[GAP Forum] A question of GAP

[Max Horn]

Dear Rulin,

> On 02 Feb 2017, at 12:45, Rulin Shen <shenrulin at hotmail.com> wrote:
> 
> Dear Prof. Cameron,
> 
> Thanks for your answer. Sorry to my question's condition should be |H^c \cap Hg|=|G|/4, where H^c the complement of H in G, and all g. So sorry!

Then the problem seems to become trivial: H^c \cap Hg either equals the empty set (when g\in H) or else Hg. By your condition, the former case must not occur for any g\neq 1, thus H must be trivial. But then |H^c \cap Hg|=1 for g\neq 1, thus |G|=4 and G is either C_4 or C_2 x C_2.

Cheers,
Max