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AΣL(1,𝔽₂₇)×C₃₁⋊C₉ #36381123

order	22599
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉ · Schur multiplier (H₂) = C₃³

Aliases

AΣL(1,𝔽₂₇)×C₃₁⋊C₉

Splittings

C₃₁ ⋊ C₉×AΣL(1,𝔽₂₇)

Subgroups

	subgroup	G/H
center	C₃²	H(3,𝔽₃)×C₃₁⋊C₃
commutator	C₃²×C₃₁	C₃²×C₉
Frattini	C₃³	C₃²×C₃₁⋊C₃
Fitting, prime radical	C₃×C₃₁×AΣL(1,𝔽₂₇)	C₃
socle	C₃²×C₃₁	C₃×H(3,𝔽₃)
cosocle	C₃³×C₃₁	C₃³
hypercenter	C₃×AΣL(1,𝔽₂₇)	C₃₁⋊C₃
hypocenter	C₃₁	C₉×AΣL(1,𝔽₂₇)
LCS	G ▷ C₃²×C₃₁ ▷ C₃×C₃₁ ▷ C₃₁
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) = 2511

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22599, 2144);