Finite Group Databasebeta

C3×#10600517 #14280436

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C8 · Schur multiplier (H2) = C2×C8

Aliases

direct productC3×#10600517

Splittings

HallC3×C5 ⋊ #1450
SylowC5 ⋊ C3×#1450

Subgroups

subgroupG/H
centerC3×C4×C8C2×D5
commutatorC2×C5C2×C3×C4×C8
FrattiniC42C22×C3×D5
FittingC2×C3×C4×C5×C8C2
socleC22×C3×C5C2×C42
prime radicalC23×C3×C5C42
cosocleC42×C5C23×C3
hypercenterC2×C3×C4×C8D5
hypocenterC5C3×#1450
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4×C8 ◁ C2×C3×C4×C8

424 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 6134);