Finite Group Databasebeta

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D₃×AGL(1,ℤ/32) #72222540

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁵

Aliases

D₃×AGL(1,ℤ/32)

Splittings

Fitting	C₃×AGL(1,ℤ/32) ⋊ C₂
Sylow	C₃ ⋊ C₂×AGL(1,ℤ/32)

Subgroups

	subgroup	G/H
center	C₂	D₃×#12067
commutator	C₃×C₁₆	C₂³×C₈
Frattini	#346	C₂³×D₃
Fitting	C₃×AGL(1,ℤ/32)	C₂
socle	C₂×C₃	C₂×#12067
prime radical	D₃×#2263	C₄
cosocle	C₃×#346	C₂⁴
hypercenter	AGL(1,ℤ/32)	D₃
hypocenter	C₃	C₂×AGL(1,ℤ/32)
LCS	G ▷ C₃×C₁₆ ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1313 ◁ AGL(1,ℤ/32)

1298 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

141 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#72222660, C₂×D₃×AGL(1,ℤ/32), C₃⋊D₃×AGL(1,ℤ/32), …
maximal normal subgroup of	C₂×D₃×AGL(1,ℤ/32)
maximal quotient of	#72222660, D₃×#72224639, C₂×D₃×AGL(1,ℤ/32), …
automorphism group of	D₉₆, Dic₄₈
holomorph of	C₃×C₃₂

GAP

Past the SmallGroups library coverage — no SmallGroups id.