[GAP Forum] AlternatingGroup(4) and its generators

[Sven Reichard]

Dear Jiayue,

to be precise, G is isomorphic to the alternating group. You can find
such an isomorphism and determine the images of the generators as follows:

gap> G := SmallGroup(12,3);
<pc group of size 12 with 3 generators>
gap> StructureDescription(G);
"A4"
gap> a4 := AlternatingGroup(4);
Alt( [ 1 .. 4 ] )
gap> iso := IsomorphismGroups(G, a4);
[ f1, f2, f3 ] -> [ (2,4,3), (1,3)(2,4), (1,2)(3,4) ]
gap> List(GeneratorsOfGroup(G), g -> Image(iso, g));
[ (2,4,3), (1,3)(2,4), (1,2)(3,4) ]

HTH,
Sven

On 21.12.2016 12:40, 齐嘉悦 wrote:
> 
> Dear Forum members,
> 
> 
> When I type this in GAP: 
> 
> 
> gap>G:=SmallGroup(12,3);
> gap>GeneratorsOfGroup(G);
> the result is [f1,f2,f3],but actually the group G here is AlternatingGroup(4) and I wonder 
> how could I know here what f1,f2,f3 exactly means by permutations respectively?  How
> could I know what are they in A4?
> 
> 
> Looking forward to any reply!
> 
> 
> Thanks a lot!
> 
> 
> Jiayue
> 
> 
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