Dear Gap-Forum,

David Joyner asked about the structure of the group
G:=Group( ( 2,23,20,17, 8,10)( 3,24,30,28,16, 9)( 4,21,18, 7)( 5,22,19, 6)
(11,12,25,26)(13,14,27,15), ( 1, 5,18,29,27,25)( 3, 6,16,28,14,24)
( 4,19,30,23)( 7,15,12,10)( 8,11,13, 9)(20,26,22,21) );

Burkhard Hofling already answered what caused the error in the
computation using NormalSubgroups, and also mentioned the function
PCore(G,2), which tells that G has an elementary abelian normal subgroup
of size 2^14.

Alternatively, the function DisplayCompositionSeries(G) returns 
<G> (16 gens, size 10712468422656000)
 | A(15)
<S> (14 gens, size 16384)
 | Z(2)
<S> (13 gens, size 8192)
 | Z(2)
<S> (12 gens, size 4096)
 | Z(2)
<S> (11 gens, size 2048)
 | Z(2)
<S> (10 gens, size 1024)
 | Z(2)
<S> (9 gens, size 512)
 | Z(2)
<S> (8 gens, size 256)
 | Z(2)
<S> (7 gens, size 128)
 | Z(2)
<S> (6 gens, size 64)
 | Z(2)
<S> (5 gens, size 32)
 | Z(2)
<S> (4 gens, size 16)
 | Z(2)
<S> (3 gens, size 8)
 | Z(2)
<S> (2 gens, size 4)
 | Z(2)
<S> (1 gens, size 2)
 | Z(2)
<1> (0 gens)

and then:

gap> IsElementaryAbelian(G.compositionSeries[2]);
true

Of course, G.compositionSeries[2] must be normal in G.compositionSeries[1] = G.

In general, it seems to be a good idea to use polynomial time algorithms
instead of ones based on backtrack, whenever it is possible.
The computation of a composition series took 2.5 seconds while,
as I write this letter, NormalSubgroups runs already for an hour with
no results yet.

Peter Blanchard analized the group similarly to methods used in the
README file. This README file was written before composition series
was implemented in GAP. The composition series algorithm uses reductions
to the primitive case similarly as in README but, of course, can handle
all primitive groups as well, not just recognizing A_n and S_n.

Best regards,
Akos Seress