Finite Group Databasebeta

← Prev (#28355907) Next (#28355909) →

C₃×H(3,𝔽₃)×#4294 #28355908

order	13851
automorphism	?
homology	Abelianization (H₁) = C₃³×C₉ · Schur multiplier (H₂) = C₃⁷

Aliases

C₃×H(3,𝔽₃)×#4294

Splittings

C₁₉ ⋊ C₃×C₉×H(3,𝔽₃)

Subgroups

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

1688 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, 3272);