Finite Group Databasebeta

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C₂×D₃×#2091 #72248070

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁹

Aliases

C₂×D₃×#2091

Splittings

Fitting	C₂×C₃×#2091 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#2091

Subgroups

	subgroup	G/H
center	C₂×C₄	D₃×#127
commutator, cosocle	C₂²×C₃×C₄	C₂⁵
Frattini	C₂²×C₄	C₂⁴×D₃
Fitting	C₂×C₃×#2091	C₂
socle	C₂²×C₃	C₂×#399
prime radical	C₂⁵×D₃	Q₈
hypercenter	C₂×#2091	D₃
hypocenter	C₃	C₂²×#2091
LCS	G ▷ C₂²×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#2091

7260 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₃×#30434, D₃×#421068, D₃×#396483
maximal normal subgroup of	C₂×D₃×#30434, D₃×#421068, D₃×#396483
maximal quotient of	D₃×#396483

GAP

Past the SmallGroups library coverage — no SmallGroups id.