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C₃×C₉×D₉ #92246

order	486
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₉ · Schur multiplier (H₂) = C₃

Aliases

C₃×C₉×D₉

Splittings

Fitting, Sylow	C₃×C₉² ⋊ C₂
derived	C₉ ⋊ C₂×C₃×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₉	D₉
commutator, hypocenter	C₉	C₂×C₃×C₉
Frattini	C₃²	C₃²×D₃
Fitting	C₃×C₉²	C₂
socle	C₃³	C₃×D₃
prime radical	C₃²×D₉	C₃
cosocle	C₃×C₉	C₂×C₃²
LCS	G ▷ C₉
UCS	C₁ ◁ C₃×C₉

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 54

A minimal faithful permutation representation — 2 generators on 21 points:

(4,5,7,6,8,10,9,11,12)(14,16)(15,19)(17,20)(18,21);(1,2,3)(13,18,16,15,20,17,19,14,21)

Conjugacy classes & character table

162 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×D₉², D₃×C₉×D₉, D₉×C₃⋊D₉, …
maximal normal subgroup of	C₃×D₉², D₃×C₉×D₉, D₉×C₃⋊D₉, …
maximal quotient of	C₃×C₉×Dic₉, C₂×C₃×C₉×D₉, C₉²×D₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 91);