Finite Group Databasebeta

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D3×#23412 #72253874

order1536
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C211

Aliases

direct productD3×#23412

Splittings

FittingC3×#23412 ⋊ C2
SylowC3 ⋊ C2×#23412

Subgroups

subgroupG/H
centerC4D3×#392
commutator, cosocleC22×C3×C4C25
FrattiniC22×C4C24×D3
FittingC3×#23412C2
socleC2×C3C22×#392
hypercenter#23412D3
hypocenterC3C2×#23412
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4 ◁ C23×C4 ◁ #23412

At least 6768 conjugacy classes of subgroups; only the 1167 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#6437576
maximal normal subgroup ofD3×#6437576

GAP

Past the SmallGroups library coverage — no SmallGroups id.