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H(3,𝔽₃)⋊(C₄₃⋊C₉) #23782720

order	10449
automorphism	?
homology	Abelianization (H₁) = C₃×C₉ · Schur multiplier (H₂) = C₃²

Aliases

unambiguous semidirect product

H(3,𝔽₃)⋊(C₄₃⋊C₉)

Splittings

C₄₃ ⋊ H(3,𝔽₃)⋊C₉

Subgroups

	subgroup	G/H
center	C₃²	C₃²⋊(C₄₃⋊C₃)
commutator	C₃²×C₄₃	C₃×C₉
Frattini	C₃³	C₃×C₄₃⋊C₃
Fitting, prime radical	C₃×H(3,𝔽₃)×C₄₃	C₃
socle	C₃²×C₄₃	H(3,𝔽₃)
cosocle	C₃³×C₄₃	C₃²
hypercenter	C₃×H(3,𝔽₃)	C₄₃⋊C₃
hypocenter	C₄₃	H(3,𝔽₃)⋊C₉
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃×H(3,𝔽₃)

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

3^5,43|a^3=d,b^a=bc,c^a=ce,f^a=f^36,c^b=ce

Conjugacy classes & character table

513 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₄₃⋊C₃×H(3,𝔽₃)⋊C₉, C₃×H(3,𝔽₃)⋊(C₄₃⋊C₉), #44533417, …
maximal normal subgroup of	C₄₃⋊C₃×H(3,𝔽₃)⋊C₉, C₃×H(3,𝔽₃)⋊(C₄₃⋊C₉), #44533417, …
maximal quotient of	H(3,𝔽₃)⋊(C₄₃⋊C₂₇), #44531901, #44531903, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10449, 104);