Is there any command in GAP to generate a Hamiltonian group of an order given?

I'm looking for in GAP-Reference Manual, but i don't find anything.

Bujalance, Etayo & Gamboa define a Hamiltonian group like a kind of group wich all subgroups are normal subgroups.

  • $\begingroup$ Regarding the structure of a H. group, it would be a case that you give any arbitrary order and want GAP to call the group of the kind. $\endgroup$
    – Mikasa
    Jan 29, 2016 at 19:45
  • 3
    $\begingroup$ There isn't such a function per se, but as the structure of Hamiltonian groups is just a direct product of $Q_8$ with a suitable abelian group, they could be constructed easily that way. $\endgroup$
    – ahulpke
    Jan 29, 2016 at 23:05
  • $\begingroup$ Ok, thanks for your comments. $\endgroup$ Jan 29, 2016 at 23:21
  • $\begingroup$ This function may be useful to determinate if the group is hamiltonian: Hamiltonian:=function(G) ls:=AllSubgroups(G);; nm:=Filtered(ls,n-> IsNormal(G,n));; a:=nm=ls;; Print(a); end; $\endgroup$ May 31, 2019 at 18:37


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