Finite Group Databasebeta

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D₃×#33557 #72255226

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

Aliases

Splittings

Fitting	C₃×#33557 ⋊ C₂
Sylow	C₃ ⋊ C₂×#33557

Subgroups

	subgroup	G/H
center	C₂	C₂×D₃×B(4,𝔽₂)
commutator, cosocle	C₂×C₃×D₄	C₂⁵
Frattini	C₂×D₄	C₂⁴×D₃
Fitting	C₃×#33557	C₂
socle	C₂×C₃	C₂²×B(4,𝔽₂)
hypercenter	#33557	D₃
hypocenter	C₃	C₂×#33557
LCS	G ▷ C₂×C₃×D₄ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂²×D₄ ◁ #33557

8456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 48

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#7622880, D₃×#511853, D₃×#511811, …
maximal normal subgroup of	D₃×#7622880, D₃×#511853, D₃×#511811

GAP

Past the SmallGroups library coverage — no SmallGroups id.