Finite Group Databasebeta

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D₃×#12067 #72219824

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁶

Aliases

Splittings

Fitting	C₃×#12067 ⋊ C₂
Sylow	C₃ ⋊ C₂×#12067

Subgroups

	subgroup	G/H
center	C₂²	D₃×#442
commutator	C₃×C₈	C₂³×C₈
Frattini	C₄×C₈	C₂³×D₃
Fitting	C₃×#12067	C₂
socle	C₂²×C₃	C₂×#442
prime radical	C₂×D₃×D₁₆	C₄
cosocle	C₃×C₄×C₈	C₂⁴
hypercenter	#12067	D₃
hypocenter	C₃	C₂×#12067
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #322 ◁ #12067

1156 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×AGL(1,ℤ/32), C₃⋊D₃×#12067, #72222659, …
maximal normal subgroup of	D₃×AGL(1,ℤ/32), C₂×D₃×#12067
maximal quotient of	D₃×AGL(1,ℤ/32), C₃⋊D₃×#12067, #72222659, …
automorphism group of	#4449, #4519, #4520, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.