Finite Group Databasebeta

C3×#10615817 #14321164

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

Aliases

direct productC3×#10615817

Splittings

HallC3×C5 ⋊ #2297
SylowC5 ⋊ C3×#2297

Subgroups

subgroupG/H
centerC22×C3×C4C22×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
Fitting, prime radicalC22×C3×C5×#41C2
socleC23×C3×C5C24
cosocleC23×C5C24×C3
hypercenterC22×C3×#41D5
hypocenterC5C3×#2297
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C22×C3×#41

1872 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 46862);