Finite Group Databasebeta

C3×#10602717 #14289488

order1920
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C22

Aliases

direct productC3×#10602717

Splittings

HallC3×C5 ⋊ #1632
SylowC5 ⋊ C3×#1632

Subgroups

subgroupG/H
centerC22×C3#4099
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#554C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterC3×#554D5
hypocenterC5C3×#1632
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#554

428 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

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, 15186);