = 2^5 PC-Relations: $.1^2 = $.4, $.2^2 = $.5, $.3^2 = $.5, $.2^$.1 = $.2 * $.5, $.3^$.1 = $.3 * $.5 Generated by [ G.1 * G.2 * G.3 * G.4 * G.5, G.1 * G.2 * G.3 * G.5 * G.6, G.2 * G.5 * G.6 ]

of type Cyclic(2) x Group(16)#10 .

The images of the generators of the cohomology of G restricted to H are

z + x ,

z + y + x ,

z + x ,

z ,

zw + zv ,

y³ + zyx + yx² + zw ,

y²w + x²w + w² + v² ,

y³x + y²x² + yx³ + y²w + x²w + y²v + x²v + v²
in the cohomology of H.

The kernel of the restriction to H of the cohomology of G is generated by

z + x .

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Maximal Subgroup H #8 Generated by [ G.1, G.4, G.6, G.5, G.3 ] .

The Group H is Isomorphic to the Group of Order 32 Number12 GrpPC of order 32 = 2^5 PC-Relations: $.1^2 = $.4, $.2^2 = $.5, $.3^2 = $.5, $.2^$.1 = $.2 * $.5, $.3^$.1 = $.3 * $.5 Generated by [ G.1 * G.3 * G.4 * G.6, G.3 * G.4, G.4 * G.5 ]

of type Cyclic(2) x Group(16)#10 .

The images of the generators of the cohomology of G restricted to H are

x ,

0 ,

z + x ,

z + y + x ,

y³ + yx² + zw + yv + xv ,

y³ + yx² + yw + xw + zv + yv + xv ,

y²v + x²v + v² ,

y²w + x²w + w²
in the cohomology of H.

The kernel of the restriction to H of the cohomology of G is generated by

y .

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Maximal Subgroup H #9 Generated by [ G.1, G.2 * G.3, G.4, G.6, G.5 ] .

The Group H is Isomorphic to the Group of Order 32 Number40 GrpPC of order 32 = 2^5 PC-Relations: $.1^2 = $.4 * $.5, $.2^2 = $.4 * $.5, $.3^2 = $.5, $.2^$.1 = $.2 * $.4, $.3^$.2 = $.3 * $.5 Generated by [ G.1 * G.2 * G.3, G.2 * G.3, G.1 * G.2 * G.3 * G.4 * G.5 * G.6 ] .

The images of the generators of the cohomology of G restricted to H are

y + x ,

z + y + x ,

z + y + x ,

y ,

y²x + w + v ,

zyx + y²x + w ,

yw + xw + yv + u ,

yw + xw + xv + u + t
in the cohomology of H.

The kernel of the restriction to H of the cohomology of G is generated by

y + x .

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Maximal Subgroup H #10 Generated by [ G.2 * G.3, G.1 * G.3, G.4, G.6, G.5 ] .

The Group H is Isomorphic to the Group of Order 32 Number12 GrpPC of order 32 = 2^5 PC-Relations: $.1^2 = $.4, $.2^2 = $.5, $.3^2 = $.5, $.2^$.1 = $.2 * $.5, $.3^$.1 = $.3 * $.5 Generated by [ G.1 * G.3 * G.4, G.2 * G.3 * G.4 * G.5 * G.6, G.1 * G.2 * G.4 ]

of type Cyclic(2) x Group(16)#10 .

The images of the generators of the cohomology of G restricted to H are

z + y ,

y + x ,

z + x ,

z + y + x ,

y²x + yx² + zw + yv + xv ,

y³ + zyx + yx² + zw + yw + xw + zv ,

y³x + yx³ + w² ,

y²x² + y²w + x²w + y²v + x²v + v²
in the cohomology of H.

The kernel of the restriction to H of the cohomology of G is generated by

z + y + x .

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Maximal Subgroup H #11 Generated by [ G.1, G.2 * G.4, G.6, G.5, G.3 ] .

The Group H is Isomorphic to the Group of Order 32 Number12 GrpPC of order 32 = 2^5 PC-Relations: $.1^2 = $.4, $.2^2 = $.5, $.3^2 = $.5, $.2^$.1 = $.2 * $.5, $.3^$.1 = $.3 * $.5 Generated by [ G.2 * G.4 * G.5, G.2 * G.3 * G.4, G.1 * G.2 * G.3 * G.4 * G.6 ]

of type Cyclic(2) x Group(16)#10 .

The images of the generators of the cohomology of G restricted to H are

x ,

z + y + x ,

z + x ,

z + y + x ,

y³ + yx² + zw + yv + xv ,

y³ + yx² + yw + xw + zv + yv + xv ,

y³x + yx³ + v² ,

w²
in the cohomology of H.

The kernel of the restriction to H of the cohomology of G is generated by

y + w .

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Maximal Subgroup H #12 Generated by [ G.1 * G.4, G.2 * G.4, G.6, G.5, G.3 ] .

The Group H is Isomorphic to the Group of Order 32 Number40 GrpPC of order 32 = 2^5 PC-Relations: $.1^2 = $.4 * $.5, $.2^2 = $.4 * $.5, $.3^2 = $.5, $.2^$.1 = $.2 * $.4, $.3^$.2 = $.3 * $.5 Generated by [ G.1 * G.2 * G.3, G.1 * G.4, G.3 ] .

The images of the generators of the cohomology of G restricted to H are

y + x ,

x ,

z + x ,

y ,

y²x + w + v ,

zyx + v ,

yw + xv + u + t ,

yw + xw + xv + u
in the cohomology of H.

The kernel of the restriction to H of the cohomology of G is generated by

z + y + w .

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Maximal Subgroup H #13 Generated by [ G.1, G.3 * G.4 * G.6, G.6, G.2, G.5 ] .

The Group H is Isomorphic to the Group of Order 32 Number40 GrpPC of order 32 = 2^5 PC-Relations: $.1^2 = $.4 * $.5, $.2^2 = $.4 * $.5, $.3^2 = $.5, $.2^$.1 = $.2 * $.4, $.3^$.2 = $.3 * $.5 Generated by [ G.1, G.2 * G.3 * G.4 * G.5, G.2 ] .

The images of the generators of the cohomology of G restricted to H are

z ,

y + x ,

y ,

y ,

zyx + w + v ,

v ,

yw + yv + xv + u + t ,

xw + yv + xv + u
in the cohomology of H.

The kernel of the restriction to H of the cohomology of G is generated by

x + w .

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Maximal Subgroup H #14 Generated by [ G.1 * G.3, G.3 * G.4 * G.6, G.5, G.6, G.2 ] .

The Group H is Isomorphic to the Group of Order 32 Number12 GrpPC of order 32 = 2^5 PC-Relations: $.1^2 = $.4, $.2^2 = $.5, $.3^2 = $.5, $.2^$.1 = $.2 * $.5, $.3^$.1 = $.3 * $.5 Generated by [ G.1 * G.2 * G.3 * G.6, G.2 * G.6, G.1 * G.2 * G.4 ]

of type Cyclic(2) x Group(16)#10 .

The images of the generators of the cohomology of G restricted to H are

z + x ,

z + y + x ,

x ,

z ,

y³ + zyx + yx² + zw + zv ,

zv ,

y³x + yx³ + y²v + x²v + v² ,

y²x² + y²w + x²w + y²v + x²v + w² + v²
in the cohomology of H.

The kernel of the restriction to H of the cohomology of G is generated by

z + x + w .

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Maximal Subgroup H #15 Generated by [ G.1, G.2 * G.3, G.3 * G.4 * G.6, G.6, G.5 ] .

The Group H is Isomorphic to the Group of Order 32 Number40 GrpPC of order 32 = 2^5 PC-Relations: $.1^2 = $.4 * $.5, $.2^2 = $.4 * $.5, $.3^2 = $.5, $.2^$.1 = $.2 * $.4, $.3^$.2 = $.3 * $.5 Generated by [ G.1 * G.3 * G.4, G.1 * G.2 * G.3, G.2 * G.3 ] .

The images of the generators of the cohomology of G restricted to H are

y + x ,

z + x ,

z + y + x ,

y ,

y²x + w + v ,

zyx + y²x + w ,

xw + yv + u ,

xw + yv + xv + u + t
in the cohomology of H.

The kernel of the restriction to H of the cohomology of G is generated by

y + x + w .

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The essential cohomology of G is generated as an ideal by

yxw² ,

zyxw + yx²w ,

zyx²u + yx³u ,

yx²wu ,

x²w²u .

It is nilpotent of degree 2.

The annihilator of the Essential Cohomology has dimension 3 .

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Inflations from Maximal Quotient Groups

Maximal Quotient Group Q #1.

The kernel of the quotient is generated by G.5 * G.6 .

The Group Q is Isomorphic to the Group of Order 32 Number10 GrpPC of order 32 = 2^5 PC-Relations: $.1^2 = $.5, $.2^2 = $.5, $.3^$.2 = $.3 * $.5, $.4^$.2 = $.4 * $.5

of type Cyclic(2) x AlmostExtraSpecial(16) .

The generators of G have images [ pcy.1 * pcy.2 * pcy.4 * pcy.5, pcy.3 * pcy.5, pcy.1 * pcy.3 * pcy.5, pcy.4 ] in the quotient group.

The images of the generators of the cohomology of Q inflated to G are

y + w ,

w ,

y + x ,

z + w ,

z²x² + y²x² + yu + wu + t
in the cohomology of G.

The kernel of the inflation to G of the cohomology of Q is generated by

zy + x² + w² ,

zx² + yx² + zw² + yw² .

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Maximal Quotient Group Q #2.

The kernel of the quotient is generated by G.6 .

The Group Q is Isomorphic to the Group of Order 32 Number10 GrpPC of order 32 = 2^5 PC-Relations: $.1^2 = $.5, $.2^2 = $.5, $.3^$.2 = $.3 * $.5, $.4^$.2 = $.4 * $.5

of type Cyclic(2) x AlmostExtraSpecial(16) .

The generators of G have images [ pcy.1 * pcy.2, pcy.1 * pcy.3 * pcy.4, pcy.1 * pcy.4 * pcy.5, pcy.1 ] in the quotient group.

The images of the generators of the cohomology of Q inflated to G are

z + y + x + w ,

w ,

x ,

y + x ,

yv + s
in the cohomology of G.

The kernel of the inflation to G of the cohomology of Q is generated by

zy + x² + w² ,

zx² + yx² + zw² + yw² .

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Maximal Quotient Group Q #3.

The kernel of the quotient is generated by G.5 .

The Group Q is Isomorphic to the Group of Order 32 Number9 GrpPC of order 32 = 2^5 PC-Relations: $.2^2 = $.5, $.3^2 = $.5, $.4^2 = $.5, $.4^$.2 = $.4 * $.5, $.4^$.3 = $.4 * $.5

of type Abelian(2,2) x Quaternion(8) .

The generators of G have images [ pcy.4, pcy.3, pcy.2 * pcy.3 * pcy.5, pcy.1 * pcy.2 ] in the quotient group.

The images of the generators of the cohomology of Q inflated to G are

z ,

z + y ,

y + x ,

w ,

y²x² + yv + zu + yu + xu + t + s
in the cohomology of G.

The kernel of the inflation to G of the cohomology of Q is generated by

z² + x² + zw + yw ,

yw² + xw² .

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Maximal Quotient Group Q #4.

The kernel of the quotient is generated by G.1 * G.3 * G.5 .

The Group Q is Isomorphic to the Group of Order 32 Number40 GrpPC of order 32 = 2^5 PC-Relations: $.1^2 = $.4 * $.5, $.2^2 = $.4 * $.5, $.3^2 = $.5, $.2^$.1 = $.2 * $.4, $.3^$.2 = $.3 * $.5 .

The generators of G have images [ pcy.1 * pcy.2 * pcy.3 * pcy.4 * pcy.5, pcy.1, pcy.3, pcy.1 * pcy.4 ] in the quotient group.

The images of the generators of the cohomology of Q inflated to G are

z + x + w ,

w ,

y + w ,

y³ + z²x + zx² + yw² + v + u ,

z²x + x³ + x²w + zw² + u ,

y³x + y²x² + zyxw + z²w² + yv + zu + xu + s ,

z²x² + y²x² + z²w² + yv + yu + t + s
in the cohomology of G.

The kernel of the inflation is zero.

Maximal Quotient Group Q #5.

The kernel of the quotient is generated by G.1 * G.3 * G.6 .

The Group Q is Isomorphic to the Group of Order 32 Number40 GrpPC of order 32 = 2^5 PC-Relations: $.1^2 = $.4 * $.5, $.2^2 = $.4 * $.5, $.3^2 = $.5, $.2^$.1 = $.2 * $.4, $.3^$.2 = $.3 * $.5 .

The generators of G have images [ pcy.1 * pcy.2 * pcy.3 * pcy.4 * pcy.5, pcy.1, pcy.3, pcy.1 * pcy.5 ] in the quotient group.

The images of the generators of the cohomology of Q inflated to G are

z + x + w ,

w ,

y + w ,

y³ + zx² + x³ + x²w + yw² + v + u ,

z²x + zx² + zw² + u ,

y³x + z²x² + y²x² + zyxw + z²w² + yv + zu + xu + s ,

y³x + zyxw + yv + yu + t + s
in the cohomology of G.

The kernel of the inflation is zero.

Maximal Quotient Group Q #6.

The kernel of the quotient is generated by G.1 * G.3 * G.5 * G.6 .

The Group Q is Isomorphic to the Group of Order 32 Number40 GrpPC of order 32 = 2^5 PC-Relations: $.1^2 = $.4 * $.5, $.2^2 = $.4 * $.5, $.3^2 = $.5, $.2^$.1 = $.2 * $.4, $.3^$.2 = $.3 * $.5 .

The generators of G have images [ pcy.1 * pcy.2 * pcy.3 * pcy.4 * pcy.5, pcy.1, pcy.3, pcy.1 ] in the quotient group.

The images of the generators of the cohomology of Q inflated to G are

z + x + w ,

w ,

y + w ,

y³ + z²x + x³ + yw² + v + u ,

u ,

yv + zu + xu + s ,

y²x² + yv + yu + t + s
in the cohomology of G.

The kernel of the inflation is zero.

Maximal Quotient Group Q #7.

The kernel of the quotient is generated by G.1 * G.3 .

The Group Q is Isomorphic to the Group of Order 32 Number40 GrpPC of order 32 = 2^5 PC-Relations: $.1^2 = $.4 * $.5, $.2^2 = $.4 * $.5, $.3^2 = $.5, $.2^$.1 = $.2 * $.4, $.3^$.2 = $.3 * $.5 .

The generators of G have images [ pcy.1 * pcy.2 * pcy.3 * pcy.4 * pcy.5, pcy.1, pcy.3, pcy.1 * pcy.4 * pcy.5 ] in the quotient group.

The images of the generators of the cohomology of Q inflated to G are

z + x + w ,

w ,

y + w ,

y³ + x²w + yw² + v + u ,

zx² + x³ + x²w + u ,

z²x² + yv + zu + xu + s ,

y³x + z²x² + zyxw + z²w² + yv + yu + t + s
in the cohomology of G.

The kernel of the inflation is zero.

Action of Automorphisms

The groups of outer automorphisms of G has order 1024, and is generated by 10 elements.

Automorphism #1

The order of the class of the automorphism in the outer automorphism group is 2. The images of the generators of G are

G.1
G.2 * G.6
G.3
G.4 * G.6
G.5
G.6 .

The images of the generators of the cohomology of G under the map induced by the automorphism are

z ,

y ,

x ,

w ,

yw² + v ,

y³ + yw² + u ,

t ,

s .

Automorphism #2

The order of the class of the automorphism in the outer automorphism group is 2. The images of the generators of G are

G.1 * G.5 * G.6
G.2 * G.5 * G.6
G.3 * G.5 * G.6
G.4
G.5
G.6 .

The images of the generators of the cohomology of G under the map induced by the automorphism are

z ,

y ,

x ,

w ,

yw² + v ,

y³ + yw² + u ,

t ,

s .

Automorphism #3

The order of the class of the automorphism in the outer automorphism group is 2. The images of the generators of G are

G.1 * G.6
G.2 * G.6
G.3 * G.6
G.4
G.5
G.6 .

The images of the generators of the cohomology of G under the map induced by the automorphism are

z ,

y ,

x ,

w ,

yw² + v ,

y³ + yw² + u ,

t ,

s .

Automorphism #4

The order of the class of the automorphism in the outer automorphism group is 2. The images of the generators of G are

G.1 * G.5 * G.6
G.2
G.3
G.4 * G.5 * G.6
G.5
G.6 .

The images of the generators of the cohomology of G under the map induced by the automorphism are

z ,

y ,

x ,

w ,

z²x + zx² + v ,

zx² + x³ + x²w + u ,

z²yx + y³x + zyx² + y²x² + zy²w + t ,

z²yx + z²x² + zyx² + z²w² + s .

Automorphism #5

The order of the class of the automorphism in the outer automorphism group is 2. The images of the generators of G are

G.1 * G.6
G.2
G.3
G.4 * G.6
G.5
G.6 .

The images of the generators of the cohomology of G under the map induced by the automorphism are

z ,

y ,

x ,

w ,

z²x + zx² + x²w + zw² + v ,

z²x + x³ + x²w + zw² + u ,

z²x² + zyxw + z²w² + t ,

z²yx + y³x + zyx² + zy²w + zyxw + s .

Automorphism #6

The order of the class of the automorphism in the outer automorphism group is 2. The images of the generators of G are

G.1
G.2
G.3
G.1 * G.3 * G.4 * G.5 * G.6
G.5
G.6 .

The images of the generators of the cohomology of G under the map induced by the automorphism are

z + w ,

y ,

x + w ,

w ,

v ,

u ,

t ,

s .

Automorphism #7

The order of the class of the automorphism in the outer automorphism group is 2. The images of the generators of G are

G.1
G.1 * G.2 * G.3 * G.5 * G.6
G.3
G.1 * G.3 * G.4 * G.5 * G.6
G.5
G.6 .

The images of the generators of the cohomology of G under the map induced by the automorphism are

z + y + w ,

y ,

y + x + w ,

w ,

y³ + yw² + v ,

u ,

t ,

s .

Automorphism #8

The order of the class of the automorphism in the outer automorphism group is 2. The images of the generators of G are

G.3
G.1 * G.2 * G.3 * G.5 * G.6
G.1
G.4
G.5
G.6 .

The images of the generators of the cohomology of G under the map induced by the automorphism are

y + x ,

y ,

z + y ,

w ,

y³ + yw² + v ,

u ,

t ,

s .

Automorphism #9

The order of the class of the automorphism in the outer automorphism group is 2. The images of the generators of G are

G.1
G.2
G.3
G.2 * G.4 * G.5
G.5
G.6 .

The images of the generators of the cohomology of G under the map induced by the automorphism are

z ,

y + w ,

x ,

w ,

v ,

u ,

z²w² + wu + t ,

zu + xu + wu + s .

Automorphism #10

The order of the class of the automorphism in the outer automorphism group is 4. The images of the generators of G are

G.1 * G.2 * G.5 * G.6
G.2
G.2 * G.3 * G.5 * G.6
G.3 * G.4 * G.5 * G.6
G.5
G.5 * G.6 .

The images of the generators of the cohomology of G under the map induced by the automorphism are

z ,

z + y + x ,

x + w ,

w ,

zw² + yw² + v ,

y³ + z²x + x³ + yw² + v + u ,

zy²w + zyxw + yu + wu + s ,

y²x² + zy²w + yv + yu + t .

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CHECKS

paramflag = true
qregflagflag = true
cmflag = true
essflag = true
centflag = true

THE COMPUTATION IS COMPLETE