[seqfan] Re: Symmetric groups

[W. Edwin Clark]

No, S_5 does not have a subgroup of order 15 says GAP. Here's  GAP code
which gives the orders
of the subgroups of S_5:

G:=SymmetricGroup(5);;
C:=ConjugacyClassesSubgroups(G);;
OrdersSubgroupsS_5:=Set(ListX(C,t->Size(Representative(t))));

                [ 1, 2, 3, 4, 5, 6, 8, 10, 12, 20, 24, 60, 120 ]

On Sun, Nov 27, 2016 at 4:14 PM, Frank Adams-Watters <franktaw at netscape.net>
wrote:

> If n divides m!, does the symmetric group S_m always have a subgroup of
> order n?
>
> If so, a comment should be added to A002034 that a(n) is the genus of the
> smallest symmetric group with a subgroup of order n. If not, where is the
> first exception? (8 in S_4?) Is the sequence so described in the OEIS? If
> not, it should be added.
>
> Franklin T. Adams-Watters
>
>
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