[GAP Forum] Diagonalize of symmetric matrix 248x248

[Bill Allombert]

On Sun, Jan 13, 2013 at 11:39:59AM +0100, Marek Mitros wrote:
> In general you are right. In this case I've got information from G. Nebe,
> that matrix is diagonalizable over rationals. So orthogonal representation
> of Th group would have rational entries.

With PARI/GP, I found that the eigenvalues are:
[238 230 228 220 218 216 214 212 210 208 206 204 202 200 198 196 194 192 190 188 186 184 182 180
178 176 174 172 170 168 166 160 158 156 24]
with multiplicities
[1 3 2 6 2 4 7 3 6 3 5 5 5 5 2 5 3 9 3 3 2 2 3 2 1 2 3 4 2 1 1 1 1 1 140]

Maybe this will allow you to complete the computation with gap.

Cheers,
Bill.