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C₃²×H(3,𝔽₃)×C₁₃⋊C₃ #23748604

order	9477
automorphism	?
homology	Abelianization (H₁) = C₃⁵ · Schur multiplier (H₂) = C₃¹¹

Aliases

C₃²×H(3,𝔽₃)×C₁₃⋊C₃

Splittings

Fitting	C₃²×C₁₃×H(3,𝔽₃) ⋊ C₃
Sylow	C₁₃ ⋊ C₃³×H(3,𝔽₃)

Subgroups

	subgroup	G/H
center	C₃³	C₃²×C₁₃⋊C₃
commutator, cosocle	C₃×C₁₃	C₃⁵
Frattini	C₃	C₃⁴×C₁₃⋊C₃
Fitting	C₃²×C₁₃×H(3,𝔽₃)	C₃
socle	C₃³×C₁₃	C₃³
hypercenter	C₃²×H(3,𝔽₃)	C₁₃⋊C₃
hypocenter	C₁₃	C₃³×H(3,𝔽₃)
LCS	G ▷ C₃×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₃³ ◁ C₃²×H(3,𝔽₃)

11744 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

693 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9477, 4013);