Finite Group Databasebeta

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D3×#382434 #72270513

order3072
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211×C4

Aliases

direct productD3×#382434

Splittings

FittingC3×#382434 ⋊ C2
SylowC3 ⋊ C2×#382434

Subgroups

subgroupG/H
centerC22D3×#2308
commutatorC24×C3C24×C4
FrattiniC25C24×D3
FittingC3×#382434C2
socleC22×C3C2×#2308
prime radicalC2×D3×#3484C2
cosocleC25×C3C25
hypercenter#382434D3
hypocenterC3C2×#382434
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C25 ◁ #382434

At least 6664 conjugacy classes of subgroups; only the 2479 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#72219160, D3×#72219157, D3×#72219158
maximal normal subgroup ofD3×#72219160, D3×#72219157, D3×#72219158

GAP

Past the SmallGroups library coverage — no SmallGroups id.