Finite Group Databasebeta

C3×#10598537 #14279228

order1920
automorphism?
homologyAbelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C1

Aliases

direct productC3×#10598537

Splittings

HallC3×C5 ⋊ #1398
SylowC5 ⋊ C3×#1398

Subgroups

subgroupG/H
centerC3×C8C4×AGL(1,𝔽5)
commutatorC4×C5C3×C4×C8
FrattiniC2×C8C2×C3×AGL(1,𝔽5)
FittingC3×C4×C5×C8C4
socleC2×C3×C5#346
prime radicalC22×C3×C5M32
cosocleC2×#672C22×C3
hypercenterC3×C4×C8AGL(1,𝔽5)
hypocenterC5C3×#1398
LCSG ▷ C4×C5 ▷ C5
UCSC1 ◁ C3×C8 ◁ C3×C4×C8

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 4926);