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AΣL(1,𝔽₂₇)×#66526 #41008579

order	26973
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉ · Schur multiplier (H₂) = C₃³

Aliases

AΣL(1,𝔽₂₇)×#66526

Splittings

Fitting	C₃₇×AΣL(1,𝔽₂₇) ⋊ C₉
Sylow	C₃₇ ⋊ C₉×AΣL(1,𝔽₂₇)

Subgroups

	subgroup	G/H
center	C₃	H(3,𝔽₃)×#66526
commutator	C₃²×C₃₇	C₃²×C₉
Frattini	C₃²	C₃²×#66526
Fitting	C₃₇×AΣL(1,𝔽₂₇)	C₉
socle	C₃×C₃₇	C₉×H(3,𝔽₃)
prime radical	AΣL(1,𝔽₂₇)×C₃₇⋊C₃	C₃
cosocle	C₃²×C₃₇⋊C₃	C₃³
hypercenter	AΣL(1,𝔽₂₇)	#66526
hypocenter	C₃₇	C₉×AΣL(1,𝔽₂₇)
LCS	G ▷ C₃²×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
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) = 333

Conjugacy classes & character table

221 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 4350);