Finite Group Databasebeta

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C₂×D₃×#1887 #72258709

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

Aliases

C₂×D₃×#1887

Splittings

Fitting	C₂×C₃×#1887 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#1887

Subgroups

	subgroup	G/H
center	C₂³	D₃×#120
commutator	C₂×C₃×C₄	C₂⁴×C₄
Frattini	C₂²×C₄	C₂⁴×D₃
Fitting	C₂×C₃×#1887	C₂
socle	C₂³×C₃	C₂×#120
prime radical	C₂²×D₃×#127	C₂
cosocle	C₂²×C₃×C₄	C₂⁵
hypercenter	C₂×#1887	D₃
hypocenter	C₃	C₂²×#1887
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#1887

19188 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₃×#23906
maximal normal subgroup of	C₂×D₃×#23906

GAP

Past the SmallGroups library coverage — no SmallGroups id.