Finite Group Databasebeta

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D3×#65231 #14319841

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD3×#65231

Splittings

HallC3×C5 ⋊ C2×#380
SylowC5 ⋊ D3×#380
SylowC3 ⋊ C2×#65231

Subgroups

subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C5×D3C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#380
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

2464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45539);