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C3×D5×#496 #14438956

order1920
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C24×C4

Aliases

direct productC3×D5×#496

Splittings

FittingC3×C5×#496 ⋊ C2
HallC3×C5 ⋊ C2×#496
SylowC5 ⋊ C2×C3×#496

Subgroups

subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#496C2
socleC22×C3×C5C22×D4
hypercenterC3×#496D5
hypocenterC5C2×C3×#496
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#496

1336 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 164654);