Finite Group Databasebeta

C3×#10602939 #14297271

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC3×#10602939

Splittings

HallC3×C5 ⋊ #1794
SylowC5 ⋊ C3×#1794

Subgroups

subgroupG/H
centerC3×C4#4099
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
Fitting, prime radicalC3×C5×#585C2
socleC2×C3×C5#379
cosocleC22×C4×C5C23×C3
hypercenterC3×#585D5
hypocenterC5C3×#1794
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#585

1096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 22969);