Finite Group Databasebeta

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D3×#65688 #14320142

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

Aliases

direct productD3×#65688

Splittings

FittingC3×C42×C5 ⋊ C2×C4
HallC3×C5 ⋊ C2×#384
SylowC5 ⋊ D3×#384
SylowC3 ⋊ C2×#65688

Subgroups

subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C42×C5C2×C4
prime radicalC22×D3×D5C23
cosocleC22×C3×D5C24
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#384
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

1776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽5)×#127, D3×#10604003, D3×#13104700, …
maximal normal subgroup ofD3×AGL(1,𝔽5)×#127, D3×#10604003
maximal quotient ofD3×#13104700, C3⋊D3×#65688

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45840);