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AΣL(1,𝔽₂₇)×C₄₃⋊C₉ #44533521

order	31347
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉ · Schur multiplier (H₂) = C₃³

Aliases

AΣL(1,𝔽₂₇)×C₄₃⋊C₉

Splittings

C₄₃ ⋊ C₉×AΣL(1,𝔽₂₇)

Subgroups

	subgroup	G/H
center	C₃²	H(3,𝔽₃)×C₄₃⋊C₃
commutator	C₃²×C₄₃	C₃²×C₉
Frattini	C₃³	C₃²×C₄₃⋊C₃
Fitting, prime radical	C₃×C₄₃×AΣL(1,𝔽₂₇)	C₃
socle	C₃²×C₄₃	C₃×H(3,𝔽₃)
cosocle	C₃³×C₄₃	C₃³
hypercenter	C₃×AΣL(1,𝔽₂₇)	C₄₃⋊C₃
hypocenter	C₄₃	C₉×AΣL(1,𝔽₂₇)
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃×AΣL(1,𝔽₂₇)

472 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 100 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) = 3483

Conjugacy classes & character table

867 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31347, 2144);