XModSelect( size [, gpnum, type, norm] )
Here the parameter size may take any value up to 47, gpnum refers
to the isomorphism class of groups of order size as ordered in the
GAP ; library. The norm parameter is only used in the case
"conj" and specifies the position of the source group in the list of
normal subgroups of the range R. The list Cat1List is used to
store the data for these groups. The allowable types are "conj"
for normal inclusions with conjugation, "aut" for automorphism
groups and "rmod" for Rmodules. If type is not specified the
default is "conj". If norm is not specified, then the
AutomorphismXMod of R is returned.
In the following example the fourteenth class of groups of size 24 is
a special linear group sl(2,3) and a double cover of a4. The
third normal subgroup of sl(2,3) is a quaternion group, and a
conjugation crossed module is returned.
gap> SX := XModSelect( 24, 14, "conj", 3 );
Crossed module [N3->sl(2,3)]
gap> XModPrint( SX );
Crossed module [N3->sl(2,3)] :-
: Source group has parent ( sl(2,3) ) and has generators:
[ (1,2,3,4)(5,8,7,6), ( 1, 5, 3, 7)( 2, 6, 4, 8) ]
: Range group = sl(2,3) and has generators:
[ (1,2,3,4)(5,8,7,6), (1,5,3,7)(2,6,4,8), (2,5,6)(4,7,8)(9,10,11) ]
: Boundary homomorphism maps source generators to:
[ (1,2,3,4)(5,8,7,6), ( 1, 5, 3, 7)( 2, 6, 4, 8) ]
: Action homomorphism maps range generators to automorphisms:
(1,2,3,4)(5,8,7,6) --> { source gens -->
[ (1,2,3,4)(5,8,7,6), ( 1, 7, 3, 5)( 2, 8, 4, 6) ] }
(1,5,3,7)(2,6,4,8) --> { source gens -->
[ (1,4,3,2)(5,6,7,8), ( 1, 5, 3, 7)( 2, 6, 4, 8) ] }
( 2, 5, 6)( 4, 7, 8)( 9,10,11) --> { source gens -->
[ ( 1, 5, 3, 7)( 2, 6, 4, 8), ( 1, 6, 3, 8)( 2, 7, 4, 5) ] }
These 3 automorphisms generate the group of automorphisms.
GAP 3.4.4