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C₃³×C₆₇⋊C₃ #19129488

order	5427
isoclinism	isoclinic class of C₆₇⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃⁴ · Schur multiplier (H₂) = C₃⁶

Aliases

direct product	C₃³×C₆₇⋊C₃
unambiguous semidirect product	C₆₇⋊C₃⁴
unambiguous semidirect product	(C₃×C₆₇)⋊C₃³

Splittings

Fitting, socle	C₃³×C₆₇ ⋊ C₃
derived, Sylow	C₆₇ ⋊ C₃⁴

Subgroups

	subgroup	G/H
center, hypercenter	C₃³	C₆₇⋊C₃
commutator, hypocenter	C₆₇	C₃⁴
Frattini	C₁	G
Fitting, socle	C₃³×C₆₇	C₃
LCS	G ▷ C₆₇
UCS	C₁ ◁ C₃³

424 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

675 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#30653817, C₃²⋊C₉×C₆₇⋊C₃, C₃×(C₃×C₆₇⋊C₃)⋊C₉, …
maximal normal subgroup of	#30653817, C₃²⋊C₉×C₆₇⋊C₃, C₃×(C₃×C₆₇⋊C₃)⋊C₉, …
maximal quotient of	C₃²×C₉×C₆₇⋊C₃, C₃³×C₆₇⋊C₉, C₃×H(3,𝔽₃)×C₆₇⋊C₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5427, 49);