Generators of a subgroup of $SL_2(\mathbb{Z}/24\mathbb{Z})$

Question

So I have this subgroup of $SL_2(\mathbb{Z}/24\mathbb{Z})$ which has $256$ elements. Is there a way in sage to get the list of its generators ? The "only" information I have on the group is the list of its elements.

If it is not implemented in Sage does anyone have a reference for an algorithm to do this ?

Answer 1

I did it by using GAP. Look at this and I hope it works, unless, tell me to remove that.

gap> SL24:=SL(4,Integers mod 24);
gap> T:=GeneratorsOfGroup( SL24);;
gap> for i in [1..Size(T)] do Print(T[i],"\n"); od;

[ [ ZmodnZObj( 0, 24 ), ZmodnZObj( 23, 24 ), ZmodnZObj( 0, 24 ),ZmodnZObj( 0, 24 ) ], 
[ ZmodnZObj( 0, 24 ), ZmodnZObj( 0, 24 ), ZmodnZObj( 1, 24 ), ZmodnZObj( 0, 24 ) ], 
[ ZmodnZObj( 0, 24 ), ZmodnZObj( 0, 24 ), ZmodnZObj( 0, 24 ), ZmodnZObj( 1, 24 ) ], 
[ ZmodnZObj( 1, 24 ), ZmodnZObj( 0, 24 ), ZmodnZObj( 0, 24 ), ZmodnZObj( 0, 24 ) ] ]

[ [ ZmodnZObj( 0, 24 ), ZmodnZObj( 23, 24 ), ZmodnZObj( 0, 24 ), ZmodnZObj( 0, 24 ) ], 
[ ZmodnZObj( 1, 24 ), ZmodnZObj( 0, 24 ), ZmodnZObj( 0, 24 ), ZmodnZObj( 0, 24 ) ], 
[ ZmodnZObj( 0, 24 ), ZmodnZObj( 0, 24 ), ZmodnZObj( 1, 24 ), ZmodnZObj( 0, 24 ) ], 
[ ZmodnZObj( 0, 24 ), ZmodnZObj( 0, 24 ), ZmodnZObj( 0, 24 ), ZmodnZObj( 1, 24 ) ] ]

[ [ ZmodnZObj( 1, 24 ), ZmodnZObj( 1, 24 ), ZmodnZObj( 0, 24 ), ZmodnZObj( 0, 24 ) ], 
[ ZmodnZObj( 0, 24 ), ZmodnZObj( 1, 24 ), ZmodnZObj( 0, 24 ), ZmodnZObj( 0, 24 ) ], 
[ ZmodnZObj( 0, 24 ), ZmodnZObj( 0, 24 ), ZmodnZObj( 1, 24 ), ZmodnZObj( 0, 24 ) ], 
[ ZmodnZObj( 0, 24 ), ZmodnZObj( 0, 24 ), ZmodnZObj( 0, 24 ), ZmodnZObj( 1, 24 ) ] ]