Restriction to the Maximal Elementary Abelian Subgroup

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

z + y ,

z + y + x + w ,

z + y + w ,

z + y + x ,

z + y + x + w ,

z⁴ + z²x² + y²x² + z²w² + y²w² + w⁴
in the cohomology of E.

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

z + x + w + v ,

y + v .

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

It is nilpotent of degree 4.

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Restrictions to Maximal Subgroups

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

The Group H 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 Generated by [ G.5, G.3, G.1, G.1 * G.4 * G.6 ]

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

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

z + y ,

0 ,

x ,

z ,

w ,

v
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 #2 Generated by [ G.1 * G.2 * G.6, G.6, G.4, G.3, G.1 * G.5 * G.6 ] .

The Group H 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 Generated by [ G.1 * G.4 * G.5 * G.6, G.2 * G.3 * G.5 * G.6, G.4, G.1 * G.3 * G.5 * G.6 ]

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

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

y + x ,

z ,

z + y ,

x + w ,

z + y + x ,

z²y² + zy³ + z²x² + zyx² + zy²w + zyxw + zxw² + v
in the cohomology of H.

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

z + y + v .

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

The Group H 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 Generated by [ G.1 * G.3 * G.5, G.1 * G.2 * G.6, G.1 * G.5 * G.6, G.1 * G.4 ]

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

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

z + y + x + w ,

y ,

x ,

z ,

x + w ,

z⁴ + z²y² + zy³ + zyx² + y²x² + zy²w + zyxw + yxw² + v
in the cohomology of H.

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

z + y + w + v .

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

The Group H 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 Generated by [ G.1 * G.2, G.2 * G.3 * G.6, G.1 * G.2 * G.5 * G.6, G.3 ]

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

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

z + y ,

z + y + x ,

x + w ,

0 ,

z ,

z²y² + z²yw + y³w + z²xw + y²xw + zxw² + yxw² + v
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 #5 Generated by [ G.2, G.6, G.4, G.3, G.1 ] .

The Group H 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 Generated by [ G.3 * G.4 * G.6, G.2, G.4, G.1 ]

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

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

x ,

w ,

z ,

z + y ,

0 ,

yxw² + v
in the cohomology of H.

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

v .

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

The Group H 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 Generated by [ G.2 * G.5 * G.6, G.2 * G.4 * G.6, G.1 * G.3 * G.6, G.3 ]

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

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

z ,

x + w ,

z + y ,

w ,

x ,

z²y² + z²yw + zy²w + z²xw + zyxw + zxw² + v
in the cohomology of H.

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

y + w + v .

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

The group H is abelian of type [ 4, 2, 2, 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, 1, 2 ] , by the ideal of relations

z² .

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

z + y + x + w ,

w ,

x ,

y ,

z + w ,

y⁴ + x⁴ + y²w² + x²w² + v²
in the cohomology of H.

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

z + x + w + v .

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Maximal Subgroup H #8 Generated by [ G.5, G.1 * G.2 * G.6, G.6, G.3, G.1 * G.4 ] .

The Group H 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 Generated by [ G.5, G.3 * G.5 * G.6, G.1 * G.2 * G.3 * G.6, G.1 * G.4 ]

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

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

z + y ,

y ,

y + x ,

z ,

x + w ,

z⁴ + z²y² + zy³ + zyx² + y²x² + v
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 #9 Generated by [ G.5, G.3 * G.4, G.2, G.6, G.1 ] .

The Group H 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 Generated by [ G.2 * G.5 * G.6, G.5, G.3 * G.4, G.1 ]

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

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

y ,

x ,

z ,

z ,

x + w ,

z⁴ + y⁴ + v
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 #10 Generated by [ G.5, G.2 * G.3 * G.6, G.6, G.4, G.1 ] .

The Group H 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 Generated by [ G.1 * G.2 * G.3 * G.4 * G.6, G.5, G.2 * G.3 * G.5, G.1 * G.2 * G.3 * G.6 ]

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

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

x + w ,

z + x + w ,

z + x + w ,

x ,

z + y ,

z⁴ + z²y² + y⁴ + y²x² + z²yw + y³w + z²xw + y²xw + zxw² + v
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 #11 Generated by [ G.2 * G.5 * G.6, G.2 * G.3 * G.6, G.6, G.4, G.1 ] .

The Group H 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 Generated by [ G.2 * G.3 * G.6, G.4, G.2 * G.4 * G.5 * G.6, G.1 ]

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

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

x ,

z + w ,

w ,

z + y ,

z ,

zy³ + z²x² + zyx² + yxw² + v
in the cohomology of H.

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

y + x + v .

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

The Group H 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 Generated by [ G.4 * G.5, G.1 * G.3 * G.6, G.2 * G.3, G.3 * G.4 * G.5 * G.6 ]

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

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

z ,

y ,

z + y + x ,

x + w ,

x + w ,

z²y² + zy³ + zyx² + zy²w + zyxw + v
in the cohomology of H.

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

w + v .

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

The Group H 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 Generated by [ G.3 * G.5, G.2 * G.4 * G.6, G.2 * G.4 * G.5, G.1 * G.3 * G.5 * G.6 ]

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

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

x ,

z + y ,

x + w ,

z + y ,

z + x + w ,

z⁴ + y⁴ + z²x² + y²x² + zxw² + yxw² + v
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 #14 Generated by [ G.5, G.1 * G.3, G.2, G.6, G.4 ] .

The Group H 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 Generated by [ G.2 * G.4, G.5, G.2, G.1 * G.3 ]

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

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

z ,

x + w ,

z ,

x ,

y ,

z⁴ + z²y² + z²yw + z²xw + zxw² + v
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 #15 Generated by [ G.5, G.1 * G.3, G.1 * G.2 * G.6, G.6, G.4 ] .

The Group H 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 Generated by [ G.1 * G.3 * G.5, G.5, G.2 * G.3 * G.5, G.4 ]

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

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

y ,

z ,

z + y ,

w ,

z + y + x ,

z⁴ + z²y² + zy³ + y⁴ + zyx² + zy²w + zyxw + v
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 #16 Generated by [ G.5, G.1 * G.3, G.1 * G.2 * G.6, G.6, G.1 * G.4 ] .

The group H is abelian of type [ 4, 2, 2, 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, 1, 2 ] , by the ideal of relations

z² .

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

y + x + w ,

w ,

x ,

y ,

z + w ,

y⁴ + x⁴ + y²w² + x²w² + w⁴ + 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 #17 Generated by [ G.1 * G.3, G.1 * G.2 * G.6, G.6, G.4, G.1 * G.5 * G.6 ] .

The Group H 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 Generated by [ G.1 * G.2 * G.4 * G.6, G.1 * G.3, G.1 * G.2 * G.6, G.1 * G.5 * G.6 ]

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

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

z + y + x + w ,

x + w ,

z ,

x ,

y ,

z⁴ + z²y² + y⁴ + y²x² + z²yw + zy²w + z²xw + zyxw + zxw² + yxw² + v
in the cohomology of H.

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

z + y + x + v .

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Maximal Subgroup H #18 Generated by [ G.2 * G.5 * G.6, G.6, G.4, G.3, G.1 ] .

The group H is abelian of type [ 4, 2, 2, 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, 1, 2 ] , by the ideal of relations

z² .

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

w ,

y ,

x ,

z + y + x + w ,

y ,

y²w² + v²
in the cohomology of H.

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

y + v .

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Maximal Subgroup H #19 Generated by [ G.1 * G.3, G.1 * G.2 * G.6, G.6, G.1 * G.4, G.1 * G.5 * G.6 ] .

The Group H 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 Generated by [ G.1 * G.2 * G.3 * G.5 * G.6, G.1 * G.3 * G.4 * G.5, G.1 * G.3, G.1 * G.5 * G.6 ]

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

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

z + y + x + w ,

w ,

z + x + w ,

x ,

y + x + w ,

z⁴ + z²y² + zy³ + z²x² + zyx² + z²yw + zy²w + z²xw + zyxw + zxw² + v
in the cohomology of H.

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

z + y + x + w + v .

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Maximal Subgroup H #20 Generated by [ G.5, G.1 * G.3, G.2, G.6, G.1 * G.4 ] .

The Group H 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 Generated by [ G.1 * G.2 * G.3 * G.5 * G.6, G.5, G.1 * G.3, G.3 * G.4 * G.5 * G.6 ]

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

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

z + w ,

w ,

z + x + w ,

x ,

y + x + w ,

z⁴ + z²y² + z²x² + z²yw + z²xw + v
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 #21 Generated by [ G.3 * G.5 * G.6, G.2, G.6, G.4, G.1 ] .

The Group H 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 Generated by [ G.1 * G.2, G.3 * G.5 * G.6, G.2 * G.3 * G.5, G.1 * G.2 * G.4 ]

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

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

x + w ,

z + x + w ,

z + y ,

x ,

z + y ,

z⁴ + z²y² + y⁴ + y²x² + z²yw + zy²w + z²xw + zyxw + zxw² + v
in the cohomology of H.

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

x + v .

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Maximal Subgroup H #22 Generated by [ G.2 * G.5 * G.6, G.2 * G.4 * G.6, G.2 * G.3 * G.6, G.6, G.1 ] .

The Group H 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 Generated by [ G.3 * G.5, G.2 * G.4 * G.6, G.1 * G.2 * G.5, G.4 * G.5 ]

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

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

z ,

z + w ,

y ,

x + w ,

z + y + x ,

z⁴ + zy³ + zyx² + z²yw + zy²w + z²xw + zyxw + zxw² + v
in the cohomology of H.

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

y + x + w + v .

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Maximal Subgroup H #23 Generated by [ G.1 * G.3, G.2, G.6, G.4, G.1 * G.5 * G.6 ] .

The Group H 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 Generated by [ G.3 * G.5, G.2 * G.3 * G.5 * G.6, G.4, G.1 * G.5 * G.6 ]

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

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

x ,

z ,

z + y ,

w ,

z + y + x ,

zy³ + y⁴ + z²x² + zyx² + zxw² + v
in the cohomology of H.

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

z + x + v .

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Maximal Subgroup H #24 Generated by [ G.5, G.2, G.6, G.4, G.3 ] .

The Group H 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 Generated by [ G.3 * G.5, G.4 * G.5, G.2 * G.3 * G.5 * G.6, G.4 ]

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

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

0 ,

z ,

z + y ,

x + w ,

z + y + x ,

v
in the cohomology of H.

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

z .

---

Maximal Subgroup H #25 Generated by [ G.5, G.2, G.6, G.3, G.1 * G.4 ] .

The Group H 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 Generated by [ G.5, G.3 * G.5 * G.6, G.2, G.1 * G.4 ]

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

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

z ,

y ,

x ,

z ,

x + w ,

z⁴ + z²y² + zy³ + y⁴ + zyx² + v
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 #26 Generated by [ G.2 * G.4 * G.6, G.5, G.2 * G.3 * G.6, G.6, G.1 ] .

The Group H 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 Generated by [ G.2 * G.4 * G.6, G.5, G.2 * G.3 * G.5, G.1 ]

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

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

w ,

z + x ,

z ,

x ,

z + y ,

z⁴ + z²y² + z²x² + y²x² + z²yw + y³w + z²xw + y²xw + v
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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Maximal Subgroup H #27 Generated by [ G.2, G.6, G.4, G.3, G.1 * G.5 * G.6 ] .

The Group H 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 Generated by [ G.1 * G.4 * G.5 * G.6, G.1 * G.2 * G.5 * G.6, G.4, G.1 * G.3 * G.5 * G.6 ]

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

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

z + y + x ,

z ,

y ,

x + w ,

z + y + x ,

zy³ + zyx² + z²yw + zy²w + z²xw + zyxw + zxw² + v
in the cohomology of H.

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

z + v .

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Maximal Subgroup H #28 Generated by [ G.5, G.2, G.6, G.4, G.1 ] .

The Group H 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 Generated by [ G.2 * G.5 * G.6, G.5, G.1, G.1 * G.4 * G.6 ]

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

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

z + y ,

x ,

0 ,

z ,

x + w ,

zy³ + y⁴ + z²x² + zyx² + v
in the cohomology of H.

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

x .

---

Maximal Subgroup H #29 Generated by [ G.2, G.6, G.3, G.1 * G.4, G.1 * G.5 * G.6 ] .

The Group H 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 Generated by [ G.1 * G.3 * G.5, G.2 * G.3, G.1 * G.5 * G.6, G.1 * G.4 ]

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

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

z + x + w ,

y ,

y + x ,

z ,

x + w ,

z⁴ + z²y² + zy³ + zyx² + zy²w + y³w + zyxw + y²xw + yxw² + v
in the cohomology of H.

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

z + w + v .

---

Maximal Subgroup H #30 Generated by [ G.3 * G.5 * G.6, G.3 * G.4, G.2, G.6, G.1 ] .

The Group H 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 Generated by [ G.1 * G.2, G.2 * G.3 * G.4, G.3 * G.5 * G.6, G.2 * G.3 * G.5 ]

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

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

w ,

z + x + w ,

z + y + x ,

x ,

z + y ,

z⁴ + z²y² + zy³ + z²x² + zyx² + z²yw + zy²w + z²xw + zyxw + zxw² + yxw² + v
in the cohomology of H.

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

x + w + v .

---

Maximal Subgroup H #31 Generated by [ G.5, G.1 * G.2 * G.6, G.6, G.4, G.3 ] .

The Group H 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 Generated by [ G.3 * G.5, G.1 * G.2 * G.5, G.4 * G.5, G.4 ]

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

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

z ,

z ,

y ,

x + w ,

z + y + x ,

z⁴ + z²yw + z²xw + v
in the cohomology of H.

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

z + y .

---

The essential cohomology of G is generated as an ideal by

zy²x⁴w²v + y²x⁵w²v + y²x⁴w³v + zy²x²w⁴v + y²x³w⁴v + y²x²w⁵v + zy²x⁴wv² + y²x⁵wv² + zy²xw⁴v² + y²xw⁵v² + y²x⁴wv³ + zx⁴w²v³ + x⁵w²v³ + x⁴w³v³ + y²xw⁴v³ + zx²w⁴v³ + x³w⁴v³ + x²w⁵v³ + zy²x²wv⁴ + y²x³wv⁴ + zx⁴wv⁴ + x⁵wv⁴ + zy²xw²v⁴ + y²xw³v⁴ + zxw⁴v⁴ + xw⁵v⁴ + y²x²wv⁵ + x⁴wv⁵ + y²xw²v⁵ + xw⁴v⁵ + zx²wv⁶ + x³wv⁶ + zxw²v⁶ + xw³v⁶ + x²wv⁷ + xw²v⁷ ,

y²x⁸w⁴v² + y²x⁴w⁸v² + y²x⁸w²v⁴ + x⁸w⁴v⁴ + y²x²w⁸v⁴ + x⁴w⁸v⁴ + x⁸w²v⁶ + x²w⁸v⁶ + y²x⁴w²v⁸ + y²x²w⁴v⁸ + x⁴w²v¹⁰ + x²w⁴v¹⁰ ,

zyx⁸w⁴v² + yx⁹w⁴v² + yx⁸w⁵v² + zyx⁴w⁸v² + yx⁵w⁸v² + yx⁴w⁹v² + zx⁸w⁴v³ + yx⁸w⁴v³ + x⁹w⁴v³ + x⁸w⁵v³ + zx⁴w⁸v³ + yx⁴w⁸v³ + x⁵w⁸v³ + x⁴w⁹v³ + zyx⁸w²v⁴ + yx⁹w²v⁴ + yx⁸w³v⁴ + x⁸w⁴v⁴ + zyx²w⁸v⁴ + yx³w⁸v⁴ + x⁴w⁸v⁴ + yx²w⁹v⁴ + zx⁸w²v⁵ + yx⁸w²v⁵ + x⁹w²v⁵ + x⁸w³v⁵ + zx²w⁸v⁵ + yx²w⁸v⁵ + x³w⁸v⁵ + x²w⁹v⁵ + x⁸w²v⁶ + x²w⁸v⁶ + zyx⁴w²v⁸ + yx⁵w²v⁸ + yx⁴w³v⁸ + zyx²w⁴v⁸ + yx³w⁴v⁸ + yx²w⁵v⁸ + zx⁴w²v⁹ + yx⁴w²v⁹ + x⁵w²v⁹ + x⁴w³v⁹ + zx²w⁴v⁹ + yx²w⁴v⁹ + x³w⁴v⁹ + x²w⁵v⁹ + x⁴w²v¹⁰ + x²w⁴v¹⁰ .

It is nilpotent of degree 2.

The annihilator of the Essential Cohomology has dimension 4 .

---

---

Inflations from Maximal Quotient Groups

Maximal Quotient Group Q #1.

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

The group Q is abelian of type [ 2, 2, 2, 2, 2 ] .

The cohomology ring of Q is a polynomial ring with variables z , y , x , w , v in degrees [ 1, 1, 1, 1, 1 ]

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

v ,

w ,

x ,

y ,

z
in the cohomology of G.

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

z² + zy + y² + zx + x² + zw + yw + xw + w² + zv + wv + v² ,

y³ + y²x + yx² + x³ + y²w + x²w + yw² + xw² + w³ + y²v + x²v + w²v + yv² + xv² + wv² + v³ .

---

---

Maximal Quotient Group Q #2.

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 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.3 * pcy.4, pcy.2, pcy.1 * pcy.2, pcy.4, pcy.1 * pcy.2 ] in the quotient group.

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

z + x ,

z + x + w ,

v ,

y + v ,

zy²x + z²yw + z²xw + zyxw + x³w + y²w² + yxw² + yw³ + xw³ + z²xv + x³v + y²wv + zxwv + yxwv + x²wv + zxv² + x²v² + ywv² + xv³ + wv³ + u
in the cohomology of G.

The kernel of the inflation is zero.

Maximal Quotient Group Q #3.

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

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.3 * pcy.4, pcy.2, pcy.1 * pcy.2, pcy.4, pcy.1 * pcy.2 * pcy.5 ] in the quotient group.

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

z + x ,

z + x + w ,

v ,

y + v ,

z⁴ + zy²x + z²yw + z²xw + zyxw + x³w + y²w² + yxw² + yw³ + xw³ + z²xv + x³v + y²wv + zxwv + yxwv + x²wv + zxv² + x²v² + ywv² + xv³ + wv³ + u
in the cohomology of G.

The kernel of the inflation is zero.

Maximal Quotient Group Q #4.

The kernel of the quotient is generated by G.1 * G.4 .

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.3 * pcy.4, pcy.2, pcy.1 * pcy.2, pcy.4, pcy.2 * pcy.5 ] in the quotient group.

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

x ,

z + x + w ,

v ,

y + v ,

z⁴ + zy²x + z²yw + z²xw + zyxw + x³w + y²w² + yxw² + yw³ + xw³ + z²xv + x³v + y²wv + zxwv + yxwv + x²wv + zxv² + x²v² + ywv² + xv³ + wv³ + u
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.4 * G.6 .

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.3 * pcy.4, pcy.2, pcy.1 * pcy.2, pcy.4, pcy.2 ] in the quotient group.

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

x ,

z + x + w ,

v ,

y + v ,

zy²x + z²yw + z²xw + zyxw + x³w + y²w² + yxw² + yw³ + xw³ + z²xv + x³v + y²wv + zxwv + yxwv + x²wv + zxv² + x²v² + ywv² + xv³ + wv³ + u
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.3 * G.4 .

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.1 * pcy.2, pcy.4, pcy.4 * pcy.5, pcy.3 * pcy.4, pcy.2 * pcy.3 * pcy.4 * pcy.5 ] in the quotient group.

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

v ,

z + v ,

z + y ,

z + y + x + w ,

z⁴ + z³y + y³x + zyx² + y²x² + z²yw + zy²w + z²xw + zyxw + x³w + z²w² + y²w² + x²w² + xw³ + z²yv + yx²v + z²wv + zxwv + yxwv + zw²v + z²v² + y²v² + x²v² + zwv² + w²v² + zv³ + xv³ + u
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.3 * G.4 * G.6 .

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.1 * pcy.2, pcy.4, pcy.4, pcy.3 * pcy.4, pcy.2 * pcy.3 * pcy.4 * pcy.5 ] in the quotient group.

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

v ,

z + v ,

z + y ,

z + y + x + w ,

zy²x + z²yw + z²xw + zyxw + x³w + y²w² + yxw² + yw³ + xw³ + z²xv + x³v + y²wv + zxwv + yxwv + x²wv + zxv² + x²v² + ywv² + xv³ + wv³ + u
in the cohomology of G.

The kernel of the inflation is zero.

Maximal Quotient Group Q #8.

The kernel of the quotient is generated by G.1 * G.2 * 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.3 * pcy.4, pcy.2, pcy.1 * pcy.2, pcy.4, pcy.3 * pcy.5 ] in the quotient group.

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

x ,

x + w ,

z + v ,

y + v ,

z⁴ + zy²x + z²yw + z²xw + zyxw + x³w + y²w² + yxw² + yw³ + xw³ + z²xv + x³v + y²wv + zxwv + yxwv + x²wv + zxv² + x²v² + ywv² + xv³ + wv³ + u
in the cohomology of G.

The kernel of the inflation is zero.

Maximal Quotient Group Q #9.

The kernel of the quotient is generated by G.1 * G.2 * G.5 * G.6 .

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.3 * pcy.4, pcy.2, pcy.1 * pcy.2, pcy.4, pcy.3 ] in the quotient group.

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

x ,

x + w ,

z + v ,

y + v ,

zy²x + z²yw + z²xw + zyxw + x³w + y²w² + yxw² + yw³ + xw³ + z²xv + x³v + y²wv + zxwv + yxwv + x²wv + zxv² + x²v² + ywv² + xv³ + wv³ + u
in the cohomology of G.

The kernel of the inflation is zero.

Maximal Quotient Group Q #10.

The kernel of the quotient is generated by G.2 * G.3 * G.5 * G.6 .

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.2 * pcy.4, 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 + x ,

w ,

y + v ,

zy²x + z²yw + z²xw + zyxw + x³w + y²w² + yxw² + yw³ + xw³ + z²xv + x³v + y²wv + zxwv + yxwv + x²wv + zxv² + x²v² + ywv² + xv³ + wv³ + v⁴ + u
in the cohomology of G.

The kernel of the inflation is zero.

Maximal Quotient Group Q #11.

The kernel of the quotient is generated by G.2 * G.3 * 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.2 * pcy.4 * 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 + x ,

w ,

y + v ,

zy²x + z²yw + z²xw + zyxw + x³w + y²w² + yxw² + yw³ + xw³ + z²xv + x³v + y²wv + zxwv + yxwv + x²wv + zxv² + x²v² + ywv² + xv³ + wv³ + u
in the cohomology of G.

The kernel of the inflation is zero.

Maximal Quotient Group Q #12.

The kernel of the quotient is generated by G.2 * G.4 * 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.4 * 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 + x ,

y + w ,

y + v ,

zy²x + z²yw + z²xw + zyxw + x³w + y²w² + yxw² + yw³ + xw³ + z²xv + x³v + y²wv + zxwv + yxwv + x²wv + zxv² + x²v² + ywv² + xv³ + wv³ + u
in the cohomology of G.

The kernel of the inflation is zero.

Maximal Quotient Group Q #13.

The kernel of the quotient is generated by G.2 * G.4 * G.5 * G.6 .

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.4, pcy.1 * pcy.2 ] in the quotient group.

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

z ,

z + x ,

y + w ,

y + v ,

zy²x + z²yw + z²xw + zyxw + x³w + y²w² + yxw² + yw³ + xw³ + z²xv + x³v + y²wv + zxwv + yxwv + x²wv + zxv² + x²v² + ywv² + xv³ + wv³ + v⁴ + u
in the cohomology of G.

The kernel of the inflation is zero.

Maximal Quotient Group Q #14.

The kernel of the quotient is generated by G.1 * G.2 * G.3 * G.4 * 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.3 * pcy.4, pcy.2, pcy.1 * pcy.2, pcy.4, pcy.1 * pcy.3 ] in the quotient group.

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

z + x ,

x + w ,

z + v ,

y + v ,

zy²x + z²yw + z²xw + zyxw + x³w + y²w² + yxw² + yw³ + xw³ + z²xv + x³v + y²wv + zxwv + yxwv + x²wv + zxv² + x²v² + ywv² + xv³ + wv³ + u
in the cohomology of G.

The kernel of the inflation is zero.

Maximal Quotient Group Q #15.

The kernel of the quotient is generated by G.1 * G.2 * G.3 * G.4 * G.5 * G.6 .

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.3 * pcy.4, pcy.2, pcy.1 * pcy.2, pcy.4, pcy.1 * pcy.3 * pcy.5 ] in the quotient group.

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

z + x ,

x + w ,

z + v ,

y + v ,

z⁴ + zy²x + z²yw + z²xw + zyxw + x³w + y²w² + yxw² + yw³ + xw³ + z²xv + x³v + y²wv + zxwv + yxwv + x²wv + zxv² + x²v² + ywv² + xv³ + wv³ + u
in the cohomology of G.

The kernel of the inflation is zero.

Action of Automorphisms

The groups of outer automorphisms of G has order 516096, and is generated by 8 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.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 ,

v ,

z⁴ + z³y + zy²x + y³x + zyx² + y²x² + zy²w + z²w² + yxw² + x²w² + yw³ + z²yv + z²xv + yx²v + x³v + z²wv + y²wv + x²wv + zw²v + z²v² + y²v² + zxv² + zwv² + ywv² + w²v² + zv³ + wv³ + u .

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.2
G.3 * G.6
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 ,

v ,

z⁴ + v⁴ + u .

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

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

z ,

y ,

x ,

w ,

v ,

z⁴ + u .

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

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

z ,

z + y + x + w + v ,

x ,

w ,

v ,

z⁴ + z²x² + z²yw + zy²w + z²xw + zyxw + x³w + z²w² + y²w² + yxw² + yw³ + xw³ + z²xv + x³v + y²wv + zxwv + yxwv + x²wv + x²v² + zwv² + ywv² + xv³ + wv³ + v⁴ + u .

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

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

z ,

y ,

y + x + v ,

w ,

v ,

zy²v + zv³ + u .

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

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

z ,

y ,

z + y + x + v ,

z + y + w + v ,

v ,

u .

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.2
G.1 * G.2 * G.3 * G.5
G.1 * 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 + x + w ,

y + x + w ,

x ,

w ,

x + w + v ,

z²x² + y²x² + z²w² + y²w² + u .

Automorphism #8

The order of the class of the automorphism in the outer automorphism group is 21. The images of the generators of G are

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

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

w + v ,

z ,

y ,

y + x ,

y + x + w ,

z⁴ + z³y + zyx² + y²x² + z²yw + zy²w + zyxw + z²w² + y²w² + z²yv + zyxv + z²wv + zxwv + zw²v + z²v² + y²v² + zxv² + x²v² + zwv² + w²v² + zv³ + u .

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CHECKS

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

THE COMPUTATION IS COMPLETE