[GAP Forum] On Small group (81,10)

[Benjamin Sambale]

Dear Siddhartha,

I'm not sure if this helps, but your group has maximal nilpotency class 
and those groups were classified by Blackburn (for p=3). Using the 
notation from [Parker-Semeraro, Fusion systems on maximal class 3-groups 
of rank two revisited] your group seems to be B(4;0,0,1).

Best wishes,
Benjamin

Am 14.07.20 um 22:18 schrieb Siddhartha Sarkar:
> Dear Forum,
>
> I am trying to get a bit more information about the origin of the group
> SmallGroup(81,10) of order 81 in the small group library.
>
> The gap command shows:
>
> gap> StructureDescription(g);
> "C3 . ((C3 x C3) : C3) = (C3 x C3) . (C3 x C3)"
>
> >From the Fp-presentation with four generators it is not so easy to look at
> it. Does the product come from an amalgam relation from a group of order
> 243?
>
> Best regards,
> Siddhartha
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