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H(3,𝔽₃)×C₁₈₁⋊C₃ #28412643

order	14661
automorphism	?
homology	Abelianization (H₁) = C₃³ · Schur multiplier (H₂) = C₃⁴

Aliases

H(3,𝔽₃)×C₁₈₁⋊C₃

Splittings

Fitting	H(3,𝔽₃)×C₁₈₁ ⋊ C₃
Sylow	C₁₈₁ ⋊ C₃×H(3,𝔽₃)

Subgroups

	subgroup	G/H
center, Frattini	C₃	C₃²×C₁₈₁⋊C₃
commutator, socle, cosocle	C₃×C₁₈₁	C₃³
Fitting	H(3,𝔽₃)×C₁₈₁	C₃
hypercenter	H(3,𝔽₃)	C₁₈₁⋊C₃
hypocenter	C₁₈₁	C₃×H(3,𝔽₃)
LCS	G ▷ C₃×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₃ ◁ H(3,𝔽₃)

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1629

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14661, 40);