Finite Group Databasebeta

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D₃×#13096364 #72269332

order	9408
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

D₃×#13096364

Splittings

Fitting	C₃×C₇²×D₄ ⋊ C₂³
Hall	C₃×C₇² ⋊ C₂²×D₈
Sylow	C₇² ⋊ C₂×D₃×D₈
Sylow	C₃ ⋊ C₂×#13096364

Subgroups

	subgroup	G/H
center	C₂	D₃×#11716115
commutator, cosocle	C₃×C₄×C₇²	C₂⁴
Frattini	C₄	C₂×D₃×D₇²
Fitting	C₃×C₇²×D₄	C₂³
socle	C₂×C₃×C₇²	C₂²×D₄
hypercenter	D₄	D₃×D₇²
hypocenter	C₃×C₇²	C₂²×D₈
LCS	G ▷ C₃×C₄×C₇² ▷ C₂×C₃×C₇² ▷ C₃×C₇²
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₄

2060 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 168

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.