Finite Group Databasebeta

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D₃×C₉×(C₃⋊D₃)⋊C₃ #72244100

order	2916
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₉ · Schur multiplier (H₂) = C₂×C₃²

Aliases

D₃×C₉×(C₃⋊D₃)⋊C₃

Splittings

Fitting, Sylow	C₃×C₉×H(3,𝔽₃) ⋊ C₂²
derived	C₃³ ⋊ C₂²×C₃×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₃×(C₃⋊D₃)⋊C₃
commutator, hypocenter	C₃³	C₂²×C₃×C₉
Frattini	C₃²	C₃²×D₃²
Fitting	C₃×C₉×H(3,𝔽₃)	C₂²
socle	C₃³	C₂×C₃²×D₃
prime radical	C₃×D₃×(C₃⋊D₃)⋊C₃	C₃
cosocle	C₃⁴	C₂²×C₃²
LCS	G ▷ C₃³
UCS	C₁ ◁ C₉

736 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 108

Conjugacy classes & character table

270 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₉⋊((C₃⋊D₃)⋊C₃), #72254045, D₃×3₋¹⁺²×(C₃⋊D₃)⋊C₃, …
maximal normal subgroup of	D₃×3₋¹⁺²×(C₃⋊D₃)⋊C₃, D₃×D₉×(C₃⋊D₃)⋊C₃
maximal quotient of	C₉×D₉⋊((C₃⋊D₃)⋊C₃), #72254045, #72269264

GAP

Past the SmallGroups library coverage — no SmallGroups id.