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H(3,𝔽₃)×#10587020 #28356980

order	13851
automorphism	?
homology	Abelianization (H₁) = C₃²×C₂₇ · Schur multiplier (H₂) = C₃⁴

Aliases

H(3,𝔽₃)×#10587020

Splittings

C₁₉ ⋊ C₂₇×H(3,𝔽₃)

Subgroups

	subgroup	G/H
center, Frattini	C₃²	C₃²×#4296
commutator	C₃×C₁₉	C₃²×C₂₇
Fitting, prime radical	C₃×C₁₉×H(3,𝔽₃)	C₉
socle	C₃²×C₁₉	C₃²×C₉
cosocle	C₃×#4294	C₃³
hypercenter	C₃×H(3,𝔽₃)	#4296
hypocenter	C₁₉	C₂₇×H(3,𝔽₃)
LCS	G ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₃×H(3,𝔽₃)

292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4617

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 4344);