Finite Group Databasebeta

C3×#10602367 #14294482

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C24

Aliases

direct productC3×#10602367

Splittings

HallC3×C5 ⋊ #1733
SylowC5 ⋊ C3×#1733

Subgroups

subgroupG/H
centerC2×C3×C4C2×C22⋊D5
commutatorC4×C5C2×C3×C42
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C5×#117C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC24×C3×C5D4
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×#117D5
hypocenterC5C3×#1733
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C23×C3×C4 ◁ C2×C3×#117

808 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 20180);