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H(3,𝔽₃)⋊#4294 #17987343

order	4617
automorphism	?
homology	Abelianization (H₁) = C₃×C₉ · Schur multiplier (H₂) = C₃²

Aliases

unambiguous semidirect product

H(3,𝔽₃)⋊#4294

Splittings

C₁₉ ⋊ H(3,𝔽₃)⋊C₉

Subgroups

	subgroup	G/H
center	C₃²	C₃²⋊(C₁₉⋊C₃)
commutator	C₃²×C₁₉	C₃×C₉
Frattini	C₃³	C₃×C₁₉⋊C₃
Fitting, prime radical	C₃×C₁₉×H(3,𝔽₃)	C₃
socle	C₃²×C₁₉	H(3,𝔽₃)
cosocle	C₃³×C₁₉	C₃²
hypercenter	C₃×H(3,𝔽₃)	C₁₉⋊C₃
hypocenter	C₁₉	H(3,𝔽₃)⋊C₉
LCS	G ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃×H(3,𝔽₃)

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1539

Polycyclic presentation:

3^5,19|a^3=d,b^a=bc,c^a=ce,f^a=f^7,c^b=ce

Conjugacy classes & character table

249 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉⋊C₃×H(3,𝔽₃)⋊C₉, C₃×H(3,𝔽₃)⋊#4294, #28354676, …
maximal normal subgroup of	C₁₉⋊C₃×H(3,𝔽₃)⋊C₉, C₃×H(3,𝔽₃)⋊#4294, #28354676, …
maximal quotient of	H(3,𝔽₃)⋊#10587018, #28353160, #28353162, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4617, 104);