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C₉×#272 #92298

order	486
isoclinism	isoclinic class of #272
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

Splittings

Fitting, Sylow	C₉×H(3,𝔽₃) ⋊ C₂
derived	H(3,𝔽₃) ⋊ C₂×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₉	C₃⋊D₃
commutator, hypocenter	H(3,𝔽₃)	C₂×C₉
Frattini, socle	C₃²	C₃×C₃⋊D₃
Fitting	C₉×H(3,𝔽₃)	C₂
prime radical	C₃×#272	C₃
cosocle	C₃×H(3,𝔽₃)	C₂×C₃
LCS	G ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₃×C₉

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 81

A minimal faithful permutation representation — 3 generators on 18 points:

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

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

derived subgroup of	(((C₃⋊D₃)⋊C₃)⋊C₂)⋊D₉, #1088⋊D₉, C₉⋊SU(3,𝔽₂)
maximal subgroup of	C₉×#1088, C₉⋊#1088, C₉×((C₃⋊D₃)⋊C₃)⋊C₂, …
maximal normal subgroup of	C₉×#1088, C₉⋊#1088, C₉×((C₃⋊D₃)⋊C₃)⋊C₂, …
maximal quotient of	C₉×#1084, C₂×C₉×#272, C₉×#4181, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 143);