Finite Group Databasebeta

C3×#10614048 #14319718

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC3×#10614048

Splittings

HallC3×C5 ⋊ #2275
SylowC5 ⋊ C3×#2275

Subgroups

subgroupG/H
centerC23×C3C23×D5
commutatorC2×C5C22×C3×C42
FrattiniC23C23×C3×D5
FittingC2×C3×C4×C5×D4C2
socleC23×C3×C5C24
prime radicalC22×C3×C5×D4C22
cosocleC23×C5C24×C3
hypercenterC2×C3×C4×D4D5
hypocenterC5C3×#2275
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4

1560 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45416);