Finite Group Databasebeta

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D3×#65018 #14414838

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD3×#65018

Splittings

FittingC3×C5×C22⋊C8 ⋊ C22
HallC3×C5 ⋊ C2×#436
SylowC5 ⋊ D3×#436
SylowC3 ⋊ C2×#65018

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D3×D5
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C22⋊C8C22
prime radicalC2×D3×C22⋊D5C4
cosocleC2×C3×C4×C5C24
hypercenterC22⋊C8D3×D5
hypocenterC3×C5C2×#436
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22⋊C8

1104 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, 140536);