Finite Group Databasebeta

C3×#10601491 #14298773

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

Aliases

direct productC3×#10601491

Splittings

HallC3×C5 ⋊ #1833
SylowC5 ⋊ C3×#1833

Subgroups

subgroupG/H
centerC3×C4#4038
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C5×#108C2
socleC2×C3×C5#382
prime radicalC23×C3×C5#41
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×#108D5
hypocenterC5C3×#1833
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#108

344 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, 24471);