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C₁₉⋊C₃×AΣL(1,𝔽₂₇) #17987482

order	4617
automorphism	?
homology	Abelianization (H₁) = C₃³ · Schur multiplier (H₂) = C₃³

Aliases

C₁₉⋊C₃×AΣL(1,𝔽₂₇)

Splittings

Fitting	C₁₉×AΣL(1,𝔽₂₇) ⋊ C₃
Sylow	C₁₉ ⋊ C₃×AΣL(1,𝔽₂₇)

Subgroups

	subgroup	G/H
center	C₃	H(3,𝔽₃)×C₁₉⋊C₃
commutator, cosocle	C₃²×C₁₉	C₃³
Frattini	C₃²	C₃²×C₁₉⋊C₃
Fitting	C₁₉×AΣL(1,𝔽₂₇)	C₃
socle	C₃×C₁₉	C₃×H(3,𝔽₃)
hypercenter	AΣL(1,𝔽₂₇)	C₁₉⋊C₃
hypocenter	C₁₉	C₃×AΣL(1,𝔽₂₇)
LCS	G ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃² ◁ AΣL(1,𝔽₂₇)

252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 171

Conjugacy classes & character table

153 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×C₁₉⋊C₃×AΣL(1,𝔽₂₇), C₁₉⋊C₃×#6908, C₁₉⋊C₃×#6909, …
maximal normal subgroup of	C₃×C₁₉⋊C₃×AΣL(1,𝔽₂₇), C₁₉⋊C₃×#6908, C₁₉⋊C₃×#6909, …
maximal quotient of	C₁₉⋊C₃×#6856, C₁₉⋊C₃×#6857, C₁₉⋊C₃×#6858, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4617, 243);