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I'm new to GAP, and I tried to adjust the code that ahulpke wrote at the link: Faithful permutation representation

to construct a faithful representation of the group $C_2\times (C_4\rtimes C_4)$ using "three orbits". I adujested the code by adding a subgroup $H_3$, and

cos:=Concatenation(RightCosets(G,H1),RightCosets(G,H2),RightCosets(G,H3));

But it didn’t work with me and I believe I made an error.

Do any GAP's codes exist that will give me a faithful permutation representation of a group with respect to provided three subgroups, where the intersection of both subgroups has a trivial core?

I appreciate your help, thank you!

sonmar bardish
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  • What did you do (concrete input and commands used) and what went wrong (wrong result? Error message?) – ahulpke Jan 02 '23 at 00:21
  • gap> f := FreeGroup( "a", "b","c");; gap> h := f / [ f.1^2, f.2^4,f.3^4,f.1^-1f.2^-1f.1f.2,f.1^-1f.3^-1f.1f.3,f.3f.2f.3^-1*f.2]; <fp group on the g
    enerators [ a, b, c ]> gap> H1:=SmallGroup(16,2); <pc group of size 16 with 4 generators> gap> H2:=SmallGroup(8,2); <pc group of size 8 with 3 generators> gap> H3:=SmallGroup(8,2); <pc group of size 8 with 3 generators> gap> cos:=Concatenation(RightCosets(G,H1),RightCosets(G,H2),RightCosets(G,H3)); Error, Variable: 'G' must
    have a value not in any functio
    n at stdin:9     – sonmar bardish Jan 02 '23 at 01:49
  • @ahulpke, above what I did and the message error that I got. – sonmar bardish Jan 02 '23 at 02:01
  • I was trying to find the faithful permutation representation, by utilising the action on the right cosets of $H1= <b, c>$, $H2= <a, c>$ and $H3= <a, b>$. – sonmar bardish Jan 02 '23 at 11:07
  • You need to use the correct variable names, your group is called h, not G, and you need to use actual subgroups of your group, not just groups that are isomorphic to them. – ahulpke Jan 03 '23 at 03:51
  • @ahulpke, thank you for brining this to my attention, I corrected the code and is working now. – sonmar bardish Jan 03 '23 at 13:42

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