Finite Group Databasebeta

← Prev (#10948623) Next (#10948625) →

D3×AGL(1,ℤ/16) #10948624

order768
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD3×AGL(1,ℤ/16)

Splittings

FittingC3×AGL(1,ℤ/16) ⋊ C2
SylowC3 ⋊ C2×AGL(1,ℤ/16)

Subgroups

subgroupG/H
centerC2D3×#442
commutatorC3×C8C23×C4
FrattiniC2×C8C23×D3
FittingC3×AGL(1,ℤ/16)C2
socleC2×C3C2×#442
prime radicalD3×#509C2
cosocleC2×C3×C8C24
hypercenterAGL(1,ℤ/16)D3
hypocenterC3C2×AGL(1,ℤ/16)
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ AGL(1,ℤ/16)

710 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

69 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72213745, D3×#33688, C2×D3×AGL(1,ℤ/16), …
maximal normal subgroup ofD3×#33688, C2×D3×AGL(1,ℤ/16), C3×D3×AGL(1,ℤ/16), …
maximal quotient of#72213745, D3×#12067, C2×D3×AGL(1,ℤ/16), …
automorphism group ofD48, Dic24
holomorph ofC3×C16

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 323005);