Finite Group Databasebeta

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C₂×#11797944 #72222709

order	2304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵×C₃

Aliases

C₂×#11797944

Splittings

Fitting	C₂×C₃²×#360 ⋊ C₂
Sylow	C₃² ⋊ C₂×AGL(1,ℤ/16)

Subgroups

	subgroup	G/H
center	C₂²	#10592484
commutator	C₃²×C₈	C₂³×C₄
Frattini	C₂×C₈	C₂³×C₃⋊D₃
Fitting	C₂×C₃²×#360	C₂
socle	C₂²×C₃²	#442
prime radical	C₂×#10592892	C₂
cosocle	C₂×C₃²×C₈	C₂⁴
hypercenter	C₂×#360	C₃⋊D₃
hypocenter	C₃²	C₂×AGL(1,ℤ/16)
LCS	G ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#360

2130 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₃⋊D₃×AGL(1,ℤ/16)
maximal normal subgroup of	C₂×C₃⋊D₃×AGL(1,ℤ/16)
maximal quotient of	C₂×#72222571

GAP

Past the SmallGroups library coverage — no SmallGroups id.