Finite Group Databasebeta

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C₂×#11661935 #72270876

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹⁵

Aliases

C₂×#11661935

Splittings

Fitting	C₂²×C₃×B(4,𝔽₂) ⋊ C₂
Sylow	C₃ ⋊ C₂×#60399

Subgroups

	subgroup	G/H
center	C₂²	C₂×D₃×#120
commutator, cosocle	C₂³×C₃	C₂⁶
Frattini	C₂³	C₂⁵×D₃
Fitting	C₂²×C₃×B(4,𝔽₂)	C₂
socle	C₂²×C₃	C₂²×#120
hypercenter	C₂²×B(4,𝔽₂)	D₃
hypocenter	C₃	C₂×#60399
LCS	G ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂²×B(4,𝔽₂)

46784 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₃×#60399
maximal normal subgroup of	C₂×D₃×#60399
maximal quotient of	#72271913, #72272046

GAP

Past the SmallGroups library coverage — no SmallGroups id.