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D3×#64879 #14280347

order1920
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productD3×#64879

Splittings

HallC3×C5 ⋊ C2×#322
SylowC5 ⋊ D3×#322
SylowC3 ⋊ C2×#64879

Subgroups

subgroupG/H
center, FrattiniC2×C4C2×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C2×C4×C8
FittingC2×C3×C5×C8C2×C4
socleC22×C3×C5C2×C42
prime radicalC22×C5×D3C42
cosocleC3×C4×Dic5C23
hypercenterC2×C8D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#322
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C8

496 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 6045);