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H(3,𝔽₃)×C₃₃₁ #22582050

order	8937
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₃₃₁ · Schur multiplier (H₂) = C₃²

Aliases

direct product	H(3,𝔽₃)×C₃₃₁
unambiguous semidirect product	C₃²⋊(C₃×C₃₃₁)

Subgroups

	subgroup	G/H
center, socle	C₃×C₃₃₁	C₃²
commutator, Frattini	C₃	C₃²×C₃₃₁
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₃₃₁ ◁ G

22 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3641 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#40999772, #40999775, #40999778, …
maximal subgroup of	AΣL(1,𝔽₂₇)×C₃₃₁, #731×C₃₃₁, #732×C₃₃₁, …
maximal normal subgroup of	AΣL(1,𝔽₂₇)×C₃₃₁, #731×C₃₃₁, #732×C₃₃₁, …
maximal quotient of	C₃²⋊C₉×C₃₃₁, AΣL(1,𝔽₂₇)×C₃₃₁, #731×C₃₃₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8937, 3);