Finite Group Databasebeta

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D3×#245233 #72253432

order3072
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C211×C4

Aliases

direct productD3×#245233

Splittings

FittingC3×#245233 ⋊ C2
SylowC3 ⋊ C2×#245233

Subgroups

subgroupG/H
centerC22D3×#2403
commutator, cosocleC25×C3C25
FrattiniC25C24×D3
FittingC3×#245233C2
socleC22×C3C2×#2403
hypercenter#245233D3
hypocenterC3C2×#245233
LCSG ▷ C25×C3 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C25 ◁ #245233

55346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal quotient ofD3×#72219165

GAP

Past the SmallGroups library coverage — no SmallGroups id.