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#28356602

order	13851
automorphism	?
homology	Abelianization (H₁) = C₃⁴ · Schur multiplier (H₂) = C₃⁶

Aliases

No aliases for this group.

Splittings

Fitting	C₃²×C₁₉×H(3,𝔽₃) ⋊ C₃
Sylow	C₁₉ ⋊ #10624930

Subgroups

	subgroup	G/H
center	C₃	C₃²×C₃²⋊(C₁₉⋊C₃)
commutator, cosocle	C₃²×C₁₉	C₃⁴
Frattini	C₃²	C₃³×C₁₉⋊C₃
Fitting	C₃²×C₁₉×H(3,𝔽₃)	C₃
socle	C₃×C₁₉	C₃²×H(3,𝔽₃)
hypercenter	C₃²×H(3,𝔽₃)	C₁₉⋊C₃
hypocenter	C₁₉	#10624930
LCS	G ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃×H(3,𝔽₃) ◁ C₃²×H(3,𝔽₃)

1118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 513

Polycyclic presentation:

3^6,19|b^a=be,e^a=ef,g^a=g^7,d^c=df

Conjugacy classes & character table

699 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 3966);