Heisenberg groups Hep
For an odd prime p, the Heisenberg group Hep is the unique non-abelian
group of order p3 of exponent p. It is the p-Sylow of GL3(𝔽p),
and is a special case of an extraspecial group Hep=p+1+2.
(The only other non-abelian group of order p3 is
p-1+2=Cp2⋊Cp,
of exponent p2.)
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