Finite Group Databasebeta

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C₂×D₃×#1903 #72248035

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

Aliases

C₂×D₃×#1903

Splittings

Fitting	C₂×C₃×#1903 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#1903

Subgroups

	subgroup	G/H
center	C₂²	D₃×#386
commutator	C₂×C₃×C₄	C₂⁴×C₄
Frattini	C₂²×C₄	C₂⁴×D₃
Fitting	C₂×C₃×#1903	C₂
socle	C₂²×C₃	C₂×#386
prime radical	C₂²×D₃×AGL(1,ℤ/8)	C₂
cosocle	C₂²×C₃×C₄	C₂⁵
hypercenter	C₂×#1903	D₃
hypocenter	C₃	C₂²×#1903
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#1903

13140 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×#30434, D₃×#417674, D₃×#418876, …
maximal normal subgroup of	C₂×D₃×#30434, D₃×#417674, D₃×#418876, …
maximal quotient of	D₃×#364468, D₃×#359476

GAP

Past the SmallGroups library coverage — no SmallGroups id.