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D₅×C₉⋊C₉ #11717600

order	810
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	D₅×C₉⋊C₉
unambiguous semidirect product	C₅⋊(C₂×C₉⋊C₉)
unambiguous semidirect product	(C₉×D₅)⋊C₉

Splittings

Fitting, Hall	C₅×C₉⋊C₉ ⋊ C₂
Sylow	C₅ ⋊ C₂×C₉⋊C₉

Subgroups

	subgroup	G/H
center, Frattini	C₃²	C₃²×D₅
commutator	C₃×C₅	C₂×C₃×C₉
Fitting	C₅×C₉⋊C₉	C₂
socle, cosocle	C₃²×C₅	C₂×C₃²
prime radical	C₃²×D₅	C₃²
hypercenter	C₉⋊C₉	D₅
hypocenter	C₅	C₂×C₉⋊C₉
LCS	G ▷ C₃×C₅ ▷ C₅
UCS	C₁ ◁ C₃² ◁ C₉⋊C₉

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 405

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	AGL(1,𝔽₅)×C₉⋊C₉, (C₉⋊C₉)⋊AGL(1,𝔽₅), D₅×D₉⋊C₉, …
maximal normal subgroup of	AGL(1,𝔽₅)×C₉⋊C₉, (C₉⋊C₉)⋊AGL(1,𝔽₅), D₅×D₉⋊C₉, …
maximal quotient of	Dic₅×C₉⋊C₉, C₂×D₅×C₉⋊C₉, D₅×#6875

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(810, 7);