Finite Group Databasebeta

C3×#10598192 #14279156

order1920
automorphism?
homologyAbelianization (H1) = C3×C42 · Schur multiplier (H2) = C22

Aliases

direct productC3×#10598192

Splittings

HallC3×C5 ⋊ #1395
SylowC5 ⋊ C3×#1395

Subgroups

subgroupG/H
centerC3×C4#3938
commutatorC2×C4×C5C3×C42
FrattiniC2×#41C2×C3×D5
FittingC3×C5×#413C2
socleC2×C3×C5#342
prime radicalC2×C3×C5×#41C22
cosocleC2×C5×#41C22×C3
hypercenterC3×#413D5
hypocenterC5C3×#1395
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C2×C3×#41 ◁ C3×#413

324 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 4854);