Finite Group Databasebeta

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C₂×#11797956 #72222702

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

Aliases

C₂×#11797956

Splittings

C₃² ⋊ C₂×AGL(1,ℤ/16)

Subgroups

	subgroup	G/H
center	C₂²	#10592851
commutator	C₃²×C₈	C₂³×C₄
Frattini	C₂×C₈	C₂³×C₃⋊D₃
Fitting, prime radical	C₂×C₃²×#509	C₂
socle	C₂²×C₃²	#442
cosocle	C₂×C₃²×C₈	C₂⁴
hypercenter	C₂×#509	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×#509

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×#72222464

GAP

Past the SmallGroups library coverage — no SmallGroups id.