Finite Group Databasebeta

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D₃×#21778 #72271998

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁰

Aliases

Splittings

Fitting	C₃×#21778 ⋊ C₂
Sylow	C₃ ⋊ C₂×#21778

Subgroups

	subgroup	G/H
center	C₂	D₃×#2308
commutator	C₂³×C₃	C₂⁴×C₄
Frattini	C₂²×C₄	C₂⁴×D₃
Fitting	C₃×#21778	C₂
socle	C₂×C₃	C₂×#2308
prime radical	D₃×#3484	C₂
cosocle	C₂²×C₃×C₄	C₂⁵
hypercenter	#21778	D₃
hypocenter	C₃	C₂×#21778
LCS	G ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #21778

10128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 48

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#6499855, D₃×#493474
maximal normal subgroup of	D₃×#6499855, D₃×#493474

GAP

Past the SmallGroups library coverage — no SmallGroups id.