Finite Group Databasebeta

C3×#10600298 #14299395

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

Aliases

direct productC3×#10600298

Splittings

HallC3×C5 ⋊ #1853
SylowC5 ⋊ C3×#1853

Subgroups

subgroupG/H
centerC23×C3C2×C22⋊D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#380C2
socleC23×C3×C5C2×D4
prime radicalC24×C3×C5D4
cosocleC22×C4×C5C23×C3
hypercenterC3×#380D5
hypocenterC5C3×#1853
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C3×#380

720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 25093);