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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.

Angel Blasco
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  • 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. – Mikasa Jan 29 '16 at 19:45
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    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. – ahulpke Jan 29 '16 at 23:05
  • Ok, thanks for your comments. – Angel Blasco Jan 29 '16 at 23:21
  • 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; – Angel Blasco May 31 '19 at 18:37

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