Finite Group Databasebeta

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D₉×#11717375 #72247612

order	14400
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶

Aliases

D₉×#11717375

Splittings

Fitting	C₂²×C₅²×C₉ ⋊ C₂²×C₄
Hall	C₅²×C₉ ⋊ C₂×C₄×D₄
Sylow	C₅² ⋊ C₄×D₄×D₉
Sylow	C₉ ⋊ C₂×#11717375

Subgroups

	subgroup	G/H
center	C₂	C₂×D₉×D₅⋊AGL(1,𝔽₅)
commutator	C₂×C₅²×C₉	C₂³×C₄
Frattini	C₂×C₃	C₂×D₃×D₅⋊AGL(1,𝔽₅)
Fitting	C₂²×C₅²×C₉	C₂²×C₄
socle	C₂×C₃×C₅²	C₂²×C₄×D₃
prime radical	D₉×#87886	C₂
cosocle	C₂×C₉×C₅⋊D₅	C₂⁴
hypercenter	C₂²	D₉×D₅⋊AGL(1,𝔽₅)
hypocenter	C₅²×C₉	C₂×C₄×D₄
LCS	G ▷ C₂×C₅²×C₉ ▷ C₅²×C₉
UCS	C₁ ◁ C₂ ◁ C₂²

3264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 180

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	AGL(1,ℤ/9)×#11717375
maximal normal subgroup of	AGL(1,ℤ/9)×#11717375

GAP

Past the SmallGroups library coverage — no SmallGroups id.