Finite Group Databasebeta

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C₂×D₃×#8541 #72253669

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁴

Aliases

C₂×D₃×#8541

Splittings

Fitting	C₂×C₃×#8541 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#8541

Subgroups

	subgroup	G/H
center	C₂³	D₃×#379
commutator	C₂⁴×C₃	C₂⁴×C₄
Frattini	C₂⁵	C₂⁴×D₃
Fitting	C₂×C₃×#8541	C₂
socle	C₂³×C₃	C₂×#379
prime radical	C₂³×D₃×#120	C₂
cosocle	C₂⁵×C₃	C₂⁵
hypercenter	C₂×#8541	D₃
hypocenter	C₃	C₂²×#8541
LCS	G ▷ C₂⁴×C₃ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂⁶ ◁ C₂×#8541

292954 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₃×#347042, D₃×#72218521, D₃×#72219158
maximal normal subgroup of	C₂×D₃×#347042, D₃×#72218521, D₃×#72219158

GAP

Past the SmallGroups library coverage — no SmallGroups id.