[GAP Forum] Problem with certains nonsolvable groups...

[Giulio Peruginelli]

Dear Gap-forum users,
I have a problem with two nonsolvable groups, (120, 35) and (504,156)
Gap3 says the 1st is A5x2 (I don't know what x2 means...) and the 2nd one is PSL(2,8).

I computed the orders of its conjugacy classes two times and I obtain two different 
results!
1st group:
G:=SmallGroup(120,35);;
C:=ConjugacyClasses(G);;
l:=[];;
for i in [1..Length(C)] do
 l[i]:=Order(G, Representative(C[i]));
od;
l;
[ 1, 2, 3, 6, 2, 2, 5, 10, 5, 10 ]
(other result: [1,5,5,10,10, 3,6,2,2,2]).


2nd group:
G:=SmallGroup(504,156);;
C:=ConjugacyClasses(G);;
l:=[];;
for i in [1..Length(C)] do
 l[i]:=Order(G, Representative(C[i]));
od;
l;
[ 1, 7, 7, 7, 2, 3, 9, 9, 9 ]
(but I computed again these orders with the help of char table and I obtain a different
result: [1,7,7,7,3, 9,9,9,2]; which is right and which is wrong? they are equal vectors,
up to the order, see the question below)

As you told me I use these two function in order to compute the representation of the
automorphism group as permutation group on the set of the conjugacy classes of G 

OnClasses:=function(cl,g)
  return ConjugacyClass(cl.group,Representative(cl)^g); 
end; 

Aut:=function(G)
   local AutomG, C ;
      AutomG:=AutomorphismGroup(G);
      C:=ConjugacyClasses(G);
      return Operation(AutomG,C,OnClasses);
end;

In the 1st case I obtain:
gap> Aut(SmallGroup(120,35));
Group( ( 2, 3)( 4, 5) )

which is impossible because the order of the 2nd and the 3rd classes of G are different.
The right answer should be  Group( ( 7, 9)( 8, 10) )


In the 2nd case:
gap> Aut(SmallGroup(504,156));
Group( (2,3,4)(6,8,7) )
impossible again for the same reason (look at the 6th and 7th classes, for the 1st output)

Where am I wrong? maybe I am using the 2 functions above in a wrong way...

by the way, in which order are the conjugacy classes of a finite group represented?
I mean, which comes 1st, after the identity and so on? do you know if it's the same
order used in magma?


thanks

best wishes

p.s. I  am using Gap3...

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