Finite Group Databasebeta

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D3×#8547 #72252302

order1536
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productD3×#8547

Splittings

FittingC3×#8547 ⋊ C2
SylowC3 ⋊ C2×#8547

Subgroups

subgroupG/H
centerC22D3×#379
commutatorC24×C3C23×C4
FrattiniC23×C4C23×D3
FittingC3×#8547C2
socleC22×C3C2×#379
prime radicalC22×D3×#120C2
cosocleC23×C3×C4C24
hypercenter#8547D3
hypocenterC3C2×#8547
LCSG ▷ C24×C3 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #8547

22468 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#346446
maximal normal subgroup ofD3×#346446

GAP

Past the SmallGroups library coverage — no SmallGroups id.