Finite Group Databasebeta

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D3×#359513 #72270372

order3072
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C212×C4

Aliases

direct productD3×#359513

Splittings

FittingC3×#359513 ⋊ C2
SylowC3 ⋊ C2×#359513

Subgroups

subgroupG/H
centerC22C2×D3×#386
commutatorC22×C3×C4C24×C4
FrattiniC23×C4C24×D3
FittingC3×#359513C2
socleC22×C3C22×#386
prime radicalC22×D3×#535C2
cosocleC23×C3×C4C25
hypercenter#359513D3
hypocenterC3C2×#359513
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C24×C4 ◁ #359513

At least 7136 conjugacy classes of subgroups; only the 2891 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#72213396
maximal normal subgroup ofD3×#72213396

GAP

Past the SmallGroups library coverage — no SmallGroups id.