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AΣL(1,𝔽₂₇)×#4296 #28356986

order	13851
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉ · Schur multiplier (H₂) = C₃³

Aliases

AΣL(1,𝔽₂₇)×#4296

Splittings

Fitting	C₁₉×AΣL(1,𝔽₂₇) ⋊ C₉
Sylow	C₁₉ ⋊ C₉×AΣL(1,𝔽₂₇)

Subgroups

	subgroup	G/H
center	C₃	H(3,𝔽₃)×#4296
commutator	C₃²×C₁₉	C₃²×C₉
Frattini	C₃²	C₃²×#4296
Fitting	C₁₉×AΣL(1,𝔽₂₇)	C₉
socle	C₃×C₁₉	C₉×H(3,𝔽₃)
prime radical	C₁₉⋊C₃×AΣL(1,𝔽₂₇)	C₃
cosocle	C₃²×C₁₉⋊C₃	C₃³
hypercenter	AΣL(1,𝔽₂₇)	#4296
hypocenter	C₁₉	C₉×AΣL(1,𝔽₂₇)
LCS	G ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃² ◁ AΣL(1,𝔽₂₇)

472 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 171

Conjugacy classes & character table

187 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 4350);