Finite Group Databasebeta

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H(3,𝔽₃)×C₃₀₇⋊C₃ #38733332

order	24867
automorphism	?
homology	Abelianization (H₁) = C₃³ · Schur multiplier (H₂) = C₃⁴

Aliases

H(3,𝔽₃)×C₃₀₇⋊C₃

Splittings

Fitting	H(3,𝔽₃)×C₃₀₇ ⋊ C₃
Sylow	C₃₀₇ ⋊ C₃×H(3,𝔽₃)

Subgroups

	subgroup	G/H
center, Frattini	C₃	C₃²×C₃₀₇⋊C₃
commutator, socle, cosocle	C₃×C₃₀₇	C₃³
Fitting	H(3,𝔽₃)×C₃₀₇	C₃
hypercenter	H(3,𝔽₃)	C₃₀₇⋊C₃
hypocenter	C₃₀₇	C₃×H(3,𝔽₃)
LCS	G ▷ C₃×C₃₀₇ ▷ C₃₀₇
UCS	C₁ ◁ C₃ ◁ H(3,𝔽₃)

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2763

Conjugacy classes & character table

1155 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24867, 40);