Finite Group Databasebeta

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C₉×#13095331 #28355917

order	13851
automorphism	?
homology	Abelianization (H₁) = C₃³×C₉ · Schur multiplier (H₂) = C₃⁵

Aliases

C₉×#13095331

Splittings

C₁₉ ⋊ C₉×#737

Subgroups

	subgroup	G/H
center	C₃×C₉	C₃²×C₁₉⋊C₃
commutator	C₃×C₁₉	C₃³×C₉
Frattini	C₃²	C₃³×C₁₉⋊C₃
Fitting	C₉×C₁₉×H(3,𝔽₃)	C₃
socle, cosocle	C₃²×C₁₉	C₃⁴
prime radical	C₃×C₁₉×H(3,𝔽₃)	C₃²
hypercenter	C₉×H(3,𝔽₃)	C₁₉⋊C₃
hypocenter	C₁₉	C₉×#737
LCS	G ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃×C₉ ◁ C₉×H(3,𝔽₃)

986 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4617

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 3281);