Finite Group Databasebeta

← Prev (#14323548) Next (#14323550) →

C3×#10617304 #14323549

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC3×#10617304

Splittings

FittingC3×C5×#123 ⋊ C4
HallC3×C5 ⋊ #2322
SylowC5 ⋊ C3×#2322

Subgroups

subgroupG/H
centerC22×C3C23×AGL(1,𝔽5)
commutatorC22×C5C23×C3×C4
FrattiniC22C23×C3×AGL(1,𝔽5)
FittingC3×C5×#123C4
socleC22×C3×C5C23×C4
prime radicalC2×C3×D4×D5C22
cosocleC22×D5C24×C3
hypercenterC3×#123AGL(1,𝔽5)
hypocenterC5C3×#2322
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×#123

1264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 49247);