Finite Group Databasebeta

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D₉×AGL(1,ℤ/16) #72244307

order	2304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

D₉×AGL(1,ℤ/16)

Splittings

Fitting	C₉×AGL(1,ℤ/16) ⋊ C₂
Sylow	C₉ ⋊ C₂×AGL(1,ℤ/16)

Subgroups

	subgroup	G/H
center	C₂	D₉×#442
commutator	C₈×C₉	C₂³×C₄
Frattini	C₂×C₃×C₈	C₂³×D₃
Fitting	C₉×AGL(1,ℤ/16)	C₂
socle	C₂×C₃	D₃×#442
prime radical	D₉×#509	C₂
cosocle	C₂×C₈×C₉	C₂⁴
hypercenter	AGL(1,ℤ/16)	D₉
hypocenter	C₉	C₂×AGL(1,ℤ/16)
LCS	G ▷ C₈×C₉ ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ AGL(1,ℤ/16)

1065 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 144

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	AGL(1,ℤ/9)×AGL(1,ℤ/16)
maximal normal subgroup of	AGL(1,ℤ/9)×AGL(1,ℤ/16)

GAP

Past the SmallGroups library coverage — no SmallGroups id.