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H(3,𝔽₃)⋊#4296 #17987564

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

Aliases

unambiguous semidirect product

H(3,𝔽₃)⋊#4296

Splittings

Fitting	C₁₉×H(3,𝔽₃) ⋊ C₉
Sylow	C₁₉ ⋊ H(3,𝔽₃)⋊C₉

Subgroups

	subgroup	G/H
center	C₃	C₃²⋊#4296
commutator	C₃²×C₁₉	C₃×C₉
Frattini	C₃²	C₃×#4296
Fitting	C₁₉×H(3,𝔽₃)	C₉
socle	C₃×C₁₉	C₃²⋊C₉
prime radical	H(3,𝔽₃)×C₁₉⋊C₃	C₃
cosocle	C₃²×C₁₉⋊C₃	C₃²
hypercenter	H(3,𝔽₃)	#4296
hypocenter	C₁₉	H(3,𝔽₃)⋊C₉
LCS	G ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃² ◁ H(3,𝔽₃)

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 171

Polycyclic presentation:

3^5,19|a^3=d,b^a=bc,c^a=ce,f^a=f^4,c^b=ce,f^d=f^7

Conjugacy classes & character table

73 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×H(3,𝔽₃)⋊#4296, #28356913, #28356914, …
maximal normal subgroup of	C₃×H(3,𝔽₃)⋊#4296, #28356913, #28356914, …
maximal quotient of	H(3,𝔽₃)⋊#10587020, #28356682, #28356686, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4617, 325);