Finite Group Databasebeta

C2×C3×#65936 #14480927

order1920
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C28

Aliases

direct productC2×C3×#65936

Splittings

HallC3×C5 ⋊ C2×#539
SylowC5 ⋊ C2×C3×#539

Subgroups

subgroupG/H
centerC23×C3C23×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
Fitting, prime radicalC2×C3×C5×#121C2
socleC23×C3×C5C24
hypercenterC2×C3×#121D5
hypocenterC5C2×C3×#539
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×#121

2288 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 206625);