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C₃²×H(3,𝔽₃)×C₁₉⋊C₃ #28356649

order	13851
automorphism	?
homology	Abelianization (H₁) = C₃⁵ · Schur multiplier (H₂) = C₃¹¹

Aliases

C₃²×H(3,𝔽₃)×C₁₉⋊C₃

Splittings

Fitting	C₃²×C₁₉×H(3,𝔽₃) ⋊ C₃
Sylow	C₁₉ ⋊ C₃³×H(3,𝔽₃)

Subgroups

	subgroup	G/H
center	C₃³	C₃²×C₁₉⋊C₃
commutator, cosocle	C₃×C₁₉	C₃⁵
Frattini	C₃	C₃⁴×C₁₉⋊C₃
Fitting	C₃²×C₁₉×H(3,𝔽₃)	C₃
socle	C₃³×C₁₉	C₃³
hypercenter	C₃²×H(3,𝔽₃)	C₁₉⋊C₃
hypocenter	C₁₉	C₃³×H(3,𝔽₃)
LCS	G ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃³ ◁ C₃²×H(3,𝔽₃)

11744 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1539

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, 4013);