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H(3,𝔽₃)×C₂₈₃⋊C₃ #37523967

order	22923
automorphism	?
homology	Abelianization (H₁) = C₃³ · Schur multiplier (H₂) = C₃⁴

Aliases

H(3,𝔽₃)×C₂₈₃⋊C₃

Splittings

Fitting	H(3,𝔽₃)×C₂₈₃ ⋊ C₃
Sylow	C₂₈₃ ⋊ C₃×H(3,𝔽₃)

Subgroups

	subgroup	G/H
center, Frattini	C₃	C₃²×C₂₈₃⋊C₃
commutator, socle, cosocle	C₃×C₂₈₃	C₃³
Fitting	H(3,𝔽₃)×C₂₈₃	C₃
hypercenter	H(3,𝔽₃)	C₂₈₃⋊C₃
hypocenter	C₂₈₃	C₃×H(3,𝔽₃)
LCS	G ▷ C₃×C₂₈₃ ▷ C₂₈₃
UCS	C₁ ◁ C₃ ◁ H(3,𝔽₃)

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2547

Conjugacy classes & character table

1067 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22923, 40);