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AGL(1,ℤ/9)×C₉⋊C₉ #72243183

order	4374
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₉ · Schur multiplier (H₂) = C₃³

Aliases

AGL(1,ℤ/9)×C₉⋊C₉

Splittings

3₋¹⁺²×C₉⋊C₉ ⋊ C₂

Subgroups

	subgroup	G/H
center	C₃²	C₃²×AGL(1,ℤ/9)
commutator	C₃×C₉	C₂×C₃²×C₉
Frattini, socle	C₃³	C₃³×D₃
Fitting	3₋¹⁺²×C₉⋊C₉	C₂
prime radical	C₃²×AGL(1,ℤ/9)	C₃²
cosocle	C₃²×C₉	C₂×C₃³
hypercenter	C₉⋊C₉	AGL(1,ℤ/9)
hypocenter	C₉	C₂×C₃×C₉⋊C₉
LCS	G ▷ C₃×C₉ ▷ C₉
UCS	C₁ ◁ C₃² ◁ C₉⋊C₉

985 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 486

Conjugacy classes & character table

330 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	AGL(1,ℤ/9)×#6900, AGL(1,ℤ/9)×D₉⋊C₉
maximal normal subgroup of	AGL(1,ℤ/9)×#6900, AGL(1,ℤ/9)×D₉⋊C₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.