A minimal set of generators for the cohomology is:

w₁(r₁₃) of degree 1
w₁(r₁₁) of degree 1
w₂(r₂₀) of degree 2
w₂(r₁₆) of degree 2
w₁(r₁₈) of degree 1
w₁(r₁₅) of degree 1

The Steenrod operations are as follows:

Sq¹(w₂(r₂₀)) = w₁(r₁₁)w₂(r₂₀) + w₂(r₂₀)w₁(r₁₈) + w₂(r₂₀)w₁(r₁₅)
Sq¹(w₂(r₁₆)) = w₂(r₁₆)w₁(r₁₈)

Here is a minimal system of equations:

(1) w₁(r₁₁)w₁(r₁₈) + w₁(r₁₈)w₁(r₁₅) = 0
(2) w₁(r₁₃)² + w₁(r₁₃)w₁(r₁₈) + w₁(r₁₁)w₁(r₁₈) + w₁(r₁₅)² = 0

Stiefel-Whitney classes:

w₁(r₁) = w₁(r₁₈)
w₁(r₂) = w₁(r₁₃) + w₁(r₁₅)
w₁(r₃) = w₁(r₁₃) + w₁(r₁₈) + w₁(r₁₅)
w₁(r₄) = w₁(r₁₁) + w₁(r₁₅)
w₁(r₅) = w₁(r₁₁) + w₁(r₁₈) + w₁(r₁₅)
w₁(r₆) = w₁(r₁₃) + w₁(r₁₁)
w₁(r₇) = w₁(r₁₃) + w₁(r₁₁) + w₁(r₁₈)
w₁(r₈) = w₁(r₁₃) + w₁(r₁₁) + w₁(r₁₈) + w₁(r₁₅)
w₁(r₉) = w₁(r₁₃) + w₁(r₁₁) + w₁(r₁₅)
w₁(r₁₀) = w₁(r₁₁) + w₁(r₁₈)
w₁(r₁₁) = w₁(r₁₁)
w₁(r₁₂) = w₁(r₁₃) + w₁(r₁₈)
w₁(r₁₃) = w₁(r₁₃)
w₁(r₁₄) = w₁(r₁₈) + w₁(r₁₅)
w₁(r₁₅) = w₁(r₁₅)
w₁(r₁₆) = w₁(r₁₈)
w₂(r₁₆) = w₂(r₁₆)
w₁(r₁₇) = w₁(r₁₈)
w₂(r₁₇) = w₁(r₁₃)² + w₁(r₁₁)² + w₂(r₁₆) + w₁(r₁₃)w₁(r₁₈) + w₁(r₁₁)w₁(r₁₈)
w₁(r₁₈) = w₁(r₁₈)
w₂(r₁₈) = w₁(r₁₁)² + w₂(r₁₆) + w₁(r₁₁)w₁(r₁₈)
w₁(r₁₉) = w₁(r₁₈)
w₂(r₁₉) = w₁(r₁₃)² + w₂(r₁₆) + w₁(r₁₃)w₁(r₁₈)
w₁(r₂₀) = w₁(r₁₁) + w₁(r₁₈) + w₁(r₁₅)
w₂(r₂₀) = w₂(r₂₀)
w₁(r₂₁) = w₁(r₁₁) + w₁(r₁₈) + w₁(r₁₅)
w₂(r₂₁) = w₁(r₁₃)² + w₁(r₁₃)w₁(r₁₁) + w₂(r₂₀) + w₁(r₁₃)w₁(r₁₈) + w₁(r₁₁)w₁(r₁₈) + w₁(r₁₃)w₁(r₁₅) + w₁(r₁₁)w₁(r₁₅)
w₁(r₂₂) = w₁(r₁₁) + w₁(r₁₈) + w₁(r₁₅)
w₂(r₂₂) = w₁(r₁₃)² + w₁(r₁₃)w₁(r₁₁) + w₂(r₂₀) + w₁(r₁₃)w₁(r₁₈) + w₁(r₁₃)w₁(r₁₅)
w₁(r₂₃) = w₁(r₁₁) + w₁(r₁₈) + w₁(r₁₅)
w₂(r₂₃) = w₂(r₂₀) + w₁(r₁₁)w₁(r₁₈) + w₁(r₁₁)w₁(r₁₅)
w₂(r₂₄) = w₁(r₁₃)² + w₁(r₁₁)² + w₁(r₁₃)w₁(r₁₈) + w₁(r₁₁)w₁(r₁₈) + w₁(r₁₈)²
w₄(r₂₄) = w₂(r₂₀)² + w₁(r₁₃)²w₂(r₁₆) + w₁(r₁₁)²w₂(r₁₆) + w₂(r₁₆)² + w₁(r₁₃)w₂(r₁₆)w₁(r₁₈) + w₁(r₁₁)w₂(r₁₆)w₁(r₁₈)
w₂(r₂₆) = w₁(r₁₃)² + w₁(r₁₁)² + w₁(r₁₃)w₁(r₁₈) + w₁(r₁₁)w₁(r₁₈) + w₁(r₁₈)²
w₄(r₂₆) = w₁(r₁₃)²w₁(r₁₁)² + w₂(r₂₀)² + w₁(r₁₃)²w₂(r₁₆) + w₁(r₁₁)²w₂(r₁₆) + w₂(r₁₆)² + w₁(r₁₃)³w₁(r₁₈) + w₁(r₁₃)²w₁(r₁₁)w₁(r₁₈) + w₁(r₁₃)w₂(r₁₆)w₁(r₁₈) + w₁(r₁₁)w₂(r₁₆)w₁(r₁₈) + w₁(r₁₃)²w₁(r₁₈)²

Chern classes:

c₁(r₁) = w₁(r₁₈)²
c₁(r₂) = w₁(r₁₃)w₁(r₁₈) + w₁(r₁₁)w₁(r₁₈)
c₁(r₃) = w₁(r₁₃)w₁(r₁₈) + w₁(r₁₁)w₁(r₁₈) + w₁(r₁₈)²
c₁(r₄) = w₁(r₁₃)² + w₁(r₁₁)² + w₁(r₁₃)w₁(r₁₈) + w₁(r₁₁)w₁(r₁₈)
c₁(r₅) = w₁(r₁₃)² + w₁(r₁₁)² + w₁(r₁₃)w₁(r₁₈) + w₁(r₁₁)w₁(r₁₈) + w₁(r₁₈)²
c₁(r₆) = w₁(r₁₃)² + w₁(r₁₁)²
c₁(r₇) = w₁(r₁₃)² + w₁(r₁₁)² + w₁(r₁₈)²
c₁(r₈) = w₁(r₁₁)² + w₁(r₁₃)w₁(r₁₈) + w₁(r₁₁)w₁(r₁₈) + w₁(r₁₈)²
c₁(r₉) = w₁(r₁₁)² + w₁(r₁₃)w₁(r₁₈) + w₁(r₁₁)w₁(r₁₈)
c₁(r₁₀) = w₁(r₁₁)² + w₁(r₁₈)²
c₁(r₁₁) = w₁(r₁₁)²
c₁(r₁₂) = w₁(r₁₃)² + w₁(r₁₈)²
c₁(r₁₃) = w₁(r₁₃)²
c₁(r₁₄) = w₁(r₁₃)² + w₁(r₁₃)w₁(r₁₈) + w₁(r₁₁)w₁(r₁₈) + w₁(r₁₈)²
c₁(r₁₅) = w₁(r₁₃)² + w₁(r₁₃)w₁(r₁₈) + w₁(r₁₁)w₁(r₁₈)
c₁(r₁₆) = w₁(r₁₈)²
c₂(r₁₆) = w₂(r₁₆)²
c₁(r₁₇) = w₁(r₁₈)²
c₂(r₁₇) = w₁(r₁₃)⁴ + w₁(r₁₁)⁴ + w₂(r₁₆)² + w₁(r₁₃)³w₁(r₁₈) + w₁(r₁₃)²w₁(r₁₁)w₁(r₁₈) + w₁(r₁₃)w₁(r₁₁)²w₁(r₁₈) + w₁(r₁₁)³w₁(r₁₈)
c₁(r₁₈) = w₁(r₁₈)²
c₂(r₁₈) = w₁(r₁₁)⁴ + w₂(r₁₆)² + w₁(r₁₃)³w₁(r₁₈) + w₁(r₁₃)²w₁(r₁₁)w₁(r₁₈) + w₁(r₁₃)w₁(r₁₁)²w₁(r₁₈) + w₁(r₁₁)³w₁(r₁₈) + w₁(r₁₃)²w₁(r₁₈)²
c₁(r₁₉) = w₁(r₁₈)²
c₂(r₁₉) = w₁(r₁₃)⁴ + w₂(r₁₆)² + w₁(r₁₃)²w₁(r₁₈)²
c₁(r₂₀) = w₁(r₁₃)² + w₁(r₁₁)² + w₁(r₁₃)w₁(r₁₈) + w₁(r₁₁)w₁(r₁₈) + w₁(r₁₈)²
c₂(r₂₀) = w₂(r₂₀)²
c₁(r₂₁) = w₁(r₁₃)² + w₁(r₁₁)² + w₁(r₁₃)w₁(r₁₈) + w₁(r₁₁)w₁(r₁₈) + w₁(r₁₈)²
c₂(r₂₁) = w₂(r₂₀)²
c₁(r₂₂) = w₁(r₁₃)² + w₁(r₁₁)² + w₁(r₁₃)w₁(r₁₈) + w₁(r₁₁)w₁(r₁₈) + w₁(r₁₈)²
c₂(r₂₂) = w₁(r₁₃)²w₁(r₁₁)² + w₂(r₂₀)² + w₁(r₁₃)³w₁(r₁₈) + w₁(r₁₃)²w₁(r₁₁)w₁(r₁₈) + w₁(r₁₃)²w₁(r₁₈)²
c₁(r₂₃) = w₁(r₁₃)² + w₁(r₁₁)² + w₁(r₁₃)w₁(r₁₈) + w₁(r₁₁)w₁(r₁₈) + w₁(r₁₈)²
c₂(r₂₃) = w₁(r₁₃)²w₁(r₁₁)² + w₂(r₂₀)² + w₁(r₁₃)³w₁(r₁₈) + w₁(r₁₃)²w₁(r₁₁)w₁(r₁₈) + w₁(r₁₃)²w₁(r₁₈)²
c₁(r₂₄) = w₁(r₁₃)² + w₁(r₁₁)² + w₁(r₁₃)w₁(r₁₈) + w₁(r₁₁)w₁(r₁₈) + w₁(r₁₈)²
c₂(r₂₄) = w₂(r₂₀)² + w₁(r₁₃)²w₂(r₁₆) + w₁(r₁₁)²w₂(r₁₆) + w₂(r₁₆)² + w₁(r₁₃)w₂(r₁₆)w₁(r₁₈) + w₁(r₁₁)w₂(r₁₆)w₁(r₁₈)
c₁(r₂₅) = w₁(r₁₃)² + w₁(r₁₁)² + w₁(r₁₃)w₁(r₁₈) + w₁(r₁₁)w₁(r₁₈) + w₁(r₁₈)²
c₂(r₂₅) = w₂(r₂₀)² + w₁(r₁₃)²w₂(r₁₆) + w₁(r₁₁)²w₂(r₁₆) + w₂(r₁₆)² + w₁(r₁₃)w₂(r₁₆)w₁(r₁₈) + w₁(r₁₁)w₂(r₁₆)w₁(r₁₈)
c₁(r₂₆) = w₁(r₁₃)² + w₁(r₁₁)² + w₁(r₁₃)w₁(r₁₈) + w₁(r₁₁)w₁(r₁₈) + w₁(r₁₈)²
c₂(r₂₆) = w₁(r₁₃)²w₁(r₁₁)² + w₂(r₂₀)² + w₁(r₁₃)²w₂(r₁₆) + w₁(r₁₁)²w₂(r₁₆) + w₂(r₁₆)² + w₁(r₁₃)³w₁(r₁₈) + w₁(r₁₃)²w₁(r₁₁)w₁(r₁₈) + w₁(r₁₃)w₂(r₁₆)w₁(r₁₈) + w₁(r₁₁)w₂(r₁₆)w₁(r₁₈) + w₁(r₁₃)²w₁(r₁₈)²
c₁(r₂₇) = w₁(r₁₃)² + w₁(r₁₁)² + w₁(r₁₃)w₁(r₁₈) + w₁(r₁₁)w₁(r₁₈) + w₁(r₁₈)²
c₂(r₂₇) = w₁(r₁₃)²w₁(r₁₁)² + w₂(r₂₀)² + w₁(r₁₃)²w₂(r₁₆) + w₁(r₁₁)²w₂(r₁₆) + w₂(r₁₆)² + w₁(r₁₃)³w₁(r₁₈) + w₁(r₁₃)²w₁(r₁₁)w₁(r₁₈) + w₁(r₁₃)w₂(r₁₆)w₁(r₁₈) + w₁(r₁₁)w₂(r₁₆)w₁(r₁₈) + w₁(r₁₃)²w₁(r₁₈)²

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