Finite Group Databasebeta

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D3×#6499867 #72271972

order3072
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C216

Aliases

direct productD3×#6499867

Splittings

FittingC3×#6499867 ⋊ C2
SylowC3 ⋊ C2×#6499867

Subgroups

subgroupG/H
centerC22C22×D3×#120
commutator, cosocleC24×C3C26
FrattiniC24C25×D3
FittingC3×#6499867C2
socleC22×C3C23×#120
hypercenter#6499867D3
hypocenterC3C2×#6499867
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C26 ◁ #6499867

288138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.