[GAP Forum] Using GAP to identify permutation groups with "well known" groups

[Marco Costantini]

Dear Alastair Donaldson and gap forum, 
the groups are isomorphic. See the documentations of the functions IdGroup 
and IsomorphismGroups, and try the following code. 
All the best, 
Marco Costantini 
 
 
G1:=Group( (5, 6)(20, 21),(6, 7)(21, 22),(8, 9)(23, 24),(9, 10)(24, 
25),(5,8) (6, 9)(7, 10)(20, 23)(21, 24)(22, 25)(2, 3)(17, 18)(14, 15),(11, 
12)(26, 27)); 
 
S2:=SymmetricGroup(2); 
S3:=SymmetricGroup(3); 
G2:=DirectProduct(S2,WreathProduct(S3,S2)); 
 
 
IdGroup(G1); 
IdGroup(G2); 
 
IsomorphismGroups(G1,G2); 
 
 
 
Scrive Alastair Donaldson <ally at dcs.gla.ac.uk>: 
 
> I have a permutation group G of the following form: 
>  
> G=<(5 6)(20 21),(6 7)(21 22),(8 9)(23 24),(9 10)(24 25),(5 8)(6 9)(7  
> 10)(20 23)(21 24)(22 25)(2 3)(17 18)(14 15),(11 12)(26 27)> 
>  
> I've used GAP to check that this is isomorphic to  
> DirectProduct(S2,WreathProduct(S3,S2)) (if it's not  
> then I've made a mistake writing the generators!).  What I'm  
> trying to do is to classify certain groups arising from graphs as  
> products/wreath products of "well known" groups like S3 and S2. 
>  
> I'm wondering if GAP has some way of automatically classifying 
> permutation  
> groups in a way similar to this. 
>  
> Any ideas? 
>  
> Thanks 
>  
> Alastair Donaldson