H(3,𝔽₃)×C₃₆₇ #23755299

order	9909
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₃₆₇ · Schur multiplier (H₂) = C₃²

Aliases

direct product	H(3,𝔽₃)×C₃₆₇
unambiguous semidirect product	C₃²⋊(C₃×C₃₆₇)

	subgroup	G/H
center, socle	C₃×C₃₆₇	C₃²
commutator, Frattini, cosocle	C₃	C₃²×C₃₆₇
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₃₆₇ ◁ G

22 conjugacy classes of subgroups.

4037 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9909, 3);