Finite Group Databasebeta

← Prev (#14412419) Next (#14412421) →

C3×D5×#419 #14412420

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC3×D5×#419

Splittings

FittingC3×C5×#419 ⋊ C2
HallC3×C5 ⋊ C2×#419
SylowC5 ⋊ C2×C3×#419

Subgroups

subgroupG/H
centerC22×C3C2×D4×D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#419C2
socleC22×C3×C5C22×D4
prime radicalC23×C3×D5D4
cosocleC2×C4×C5C24×C3
hypercenterC3×#419D5
hypocenterC5C2×C3×#419
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#419

1504 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, 138118);