[GAP Forum] Orbit calculation in GUAVA

[Siddhartha Sarkar]

Dear forum,

I have just started with coding and trying to experiment with GUAVA.

I am trying to reproduce the following calculation briefed in Robert
Wilson's book
"The Finite Simple Groups" Page 184 on hexacodes.

Hexacode W, as defined, is a GF(4)-subspace of GF(4)^6 generated by
the following
vectors : (w, w^2, w^2, w, w^2, w), (w^2, w, w, w^2, w^2, w), (w^2, w,
w^2, w, w, w^2)

where GF(4) = { 0, 1, w, w^2 }

3 X S_4 seems to be a symmetry group : 3 by multiplying scalers from
GF(4)* and S_4
by the permutation subgroup of S_6 generated by (1,2)(3,4),
(1,3,5)(2,4,6), (1,3)(2,4)

I wish to reproduce the orbit calculation of 3 X S_4 to W.

Any help please.

best,
Siddhartha