Finite Group Databasebeta

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C₉×D₉⋊H(3,𝔽₃) #72243807

order	4374
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₉ · Schur multiplier (H₂) = C₃⁴

Aliases

C₉×D₉⋊H(3,𝔽₃)

Splittings

C₉×C₉⋊H(3,𝔽₃) ⋊ C₂

Subgroups

	subgroup	G/H
center	C₃×C₉	C₃×AGL(1,ℤ/9)
commutator	C₃×C₉	C₂×C₃²×C₉
Frattini, socle	C₃³	C₃³×D₃
Fitting	C₉×C₉⋊H(3,𝔽₃)	C₂
prime radical	C₃×D₉⋊H(3,𝔽₃)	C₃
cosocle	C₃²×C₉	C₂×C₃³
hypercenter	C₃²×C₉	AGL(1,ℤ/9)
hypocenter	C₉	C₂×C₉×H(3,𝔽₃)
LCS	G ▷ C₃×C₉ ▷ C₉
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉

1183 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 162

Conjugacy classes & character table

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

Relationships

maximal subgroup of	#72243853, D₉×D₉⋊H(3,𝔽₃), C₉×D₉⋊((C₃⋊D₃)⋊C₃), …
maximal normal subgroup of	#72243853, D₉×D₉⋊H(3,𝔽₃), C₉×D₉⋊((C₃⋊D₃)⋊C₃), …

GAP

Past the SmallGroups library coverage — no SmallGroups id.