Finite Group Databasebeta

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D3×#20615 #72248156

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

Aliases

direct productD3×#20615

Splittings

FittingC3×#20615 ⋊ C2
SylowC3 ⋊ C2×#20615

Subgroups

subgroupG/H
centerC2×C4D3×#120
commutatorC2×C3×C4C24×C4
FrattiniC22×C4C24×D3
FittingC3×#20615C2
socleC22×C3C22×#120
prime radicalC2×D3×#585C2
cosocleC22×C3×C4C25
hypercenter#20615D3
hypocenterC3C2×#20615
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #20615

34764 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×#498885, D3×#494622, D3×#498909, …
maximal normal subgroup ofD3×#498885, D3×#494622, D3×#498909, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.