Finite Group Databasebeta

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C₃×D₃×#1705 #72244999

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

Aliases

C₃×D₃×#1705

Splittings

Fitting	C₃²×#1705 ⋊ C₂
Sylow	C₃² ⋊ C₂×#1705

Subgroups

	subgroup	G/H
center	C₂²×C₃	D₃×#127
commutator, cosocle	C₃×C₄²	C₂⁴×C₃
Frattini	C₄²	C₂³×C₃×D₃
Fitting	C₃²×#1705	C₂
socle	C₂²×C₃²	C₂×#127
prime radical	C₃×D₃×#127	C₂²
hypercenter	C₃×#1705	D₃
hypocenter	C₃	C₂×C₃×#1705
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#1705

2095 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 384

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×D₃×#19745, AGL(1,ℤ/9)×#1705
maximal normal subgroup of	C₃×D₃×#19745
maximal quotient of	AGL(1,ℤ/9)×#1705

GAP

Past the SmallGroups library coverage — no SmallGroups id.