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C₃×H(3,𝔽₃)×C₆₇ #19129451

order	5427
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃³×C₆₇ · Schur multiplier (H₂) = C₃⁴

Aliases

direct product	C₃×H(3,𝔽₃)×C₆₇
unambiguous semidirect product	C₃²⋊(C₃²×C₆₇)

Subgroups

	subgroup	G/H
center, socle	C₃²×C₆₇	C₃²
commutator, Frattini	C₃	C₃³×C₆₇
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₆₇ ◁ G

112 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2211 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#30653792, #30653795, #30653801, …
maximal subgroup of	C₆₇×#6856, C₆₇×#6857, C₆₇×#6859, …
maximal normal subgroup of	C₆₇×#6856, C₆₇×#6857, C₆₇×#6859, …
maximal quotient of	C₃×C₆₇×C₃²⋊C₉, C₉×H(3,𝔽₃)×C₆₇, C₆₇×C₃²⋊H(3,𝔽₃), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5427, 12);