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#28357047

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

Aliases

No aliases for this group.

Splittings

Fitting	C₃×C₁₉×H(3,𝔽₃) ⋊ C₉
Sylow	C₁₉ ⋊ #10624862

Subgroups

	subgroup	G/H
center, Frattini	C₃	C₃³×#4296
commutator, socle	C₃×C₁₉	C₃³×C₉
Fitting	C₃×C₁₉×H(3,𝔽₃)	C₉
prime radical	C₃×H(3,𝔽₃)×C₁₉⋊C₃	C₃
cosocle	C₃×C₁₉⋊C₃	C₃⁴
hypercenter	C₃×H(3,𝔽₃)	#4296
hypocenter	C₁₉	#10624862
LCS	G ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃×H(3,𝔽₃)

1178 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 513

Polycyclic presentation:

3^6,19|a^3=f,b^a=be,d^a=de,g^a=g^4,c^b=ce,g^f=g^7

Conjugacy classes & character table

315 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 4411);