Identify group given by explicit representations of its generators

Question

I come to a situation that I have the explicit $3 \times 3$ real matrix representations of all generators and can prove that they span a finite group. But I don't know the name of this group and its overall structures. Is there any simple way or sample GAP code that I can use for this purpose? I'm a total new comer to GAP which seems to be the right tool that I need.

Thanks!

Shao-Feng

Answer 1

To remove this question from the unanswered queue, just a simple example of a calculation in GAP which you may have in mind. Here we are dealing with the irreducible representation of $A_5$ of degree 3:

gap> gens:=
> [ [ [                             -1,   0,                    E(5)+E(5)^4 ], 
>     [                              0,   1,                              1 ], 
>     [                   -E(5)-E(5)^4,   0,                   -E(5)-E(5)^4 ] 
>   ], 
>   [ [                              0,   0,                             -1 ], 
>     [ -2*E(5)-E(5)^2-E(5)^3-2*E(5)^4,   1, -2*E(5)-E(5)^2-E(5)^3-2*E(5)^4 ], 
>     [                    E(5)+E(5)^4, - 1,                             -1 ] ] 
> ];;
gap> G:=Group(gens);;
gap> Size(G);
60
gap> StructureDescription(G);
"A5"

Remark: GAP ignores whitespace symbols in the input, so the matrices are formatted this way just for easy reading.