# SOTGrps, chapter 1
#
# DO NOT EDIT THIS FILE - EDIT EXAMPLES IN THE SOURCE INSTEAD!
#
# This file has been generated by AutoDoc. It contains examples extracted from
# the package documentation. Each example is preceded by a comment which gives
# the name of a GAPDoc XML file and a line range from which the example were
# taken. Note that the XML file in turn may have been generated by AutoDoc
# from some other input.
#
gap> START_TEST("sotgrps01.tst");
# doc/_Chapter_The_SOTGrps_package.xml:42-51
gap> AllSOTGroups(60);
[ <pc group of size 60 with 4 generators>, <pc group of size 60 with 4 generators>,
<pc group of size 60 with 4 generators>, <pc group of size 60 with 4 generators>,
<pc group of size 60 with 4 generators>, <pc group of size 60 with 4 generators>,
<pc group of size 60 with 4 generators>, <pc group of size 60 with 4 generators>,
<pc group of size 60 with 4 generators>, <pc group of size 60 with 4 generators>,
<pc group of size 60 with 4 generators>, <pc group of size 60 with 4 generators>,
Alt( [ 1 .. 5 ] ) ]
# doc/_Chapter_The_SOTGrps_package.xml:63-69
gap> NumberOfSOTGroups(2*3*5*7);
12
gap> NumberOfSOTGroups(2*3*5*7*11);
Error, Order 2310 is not supported by SOTGrps.
Please refer to the SOTGrps documentation for the list of supported orders.
# doc/_Chapter_The_SOTGrps_package.xml:83-86
gap> SOTGroup(2*3*5*7, 1);
<pc group of size 210 with 4 generators>
# doc/_Chapter_The_SOTGrps_package.xml:109-114
gap> G:=Image(IsomorphismPermGroup(SmallGroup(690,1)));;
gap> H:=Image(IsomorphismPcGroup(SmallGroup(690,1)));;
gap> IsIsomorphicSOTGroups(G,H);
true
# doc/_Chapter_The_SOTGrps_package.xml:136-168
gap> SOTGroupsInformation(2^2*3*19);
There are 15 groups of order 228.
The groups of order p^2qr are either solvable or isomorphic to Alt(5).
The solvable groups are sorted by their Fitting subgroup.
SOT 1 - 2 are the nilpotent groups.
SOT 3 has Fitting subgroup of order 57.
SOT 4 - 7 have Fitting subgroup of order 76.
SOT 8 - 9 have Fitting subgroup of order 38.
SOT 10 - 15 have Fitting subgroup of order 114.
gap> SOTGroupsInformation(2662);
There are 15 groups of order 2662.
The groups of order p^3q are solvable by Burnside's pq-Theorem.
These groups are sorted by their Sylow subgroups.
1 - 3 are abelian.
4 - 5 are nonabelian nilpotent and have a normal Sylow 11-subgroup and a
normal Sylow 2-subgroup.
6 is non-nilpotent and has a normal Sylow 2-subgroup with Sylow
11-subgroup [ 1331, 1 ].
7 - 9 are non-nilpotent and have a normal Sylow 2-subgroup with Sylow
11-subgroup [ 1331, 2 ].
10 - 12 are non-nilpotent and have a normal Sylow 2-subgroup with Sylow
11-subgroup [ 1331, 5 ].
13 - 14 are non-nilpotent and have a normal Sylow 2-subgroup with Sylow
11-subgroup [ 1331, 3 ].
15 is non-nilpotent and has a normal Sylow 2-subgroup with Sylow
11-subgroup [ 1331, 4 ].
#
gap> STOP_TEST("sotgrps01.tst", 1);
