Finite Group Databasebeta

D3×#69091 #72222735

order2304
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD3×#69091

Splittings

FittingC32×#347 ⋊ C22
SylowC32 ⋊ C2×AGL(1,ℤ/16)

Subgroups

subgroupG/H
centerC2D3×#4711
commutatorC32×C8C23×C4
FrattiniC2×C8C22×D32
FittingC32×#347C22
socleC2×C32C2×#442
prime radicalD3×#4908C2
cosocleC2×C32×C8C24
hypercenter#347D32
hypocenterC32C2×AGL(1,ℤ/16)
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #347

1497 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

135 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD32×AGL(1,ℤ/16)
maximal normal subgroup ofD32×AGL(1,ℤ/16)

GAP

Past the SmallGroups library coverage — no SmallGroups id.