Finite Group Databasebeta

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D₉×#3018 #72252913

order	2304
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹⁰

Aliases

Splittings

Fitting	C₉×#3018 ⋊ C₂
Sylow	C₉ ⋊ C₂×#3018

Subgroups

	subgroup	G/H
center	C₄	D₉×#120
commutator, cosocle	C₂×C₄×C₉	C₂⁵
Frattini	C₂×C₃×C₄	C₂⁴×D₃
Fitting	C₉×#3018	C₂
socle	C₂×C₃	C₂×D₃×#120
hypercenter	#3018	D₉
hypocenter	C₉	C₂×#3018
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #3018

7275 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 144

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₉×#61110
maximal normal subgroup of	D₉×#61110

GAP

Past the SmallGroups library coverage — no SmallGroups id.