Finite Group Databasebeta

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C₃×D₃×#19745 #72245236

order	4608
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃ · Schur multiplier (H₂) = C₂⁷×C₈

Aliases

C₃×D₃×#19745

Splittings

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

Subgroups

	subgroup	G/H
center	C₂²×C₃	C₂×D₃×#127
commutator, cosocle	C₃×C₄²	C₂⁵×C₃
Frattini	C₄²	C₂⁴×C₃×D₃
Fitting	C₃²×#19745	C₂
socle	C₂²×C₃²	C₂²×#127
hypercenter	C₃×#19745	D₃
hypocenter	C₃	C₂×C₃×#19745
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄² ◁ C₃×#19745

12489 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 384

Conjugacy classes & character table

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

Relationships

maximal subgroup of	AGL(1,ℤ/9)×#19745
maximal quotient of	AGL(1,ℤ/9)×#19745

GAP

Past the SmallGroups library coverage — no SmallGroups id.