Finite Group Databasebeta

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D₉×#3184 #72244428

order	2304
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁷×C₄

Aliases

Splittings

Fitting	C₉×#3184 ⋊ C₂
Sylow	C₉ ⋊ C₂×#3184

Subgroups

	subgroup	G/H
center	C₂²	C₂²×D₄×D₉
commutator, cosocle	C₂×C₄×C₉	C₂⁵
Frattini	C₂×C₃×C₄	C₂⁴×D₃
Fitting	C₉×#3184	C₂
socle	C₂²×C₃	C₂²×D₃×D₄
hypercenter	#3184	D₉
hypocenter	C₉	C₂×#3184
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3184

3771 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 576

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₉×#19745, AGL(1,ℤ/9)×#3184
maximal normal subgroup of	D₉×#19745, AGL(1,ℤ/9)×#3184

GAP

Past the SmallGroups library coverage — no SmallGroups id.