Finite Group Databasebeta

← Prev (#23782858) Next (#23782860) →

AΣL(1,𝔽₂₇)×C₄₃⋊C₃ #23782859

order	10449
automorphism	?
homology	Abelianization (H₁) = C₃³ · Schur multiplier (H₂) = C₃³

Aliases

AΣL(1,𝔽₂₇)×C₄₃⋊C₃

Splittings

Fitting	C₄₃×AΣL(1,𝔽₂₇) ⋊ C₃
Sylow	C₄₃ ⋊ C₃×AΣL(1,𝔽₂₇)

Subgroups

	subgroup	G/H
center	C₃	H(3,𝔽₃)×C₄₃⋊C₃
commutator, cosocle	C₃²×C₄₃	C₃³
Frattini	C₃²	C₃²×C₄₃⋊C₃
Fitting	C₄₃×AΣL(1,𝔽₂₇)	C₃
socle	C₃×C₄₃	C₃×H(3,𝔽₃)
hypercenter	AΣL(1,𝔽₂₇)	C₄₃⋊C₃
hypocenter	C₄₃	C₃×AΣL(1,𝔽₂₇)
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃² ◁ AΣL(1,𝔽₂₇)

252 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

289 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×AΣL(1,𝔽₂₇)×C₄₃⋊C₃, C₄₃⋊C₃×#6908, C₄₃⋊C₃×#6909, …
maximal normal subgroup of	C₃×AΣL(1,𝔽₂₇)×C₄₃⋊C₃, C₄₃⋊C₃×#6908, C₄₃⋊C₃×#6909, …
maximal quotient of	C₄₃⋊C₃×#6856, C₄₃⋊C₃×#6857, C₄₃⋊C₃×#6858, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10449, 243);