A minimal set of generators for the cohomology is:

w₂(r₁₁) of degree 2
w₁(r₁₉) of degree 1
w₁(r₃) of degree 1
w₂(r₁₉) of degree 2

The Steenrod operations are as follows:

Sq¹(w₂(r₁₁)) = 0
Sq¹(w₂(r₁₉)) = w₁(r₁₉)w₂(r₁₉)

Here is a minimal system of equations:

(1) w₁(r₁₉)² = 0
(2) w₁(r₁₉)w₁(r₃) + w₁(r₃)² = 0

Stiefel-Whitney classes:

w₁(r₁) = w₁(r₁₉)
w₁(r₂) = w₁(r₁₉) + w₁(r₃)
w₁(r₃) = w₁(r₃)
w₂(r₄) = 0
w₂(r₆) = w₁(r₁₉)w₁(r₃)
w₂(r₈) = w₂(r₁₁) + w₁(r₁₉)w₁(r₃)
w₂(r₉) = w₂(r₁₁) + w₁(r₁₉)w₁(r₃)
w₂(r₁₀) = w₂(r₁₁)
w₂(r₁₁) = w₂(r₁₁)
w₁(r₁₆) = w₁(r₁₉)
w₂(r₁₆) = 0
w₄(r₁₇) = 0
w₁(r₁₈) = w₁(r₁₉)
w₂(r₁₈) = w₂(r₁₉)
w₁(r₁₉) = w₁(r₁₉)
w₂(r₁₉) = w₂(r₁₉)
w₄(r₂₀) = w₂(r₁₉)²
w₄(r₂₁) = w₂(r₁₉)²
w₂(r₂₂) = 0
w₄(r₂₂) = w₂(r₁₁)²
w₂(r₂₄) = 0
w₄(r₂₄) = w₂(r₁₁)² + w₂(r₁₉)²
w₂(r₂₅) = 0
w₄(r₂₅) = w₂(r₁₁)² + w₂(r₁₉)²

Chern classes:

c₁(r₁) = 0
c₁(r₂) = w₁(r₁₉)w₁(r₃)
c₁(r₃) = w₁(r₁₉)w₁(r₃)
c₁(r₄) = 0
c₁(r₅) = 0
c₁(r₆) = w₁(r₁₉)w₁(r₃)
c₁(r₇) = w₁(r₁₉)w₁(r₃)
c₁(r₈) = w₂(r₁₁) + w₁(r₁₉)w₁(r₃)
c₁(r₉) = w₂(r₁₁) + w₁(r₁₉)w₁(r₃)
c₁(r₁₀) = w₂(r₁₁)
c₁(r₁₁) = w₂(r₁₁)
c₁(r₁₂) = w₂(r₁₁) + w₁(r₁₉)w₁(r₃)
c₁(r₁₃) = w₂(r₁₁) + w₁(r₁₉)w₁(r₃)
c₁(r₁₄) = w₂(r₁₁)
c₁(r₁₅) = w₂(r₁₁)
c₁(r₁₆) = 0
c₂(r₁₆) = 0
c₂(r₁₇) = 0
c₁(r₁₈) = 0
c₂(r₁₈) = w₂(r₁₉)²
c₁(r₁₉) = 0
c₂(r₁₉) = w₂(r₁₉)²
c₂(r₂₀) = w₂(r₁₉)²
c₂(r₂₁) = w₂(r₁₉)²
c₁(r₂₂) = 0
c₂(r₂₂) = w₂(r₁₁)²
c₁(r₂₃) = 0
c₂(r₂₃) = w₂(r₁₁)²
c₁(r₂₄) = 0
c₂(r₂₄) = w₂(r₁₁)² + w₂(r₁₉)²
c₁(r₂₅) = 0
c₂(r₂₅) = w₂(r₁₁)² + w₂(r₁₉)²
c₁(r₂₆) = 0
c₂(r₂₆) = w₂(r₁₁)² + w₂(r₁₉)²
c₁(r₂₇) = 0
c₂(r₂₇) = w₂(r₁₁)² + w₂(r₁₉)²

The algebra of Milnor constants is generated by:

c₁(r₂) + c₁(r₈)
c₁(r₂)
c₂(r₁₈)
w₁(r₁₉)w₁(r₃)w₂(r₁₉) which is not a combination of Chern classes; it is nilpotent of order 2

The results above have been produced during the second run in April, 2008.