Finite Group Databasebeta

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C₂×D₃×#1911 #72248178

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹¹

Aliases

C₂×D₃×#1911

Splittings

Fitting	C₂×C₃×#1911 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#1911

Subgroups

	subgroup	G/H
center	C₂²	D₃×#386
commutator	C₂×C₃×C₄	C₂⁴×C₄
Frattini	C₂²×C₄	C₂⁴×D₃
Fitting	C₂×C₃×#1911	C₂
socle	C₂²×C₃	C₂×#386
prime radical	C₂×D₃×#535	C₂
cosocle	C₂²×C₃×C₄	C₂⁵
hypercenter	C₂×#1911	D₃
hypocenter	C₃	C₂²×#1911
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#1911

14380 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	C₂×D₃×#23897, D₃×#146654, D₃×#147819, …
maximal normal subgroup of	C₂×D₃×#23897, D₃×#146654, D₃×#147819, …
maximal quotient of	D₃×#359509, D₃×#392696

GAP

Past the SmallGroups library coverage — no SmallGroups id.