Finite Group Databasebeta

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C₂×D₃×#1891 #72248084

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

Aliases

C₂×D₃×#1891

Splittings

Fitting	C₂×C₃×#1891 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#1891

Subgroups

	subgroup	G/H
center	C₂×C₄	D₃×#120
commutator	C₂³×C₃	C₂⁴×C₄
Frattini	C₂²×C₄	C₂⁴×D₃
Fitting	C₂×C₃×#1891	C₂
socle	C₂²×C₃	C₂×#386
prime radical	C₂×D₃×#525	C₂
cosocle	C₂²×C₃×C₄	C₂⁵
hypercenter	C₂×#1891	D₃
hypocenter	C₃	C₂²×#1891
LCS	G ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#1891

13692 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×#30434, C₂×D₃×#23882, D₃×#417597, …
maximal normal subgroup of	C₂×D₃×#30434, C₂×D₃×#23882, D₃×#417597, …
maximal quotient of	D₃×#364416, D₃×#359507

GAP

Past the SmallGroups library coverage — no SmallGroups id.