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H(3,𝔽₃)×C₂²⋊C₉ #11757831

order	972
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉ · Schur multiplier (H₂) = C₂×C₃⁴

Aliases

H(3,𝔽₃)×C₂²⋊C₉

Splittings

C₂² ⋊ C₉×H(3,𝔽₃)

Subgroups

	subgroup	G/H
center, Frattini	C₃²	C₃²×A₄
commutator	C₂²×C₃	C₃²×C₉
Fitting, prime radical	C₂²×C₃×H(3,𝔽₃)	C₃
socle, cosocle	C₂²×C₃²	C₃³
hypercenter	C₃×H(3,𝔽₃)	A₄
hypocenter	C₂²	C₉×H(3,𝔽₃)
LCS	G ▷ C₂²×C₃ ▷ C₂²
UCS	C₁ ◁ C₃² ◁ C₃×H(3,𝔽₃)

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 162

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

derived subgroup of	#14518115
maximal subgroup of	H(3,𝔽₃)×(C₂²⋊C₉)⋊C₂, #14518061, #14518115, …
maximal normal subgroup of	H(3,𝔽₃)×(C₂²⋊C₉)⋊C₂, #14518061, #14518115, …
maximal quotient of	H(3,𝔽₃)×Q₈⋊C₉, C₂×H(3,𝔽₃)×C₂²⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(972, 556);