Finite Group Databasebeta

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D₃×#61468 #72258758

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

Aliases

Splittings

Fitting	C₃×#61468 ⋊ C₂
Sylow	C₃ ⋊ C₂×#61468

Subgroups

	subgroup	G/H
center	C₂²	C₂³×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁶
Frattini	C₂×C₄	C₂⁵×D₃
Fitting	C₃×#61468	C₂
socle	C₂²×C₃	C₂⁴×D₄
hypercenter	#61468	D₃
hypocenter	C₃	C₂×#61468
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #61468

At least 7660 conjugacy classes of subgroups; only the 3653 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.