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D3×#65487 #14424974

order1920
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productD3×#65487

Splittings

FittingC3×C5×AGL(1,ℤ/8) ⋊ C22
HallC3×C5 ⋊ C2×#453
SylowC5 ⋊ D3×#453
SylowC3 ⋊ C2×#65487

Subgroups

subgroupG/H
centerC2D3×#4083
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×AGL(1,ℤ/8)C22
socleC2×C3×C5C2×#120
hypercenterAGL(1,ℤ/8)D3×D5
hypocenterC3×C5C2×#453
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

1688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

114 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×D5×#453
maximal normal subgroup ofD3×D5×#453

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 150672);