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H(3,𝔽₃)×C₂₇₇ #21418798

order	7479
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₂₇₇ · Schur multiplier (H₂) = C₃²

Aliases

direct product	H(3,𝔽₃)×C₂₇₇
unambiguous semidirect product	C₃²⋊(C₃×C₂₇₇)

Subgroups

	subgroup	G/H
center, socle	C₃×C₂₇₇	C₃²
commutator, Frattini	C₃	C₃²×C₂₇₇
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₂₇₇ ◁ G

22 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3047 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#36376235, #36376238, #36376241, …
maximal subgroup of	AΣL(1,𝔽₂₇)×C₂₇₇, #731×C₂₇₇, #732×C₂₇₇, …
maximal normal subgroup of	AΣL(1,𝔽₂₇)×C₂₇₇, #731×C₂₇₇, #732×C₂₇₇, …
maximal quotient of	C₃²⋊C₉×C₂₇₇, AΣL(1,𝔽₂₇)×C₂₇₇, #731×C₂₇₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7479, 3);