Finite Group Databasebeta

C3×#10602002 #14292157

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

Aliases

direct productC3×#10602002

Splittings

HallC3×C5 ⋊ #1682
SylowC5 ⋊ C3×#1682

Subgroups

subgroupG/H
centerC22×C3#4084
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#486C2
socleC22×C3×C5#121
prime radicalC3×C5×#127C22
hypercenterC3×#486D5
hypocenterC5C3×#1682
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#486

332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

219 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 17855);