Finite Group Databasebeta

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D3×#20667 #72270185

order1536
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productD3×#20667

Splittings

FittingC3×#20667 ⋊ C2
SylowC3 ⋊ C2×#20667

Subgroups

subgroupG/H
centerC2×C4C22×D3×D4
commutatorC2×C3×C4C24×C4
FrattiniC22×C4C24×D3
FittingC3×#20667C2
socleC22×C3C23×C4⋊C4
prime radicalC25×D3Q8
cosocleC22×C3×C4C25
hypercenter#20667D3
hypocenterC3C2×#20667
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ #20667

10180 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×#401626, D3×#396483
maximal normal subgroup ofD3×#6442584, D3×#401626, D3×#396483

GAP

Past the SmallGroups library coverage — no SmallGroups id.