Finite Group Databasebeta

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D3×D9×#120 #72276242

order3456
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C211

Aliases

direct productD3×D9×#120

Splittings

FittingC3×C9×#120 ⋊ C22
SylowC3×C9 ⋊ C22×#120

Subgroups

subgroupG/H
centerC22C23×D3×D9
commutator, cosocleC22×C3×C9C25
FrattiniC22×C3C23×D32
FittingC3×C9×#120C22
socleC22×C32C24×D3
hypercenter#120D3×D9
hypocenterC3×C9C22×#120
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ #120

14294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.