Finite Group Databasebeta

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C₂×#10943956 #72253427

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹³

Aliases

C₂×#10943956

Splittings

Fitting	C₂²×C₃×B(4,𝔽₂) ⋊ C₂
Sylow	C₃ ⋊ C₂×#32898

Subgroups

	subgroup	G/H
center	C₂³	D₃×#120
commutator, cosocle	C₂⁴×C₃	C₂⁵
Frattini	C₂⁴	C₂⁴×D₃
Fitting	C₂²×C₃×B(4,𝔽₂)	C₂
socle	C₂³×C₃	C₂×#120
hypercenter	C₂²×B(4,𝔽₂)	D₃
hypocenter	C₃	C₂×#32898
LCS	G ▷ C₂⁴×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂⁵ ◁ C₂²×B(4,𝔽₂)

39956 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 192

Conjugacy classes & character table

162 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₃×#32898
maximal normal subgroup of	C₂×D₃×#32898
maximal quotient of	C₂×#72231325, C₂×#72219817

GAP

Past the SmallGroups library coverage — no SmallGroups id.