Action of $S_7$ on the set of $3$-subsets of $\Omega$

Question

Reviewing the great book in Permutation Groups by J.D.Dixon, I encountered the following problem:

Show that $S_7$ acting on the set of $3$-subsets of $\Omega=\{1,2,3,4,5,6,7\}$ has degree $35$ and rank $4$ with subdegrees $1,4,12,18$.

I wanted to probe the problem by making a good program in GAP's environment so I did:

 gap> S7:=SymmetricGroup(7);;
 gap> O:=[1..7];;
 gap> 3s:=Combinations( O,3);;
 gap> Size(3s);
                                          35
 gap> G1:=Stabilizer(S7,3s[1],OnSets);
               Group([ (6,7), (5,7), (4,7), (2,3)(5,7), (1,2,3)(5,7) ])
 gap> D1:=[];;
 gap> for k in [1..35] do D1[k]:=Size(Orbit(G1,3s[k],OnSets)); od;;
 gap> List([1..35],k->D1[k]);

 [ 1, 12, 12, 12, 12, 12, 12, 12, 12, 18, 18, 18, 18, 18, 18, 12, 12, 12, 12, 18,
   18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 4, 4, 4, 4 ]

However, I can read the results as above, they are not in an order $1,4,8,12$ and I couldn't make them be happened just for one time.

Answer 1

Try

SortParallel(D1, 3s); 

and then redo the steps

D := [];
for k in [1..35] do D1[k]:=Size(Orbit(G1,3s[k],OnSets)); od;;
D1;

Is this that you want?