Finite Group Databasebeta

← Prev (#31825598) Next (#31825600) →

H(3,𝔽₃)×C₂₂₃⋊C₃ #31825599

order	18063
automorphism	?
homology	Abelianization (H₁) = C₃³ · Schur multiplier (H₂) = C₃⁴

Aliases

H(3,𝔽₃)×C₂₂₃⋊C₃

Splittings

Fitting	H(3,𝔽₃)×C₂₂₃ ⋊ C₃
Sylow	C₂₂₃ ⋊ C₃×H(3,𝔽₃)

Subgroups

	subgroup	G/H
center, Frattini	C₃	C₃²×C₂₂₃⋊C₃
commutator, socle, cosocle	C₃×C₂₂₃	C₃³
Fitting	H(3,𝔽₃)×C₂₂₃	C₃
hypercenter	H(3,𝔽₃)	C₂₂₃⋊C₃
hypocenter	C₂₂₃	C₃×H(3,𝔽₃)
LCS	G ▷ C₃×C₂₂₃ ▷ C₂₂₃
UCS	C₁ ◁ C₃ ◁ H(3,𝔽₃)

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2007

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18063, 40);