Finite Group Databasebeta

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D₃×#33531 #72270611

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹⁰

Aliases

Splittings

Fitting	C₃×#33531 ⋊ C₂
Sylow	C₃ ⋊ C₂×#33531

Subgroups

	subgroup	G/H
center	C₂	C₂×D₃×#447
commutator, cosocle	C₂×C₃×C₈	C₂⁵
Frattini	C₂×C₈	C₂⁴×D₃
Fitting	C₃×#33531	C₂
socle	C₂×C₃	C₂²×#447
hypercenter	#33531	D₃
hypocenter	C₃	C₂×#33531
LCS	G ▷ C₂×C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #33531

7860 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#7623148
maximal normal subgroup of	D₃×#7623148

GAP

Past the SmallGroups library coverage — no SmallGroups id.