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C₃×C₆₇⋊C₂₇ #19129463

order	5427
automorphism	?
homology	Abelianization (H₁) = C₃×C₂₇ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₆₇⋊C₂₇
unambiguous semidirect product	(C₃×C₆₇)⋊C₂₇

Splittings

C₆₇ ⋊ C₃×C₂₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₉	C₆₇⋊C₃
commutator, hypocenter	C₆₇	C₃×C₂₇
Frattini	C₉	C₃×C₆₇⋊C₃
Fitting	C₃×C₉×C₆₇	C₃
socle	C₃²×C₆₇	C₉
LCS	G ▷ C₆₇
UCS	C₁ ◁ C₃×C₉

28 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

675 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₇×C₆₇⋊C₉, C₉×C₆₇⋊C₂₇, #30653812, …
maximal normal subgroup of	C₂₇×C₆₇⋊C₉, C₉×C₆₇⋊C₂₇, #30653812, …
maximal quotient of	C₉×C₆₇⋊C₂₇, C₃²⋊(C₆₇⋊C₂₇), #30653839, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5427, 24);