Finite Group Databasebeta

C3×#10610649 #14430787

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

Aliases

direct productC3×#10610649

Splittings

HallC3×C5 ⋊ #3081
SylowC5 ⋊ C3×#3081

Subgroups

subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#418C2
socleC22×C3×C5C22×D4
prime radicalC22×C3×C5×D4C22
hypercenterC3×#418D5
hypocenterC5C3×#3081
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#418

796 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 156485);