Finite Group Databasebeta

← Prev (#72245043) Next (#72245045) →

C₃×#10784427 #72245044

order	2304
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂³×C₈

Aliases

C₃×#10784427

Splittings

Fitting	C₃²×#1721 ⋊ C₂
Sylow	C₃² ⋊ #19745

Subgroups

	subgroup	G/H
center	C₂²×C₃	D₃×#127
commutator, cosocle	C₃×C₄²	C₂⁴×C₃
Frattini	C₄²	C₂³×C₃×D₃
Fitting	C₃²×#1721	C₂
socle	C₂²×C₃²	C₂×#127
hypercenter	C₃×#1721	D₃
hypocenter	C₃	C₃×#19745
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#1721

2109 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 384

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×D₃×#19745, #72268944
maximal normal subgroup of	C₃×D₃×#19745
maximal quotient of	#72268944

GAP

Past the SmallGroups library coverage — no SmallGroups id.