Finite Group Databasebeta

← Prev (#72222736) Next (#72222738) →

D₃×#71515 #72222737

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

Aliases

Splittings

C₃² ⋊ C₂×AGL(1,ℤ/16)

Subgroups

	subgroup	G/H
center	C₂	D₃×#5152
commutator	C₃²×C₈	C₂³×C₄
Frattini	C₂×C₈	C₂²×D₃²
Fitting	C₃²×#509	C₂²
socle	C₂×C₃²	C₂×#442
prime radical	C₃×D₃×#509	C₂
cosocle	C₂×C₃²×C₈	C₂⁴
hypercenter	#509	D₃²
hypocenter	C₃²	C₂×AGL(1,ℤ/16)
LCS	G ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #509

1497 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

117 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃²×AGL(1,ℤ/16)
maximal normal subgroup of	D₃²×AGL(1,ℤ/16)

GAP

Past the SmallGroups library coverage — no SmallGroups id.