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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