On IsSimple() in Magma.

Question

It is known that $S_{11}$ is a Atlas group and is not a simple group. In Magma,

IsSimple(ATLASGroup("S11"));

Runtime error in 'IsSimple': Bad argument types Argument types given: GrpAtlas

We want to know how to avoid this error in Magma.

Answer 1

In Magma, the answer to ATLASGroup("S11") is not a Permutation Group or a Matrix Group, but an element of a different type, and you cannot ask it if it is simple. You need to convert it to an actual group, by using the keys.

It is described in the documentation.

In your case you can do:

K:=MatRepKeys(ATLASGroup("S11"));

G:=MatrixGroup(K[1]);

IsSimple(G);

First you get the list of keys. There is only one. Then you use the key to get a Matrix Group G. Then you ask what you want.