Finite Group Databasebeta

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C3×D5×#500 #14439802

order1920
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25

Aliases

direct productC3×D5×#500

Splittings

FittingC3×C5×#500 ⋊ C2
HallC3×C5 ⋊ C2×#500
SylowC5 ⋊ C2×C3×#500

Subgroups

subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#500C2
socleC22×C3×C5C22×D4
prime radicalC22×C3×D5C2×D4
hypercenterC3×#500D5
hypocenterC5C2×C3×#500
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#500

848 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

264 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 165500);