Finite Group Databasebeta

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D₉×#1790 #72269020

order	2304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

Splittings

Fitting	C₉×#1790 ⋊ C₂
Sylow	C₉ ⋊ C₂×#1790

Subgroups

	subgroup	G/H
center	C₂²	D₉×#120
commutator	C₂³×C₉	C₂³×C₄
Frattini	C₂⁴×C₃	C₂³×D₃
Fitting	C₉×#1790	C₂
socle	C₂²×C₃	D₃×#120
prime radical	C₂×D₉×H(5,𝔽₂)	C₂
cosocle	C₂⁴×C₉	C₂⁴
hypercenter	#1790	D₉
hypocenter	C₉	C₂×#1790
LCS	G ▷ C₂³×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #1790

6603 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 288

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.