Finite Group Databasebeta

C3×#10599729 #14312465

order1920
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×#10599729

Splittings

HallC3×C5 ⋊ #2103
SylowC5 ⋊ C3×#2103

Subgroups

subgroupG/H
centerC3×C4#4031
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#341C2
socleC2×C3×C5#400
prime radicalC23×C3×C5C2×Q8
hypercenterC3×#341D5
hypocenterC5C3×#2103
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#341

296 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

246 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 38163);