Finite Group Databasebeta

C3×#10599490 #14294964

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

Aliases

direct productC3×#10599490

Splittings

HallC3×C5 ⋊ #1747
SylowC5 ⋊ C3×#1747

Subgroups

subgroupG/H
centerC3×C4C42×D5
commutatorC4×C5C2×C3×C42
FrattiniC22×C4C22×C3×D5
FittingC3×C5×H(3,ℤ/4)C2
socleC2×C3×C5#376
prime radicalC23×C3×C5#41
cosocleC22×C4×C5C23×C3
hypercenterC3×H(3,ℤ/4)D5
hypocenterC5C3×#1747
LCSG ▷ C4×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C3×H(3,ℤ/4)

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 20662);