Finite Group Databasebeta

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D3×#20591 #72270239

order1536
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C212

Aliases

direct productD3×#20591

Splittings

FittingC3×#20591 ⋊ C2
SylowC3 ⋊ C2×#20591

Subgroups

subgroupG/H
centerC2×C4C2×D3×C22⋊C4
commutatorC23×C3C24×C4
FrattiniC22×C4C24×D3
FittingC3×#20591C2
socleC22×C3C23×C22⋊C4
prime radicalC23×D3×#41C2
cosocleC22×C3×C4C25
hypercenter#20591D3
hypocenterC3C2×#20591
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ #20591

36868 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#6442584, D3×#395409, D3×#359507
maximal normal subgroup ofD3×#6442584, D3×#395409, D3×#359507

GAP

Past the SmallGroups library coverage — no SmallGroups id.