Finite Group Databasebeta

C3×#10602375 #14295084

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC3×#10602375

Splittings

HallC3×C5 ⋊ #1750
SylowC5 ⋊ C3×#1750

Subgroups

subgroupG/H
centerC22×C3×C4C22×D5
commutatorC22×C5C2×C3×C42
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C5×#117C2
socleC23×C3×C5C22×C4
prime radicalC24×C3×C5C2×C4
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×#117D5
hypocenterC5C3×#1750
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×#117

672 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, 20782);