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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