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C₃×#13048733 #72259709

order	3888
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³×C₃

Aliases

C₃×#13048733

Splittings

Fitting	C₂²×C₃²×H(3,𝔽₃) ⋊ C₂²
Sylow	C₃²×H(3,𝔽₃) ⋊ C₂×D₄

Subgroups

	subgroup	G/H
center	C₂×C₃	C₂×((C₃⋊D₃)⋊C₃)⋊D₃
commutator, cosocle	C₂×C₃×H(3,𝔽₃)	C₂³×C₃
Frattini	C₂×C₃	C₂×C₃×D₃×C₃⋊D₃
Fitting	C₂²×C₃²×H(3,𝔽₃)	C₂²
socle	C₂×C₃³	C₂×D₃²
hypercenter	C₂²×C₃	((C₃⋊D₃)⋊C₃)⋊D₃
hypocenter	C₃×H(3,𝔽₃)	C₂×C₃×D₄
LCS	G ▷ C₂×C₃×H(3,𝔽₃) ▷ C₃×H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₃ ◁ C₂²×C₃

2412 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 72

Conjugacy classes & character table

189 conjugacy classes — view the full character table.

Relationships

maximal subgroup of

GAP

Past the SmallGroups library coverage — no SmallGroups id.