Finite Group Databasebeta

C2×C3×#65510 #14320776

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

Aliases

direct productC2×C3×#65510

Splittings

HallC3×C5 ⋊ C2×#390
SylowC5 ⋊ C2×C3×#390

Subgroups

subgroupG/H
centerC24×C3C22×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
Fitting, prime radicalC23×C3×C5×D4C2
socleC24×C3×C5C23
cosocleC23×C5C24×C3
hypercenterC23×C3×D4D5
hypocenterC5C2×C3×#390
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24×C3 ◁ C23×C3×D4

2720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 46474);