Finite Group Databasebeta

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C₃×D₃×#1715 #72244958

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

Aliases

C₃×D₃×#1715

Splittings

Fitting	C₃²×#1715 ⋊ C₂
Sylow	C₃² ⋊ C₂×#1715

Subgroups

	subgroup	G/H
center	C₂²×C₃	D₃×#127
commutator, cosocle	C₃×C₄²	C₂⁴×C₃
Frattini	C₄²	C₂³×C₃×D₃
Fitting	C₃²×#1715	C₂
socle	C₂²×C₃²	C₂×#127
prime radical	C₃×D₃×#493	C₂
hypercenter	C₃×#1715	D₃
hypocenter	C₃	C₂×C₃×#1715
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#1715

2170 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 384

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×D₃×#19745, AGL(1,ℤ/9)×#1715
maximal normal subgroup of	C₃×D₃×#19745
maximal quotient of	AGL(1,ℤ/9)×#1715

GAP

Past the SmallGroups library coverage — no SmallGroups id.