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

[Alastair Donaldson]

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