Finite Group Databasebeta

D32×#347 #72222725

order2304
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25

Aliases

direct productD32×#347

Splittings

FittingC32×#347 ⋊ C22
SylowC32 ⋊ C22×#347

Subgroups

subgroupG/H
centerC4C42×D32
commutatorC32×C4C22×C42
FrattiniC2×C8C22×D32
FittingC32×#347C22
socleC2×C32C22×#97
prime radicalC22×D32M16
cosocleC2×C32×C8C24
hypercenter#347D32
hypocenterC32C22×#347
LCSG ▷ C32×C4 ▷ C32
UCSC1 ◁ C4 ◁ #347

1648 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD32×AGL(1,ℤ/16), #72228223
maximal normal subgroup ofD32×AGL(1,ℤ/16), #72228223

GAP

Past the SmallGroups library coverage — no SmallGroups id.