Finite Group Databasebeta

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D3×#449475 #72253462

order3072
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C214

Aliases

direct productD3×#449475

Splittings

FittingC3×#449475 ⋊ C2
SylowC3 ⋊ C2×#449475

Subgroups

subgroupG/H
centerC23C2×D3×#120
commutator, cosocleC25×C3C25
FrattiniC25C24×D3
FittingC3×#449475C2
socleC23×C3C22×#120
hypercenter#449475D3
hypocenterC3C2×#449475
LCSG ▷ C25×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C26 ◁ #449475

275090 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

222 conjugacy classes — view the full character table.

Relationships

maximal quotient ofD3×#72219165

GAP

Past the SmallGroups library coverage — no SmallGroups id.