Finite Group Databasebeta

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D32×#496 #72252604

order2304
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28×C4

Aliases

direct productD32×#496

Splittings

FittingC32×#496 ⋊ C22
SylowC32 ⋊ C22×#496

Subgroups

subgroupG/H
centerC22C2×D32×D4
commutator, cosocleC2×C32×C4C25
FrattiniC2×C4C23×D32
FittingC32×#496C22
socleC22×C32C23×D4
hypercenter#496D32
hypocenterC32C22×#496
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #496

8410 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD32×#3151
maximal normal subgroup ofD32×#3151

GAP

Past the SmallGroups library coverage — no SmallGroups id.