> < ^ Date: Thu, 02 Dec 1999 08:52:31 +0100
< ^ From: XIAO Gang <xiao@unice.fr >
> ^ Subject: Subgroup Lattice question

Trying to add subgroup lattice into my PermGroup page
the following output from GAP which I am unable to interprete.

```--------------------------------------------
gap> g:=SmallGroup(18,3);
<pc group of size 18 with 3 generators>
gap> l:=LatticeSubgroups(g);
LatticeSubgroups(Group( [ f1, f2, f3 ] ),# 9 classes, 14 subgroups)
gap> c:=List(ConjugacyClassesSubgroups(g),Representative);
[ Group([  ]), Group([ f3 ]), Group([ f2 ]), Group([ f2*f3 ]),
Group([ f2, f3 ]), Group([ f2, f3, f1 ]), Group([ f1 ]), Group([ f1,
f3 ]),
Group([ f1, f2 ]) ]
gap> List(c,Size);
[ 1, 3, 3, 3, 9, 18, 2, 6, 6 ]
gap> MaximalSubgroupsLattice(l);
[ [  ], [ [ 1, 1 ] ], [ [ 1, 1 ] ], [ [ 1, 1 ] ],
[ [ 4, 1 ], [ 4, 2 ], [ 3, 1 ], [ 2, 1 ] ], [ [ 5, 1 ] ], [ [ 1, 1 ]
],
[ [ 7, 1 ], [ 7, 2 ], [ 7, 3 ], [ 2, 1 ] ], [ [ 8, 1 ], [ 6, 1 ] ] ]
gap>
--------------------------------------------
```

The output seems to tell that the class #6, or order 6, has class #6
which is the whole group, as a maximal subgroup. What is wrong?

```--

XIAO Gang (~{P\$8U~})                          xiao@unice.fr
http://pcmath126.unice.fr/xiao.html
```