Finite Group Databasebeta

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D32×#360 #72222812

order2304
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD32×#360

Splittings

FittingC32×#360 ⋊ C22
SylowC32 ⋊ C22×#360

Subgroups

subgroupG/H
centerC2D32×#102
commutatorC32×C8C23×C4
FrattiniC2×C8C22×D32
FittingC32×#360C22
socleC2×C32C22×#102
prime radicalD32×#135C2
cosocleC2×C32×C8C24
hypercenter#360D32
hypocenterC32C22×#360
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

2544 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

144 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.