Finite Group Databasebeta

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D₃×#60644 #72249222

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹³×C₄

Aliases

Splittings

Fitting	C₃×#60644 ⋊ C₂
Sylow	C₃ ⋊ C₂×#60644

Subgroups

	subgroup	G/H
center	C₂²	C₂³×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁶
Frattini	C₂×C₄	C₂⁵×D₃
Fitting	C₃×#60644	C₂
socle	C₂²×C₃	C₂⁴×D₄
hypercenter	#60644	D₃
hypocenter	C₃	C₂×#60644
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂×#117 ◁ #60644

26428 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#417774, D₃×#10576108
maximal normal subgroup of	D₃×#417774, D₃×#10576108

GAP

Past the SmallGroups library coverage — no SmallGroups id.